NON-INVASIVE CARDIAC OUTPUT DETERMINATION

Abstract

A method of controlling a gas delivery apparatus including an apparatus controllable variable using an iterative algorithm to deliver a test gas (TG) for non-invasively determining a subject's pulmonary blood flow comprising iteratively generating and evaluating test values of a iterated variable based on an iterative algorithm in order output a test value of the iterated variable that meets a test criterion wherein iterative algorithm is characterized in that it defines a test mathematical relationship between the at least one apparatus controllable variable, the iterated variable and an end tidal concentration of test gas attained by setting the apparatus controllable variable, such that the iterative algorithm is determinative of whether iteration on the test value satisfies a test criterion or iteratively generates a progressively refined test value.

Claims

1-29. (canceled)

30. A method of controlling a gas delivery apparatus to deliver a test gas (TG) for non-invasively determining a subject's pulmonary blood flow comprising the steps of: (a) Using an iterative algorithm to control at least one apparatus controllable variable to test one or more test values for an iterated variable by: A) Obtaining input of a steady state value of an end tidal test gas concentration and a corresponding value of at least one apparatus controllable variable for use in the iterative algorithm; B) providing an inspired concentration of a test gas that achieves a test concentration of the test gas in the subject's end tidal exhaled gas; C) using a test value of the iterated variable in the iterative algorithm to set the gas delivery apparatus to deliver, for at least one series of inspiratory cycles, an inspiratory gas comprising a test gas that is computed to maintain the test concentration of the test gas in the subject's end tidal exhaled gas; D) obtaining input comprising measurements of end tidal concentrations of test gas for expiratory cycles corresponding to the at least one series of inspiratory cycles and a corresponding value of at least one apparatus controllable variable for use in the iterative algorithm; E) using at least one measurement obtained in step D) as a reference end tidal concentration value to generate at least one of the following outputs: (1) the test value satisfies a test criterion; (2) a refined test value; wherein the reference end tidal concentration is a surrogate steady state value and the reference end tidal concentration is used to refine the test value; (b) If output (1) is not obtained, repeating step (a) as necessary at least until output (1) is obtained; and (c) If output (1) is obtained, outputting a value for pulmonary blood flow which, based on the test criterion, sufficiently represents a subject's true pulmonary blood flow.

31. A method according to claim 30, wherein the reference end tidal concentration is the last measurement obtained prior to a recirculation or an average of such last measurements.

32. A method according to claim 31, wherein the test gas is carbon dioxide.

33. A method according to claim 30, wherein the iterative algorithm is characterized in that it defines a mathematical relationship between the at least one apparatus controllable variable, the iterated variable and the end tidal concentration of test gas attained by setting the apparatus controllable variable, such that the iterative algorithm is determinative of whether iteration on the test value satisfies a test criterion or iteratively generates a progressively refined test value.

34. A method according to claim 30, wherein the iterative algorithm employs a test mathematical relationship based on the Fick equation.

35. A method according to claim 34, wherein the refined test value is ascertained based on the differential Fick equation.

36. A method according to claim 30, wherein the apparatus controllable variable is the inspired concentration of test gas in the inspiratory gas.

37. A method according to claim 30, wherein the apparatus controllable variable is rate of flow of test gas containing inspiratory gas into the circuit, where the rate of flow is determinative of the alveolar ventilation.

38. A method according to claim 30, wherein the iterated variable is selected from the group consisting of pulmonary blood flow, a variable determined by pulmonary flow from which pulmonary blood flow can be mathematically computed, and a mixed venous concentration of test gas.

39. A gas delivery system adapted to deliver a test gas (TG) for non-invasively determining a subject's pulmonary blood flow comprising: A gas delivery apparatus; A control system for controlling the gas delivery apparatus including at least one apparatus controllable variable to test one or more test values for a iterated variable, the control system comprising a computer for executing an iterative algorithm, the gas delivery system including means for: A) Obtaining input of a steady state value of an end tidal test gas concentration and a corresponding value of at least one apparatus controllable variable for use in the iterative algorithm; B) providing an inspired concentration of a test gas that achieves a test concentration of the test gas in the subject's end tidal exhaled gas; C) using a test value of the iterated variable in an iterative algorithm to set the gas delivery apparatus to deliver, for at least one series of inspiratory cycles, an inspiratory gas comprising a test gas that is computed to maintain the test concentration of the test gas based a test value of the iterated variable; D) obtaining input comprising measurements of end tidal concentrations of test gas for expiratory cycles corresponding to the at least one series of inspiratory cycles; E) using at least one measurement obtained in step C) as a reference end tidal concentration value to generate at least one of the following outputs: (1) the test value satisfies the test criterion; (2) a refined test value; wherein the reference end tidal concentration is a surrogate steady state value and is used to generate the refined test value; wherein the iterative algorithm uses at least one apparatus controllable variable to iteratively test one or more of test values for the iterated variable based on the following criteria: If output (1) is not obtained, repeating step (B) to (E) as necessary at least until output (1) is obtained; and If output (1) is obtained, outputting a value for pulmonary blood flow which, based on the test criterion, sufficiently represents a subject's true pulmonary blood flow.

40. A gas delivery system according to claim 39, wherein the gas delivery apparatus comprises at least one input port for receiving an inspiratory gas containing the test gas, at least one output port for connection to a breathing circuit and a flow controller for controlling the rate of flow of the inspiratory gas.

41. A gas delivery system according to claim 39, wherein the computer is CPU.

42. A gas delivery system according to claim 39, wherein reference end tidal concentration is the last measurement obtained prior to a recirculation or an average of such last measurements.

43. A gas delivery system according to claim 39, wherein the test gas is carbon dioxide.

44. A gas delivery system according to claim 39, wherein the iterative algorithm is characterized in that it defines a mathematical relationship between the at least one apparatus controllable variable, the iterated variable and the end tidal concentration of test gas attained by setting the apparatus controllable variable, such that the iterative algorithm is determinative of whether iteration on the test value satisfies a test criterion or iteratively generates a progressively refined test value.

45. A gas delivery system according to claim 44, wherein the iterative algorithm employs a test mathematical relationship based on the Fick equation.

46. A gas delivery system according to claim 39, wherein the apparatus controllable variable is the inspired concentration of test gas in the inspiratory gas.

47. A gas delivery system according claim 39, wherein the apparatus controllable variable is rate of flow of test gas containing inspiratory gas into the circuit, where the rate of flow is determinative of the alveolar ventilation.

48. A method according to claim 39, wherein the iterated variable is selected from the group consisting of pulmonary blood flow, a variable determined by pulmonary flow from which pulmonary blood flow can be mathematically computed, and a mixed venous concentration of test gas.

49. A computer program product comprising a non-transitory computer readable medium encoded with program code for controlling the operation of gas delivery apparatus including at least one apparatus controllable variable, the program code including code for iteratively generating and evaluating test values of a iterated variable based on an iterative algorithm in order output a test value of the iterated variable that meets a test criterion including program code for: A) Obtaining input of a steady state value of an end tidal test gas concentration and a corresponding value of at least one apparatus controllable variable for use in the iterative algorithm; B) providing an inspired concentration of a test gas that achieves a test concentration of the test gas in the subject's end tidal exhaled gas and using the test value of the iterated variable in the iterative algorithm to set the gas delivery apparatus to deliver, for at least one series of inspiratory cycles, an inspiratory gas comprising a test gas that is computed to maintain the test concentration of the test gas; C) obtaining input comprising measurements of end tidal concentrations of test gas for expiratory cycles corresponding to the at least one series of inspiratory cycles; D) using at least one measurement obtained in step C) as a reference end tidal concentration value to generate at least one of the following outputs: (3) the test value satisfies the test criterion; (4) a refined test value; wherein the reference end tidal concentration is a surrogate steady state value and is used to obtain the refined test value; wherein the iterative algorithm uses at least one apparatus controllable variable to iteratively test one or more of test values for the iterated variable based on the following criteria: If output (1) is not obtained, repeating step (B) to (D) as necessary at least until output (1) is obtained; and If output (1) is obtained, outputting a value for pulmonary blood flow which, based on the test criterion, sufficiently represents a subject's true pulmonary blood flow.

Description

BRIEF DESCRIPTION OF THE FIGURES

[0100] FIG. 1 is a schematic representation of one embodiment of a gas delivery system according to the invention.

[0101] FIG. 2 is a flowchart describing an iterative algorithm employed to recursively determine pulmonary blood flow according to a preferred embodiment of the invention.

[0102] FIG. 3 is a series of a graphical depictions of iterations of the iterative algorithm in which the effect on maintaining a test concentration of test gas for different test values for pulmonary flow is depicted.

[0103] FIG. 4 is a graphical depiction of the effect of over-estimating, under-estimating and correctly estimating a test value for a test variable, in this case, pulmonary blood flow.

DETAILED DESCRIPTION OF THE INVENTION

[0104] Table 1 (below) sets out a list of abbreviations used to express the mathematical relationships employed in the description of several embodiments of the invention described herein.

TABLE-US-00001 TABLE 1 SGD Sequential gas delivery G1 The gas being supplied to the SGD circuit from a gas blender {dot over (V)}.sub.g1 The flow rate of G1 gas from the gas blender to the SGD circuit Alveolar The minute volume of gas that reaches the alveoli and may contribute to gas ventilation exchange. Alveolar ventilation = {dot over (V)}.sub.g1 when SGD is implemented. {dot over (V)}.sub.g1,R The flow rate of G1 gas from the gas blender to the SGD circuit throughout the baseline phase {dot over (V)}.sub.g1,T The flow rate of G1 gas from the gas blender to the SGD circuit throughout the test phase FICO.sub.2,g1 Fractional concentration of CO.sub.2 in the G1 gas FIO.sub.2,g1 Fractional concentration of O.sub.2 in the G1 gas FETCO.sub.2 End-tidal fractional concentration of CO.sub.2 FETO.sub.2 End-tidal fractional concentration of O.sub.2 CaCO.sub.2 Concentration of CO.sub.2 in the arterial blood CvCO.sub.2 Concentration of CO.sub.2 in the mixed-venous blood {dot over (Q)} Pulmonary blood flow {dot over (V)}CO.sub.2 Minute volume of expired CO.sub.2 FICO.sub.2,g1,R Fractional concentration of CO.sub.2 in the G1 gas throughout the baseline phase FETCO.sub.2,R End-tidal fractional concentration of CO.sub.2 at the end of the baseline phase FETO.sub.2,R Average end-tidal fractional concentration of O.sub.2 during the baseline phase CaCO.sub.2,R Concentration of CO.sub.2 in the arterial blood at the end of the baseline phase {dot over (V)}CO.sub.2,R Minute volume of expired CO.sub.2 at the end of baseline phase FICO.sub.2,g1,T Fractional concentration of CO.sub.2 in G1 gas throughout the test phase FETCO.sub.2,T End-tidal fractional concentration of CO.sub.2 at the end of the test phase FETO.sub.2,T Average end-tidal fractional concentration of O.sub.2 during the test phase CaCO.sub.2,T Concentration of CO.sub.2 in the arterial blood at the end of the test phase {dot over (V)}CO.sub.2,T Minute volume of expired CO.sub.2 at the end of the test phase FICO.sub.2,g1,B Fractional concentration of CO.sub.2 in the G1 gas for the bolus breath FETCO.sub.2,B End-tidal fractional concentration of CO.sub.2 of the exhalation immediately after inhalation of the bolus CaCO.sub.2,B Concentration of CO.sub.2 in the arterial blood immediately after inhalation of the bolus {dot over (Q)}.sub.est An estimate of pulmonary blood flow used to try and clamp the end-tidal CO.sub.2 during the test phase CvCO.sub.2,est An estimate of the concentration of CO.sub.2 in the mixed-venous blood used to try and clamp the end-tidal CO.sub.2 during the test phase {dot over (Q)}.sub.calc The pulmonary blood flow calculated at the end of the test phase CvCO.sub.2,calc The concentration of CO.sub.2 in the mixed-venous blood calculated at the end of the test phase {dot over (Q)}.sub.act The subject's actual pulmonary blood flow CvCO.sub.2,act The subject's actual concentration of CO.sub.2 in the mixed-venous FRC Functional residual capacity RR Respiratory rate

[0105] Table 2 (below) lists the various mathematical relationships employed in the description of embodiments of the invention described herein.

TABLE-US-00002 TABLE 2 Label Equation Description 1 {dot over (V)}CO.sub.2 = {dot over (Q)}(CvCO.sub.2 − CaCO.sub.2) Fick equation which mathetmatically expresses the fact that if the end-tidal CO.sub.2 is not changing, the minute volume (flux) of expired CO.sub.2 is equal to the CO.sub.2 deposited in the lung from the circulation 2 {dot over (V)}CO.sub.2′ = {dot over (Q)}(CvCO.sub.2 − CaCO.sub.2′) Fick equation showing that end- tidal and arterial CO.sub.2 can be maintained steady at any level for a constant cardiac output and mixed-venous concentration 3a1 [00002]$\stackrel{.}{Q}=\frac{\stackrel{.}{V}.Math.{C.Math.O}_2^{\prime }-\stackrel{.}{V}.Math.{\mathrm{CO}}_2}{{\mathrm{CaCO}}_2-{\mathrm{CaCO}}_2^{\prime }}$ If two steady states of end-tidal CO.sub.2 can be induced and measured for a constant cardiac output and mixed-venous CO.sub.2, (1) and (2) can be solved simultaneously for the cardiac output 3b1 [00003]$C.Math.\stackrel{\_}{v}.Math.{\mathrm{CO}}_2=\frac{\mathrm{CaCO}.Math.\stackrel{.}{V}.Math.{\mathrm{CO}}_2^{\prime }-{\mathrm{CaCO}}_2^{\prime }.Math.\stackrel{.}{V}.Math.{\mathrm{CO}}_2}{\stackrel{.}{V}.Math.{\mathrm{CO}}_2^{\prime }-\stackrel{.}{V}.Math.{\mathrm{CO}}_2}$ If two steady states of end-tidal CO.sub.2 can be induced and measured for a constant cardiac output and mixed-venous CO.sub.2, (1) and (2) can be solved simultaneously for the mixed- venous CO.sub.2 concentration 4 [00004]$\stackrel{.}{V}.Math.{\mathrm{CO}}_2={\stackrel{.}{V}}_{g.Math..Math.1}.Math.\frac{310}{\underset{\underset{\mathrm{BTPS}}{}}{293}}.Math.\left[\underset{\underset{\mathrm{Haldane}}{}}{\left(\frac{1-{\mathrm{FICO}}_{2,g.Math..Math.1}-{\mathrm{FIO}}_{2,g.Math..Math.1}}{1-{\mathrm{FECO}}_2-{\mathrm{FETO}}_2}\right)}.Math.{\mathrm{FETCO}}_2-{\mathrm{FICO}}_{2,g.Math..Math.1}\right]$ Calculation of the minute volume (flux) of expired CO2 from the end-tidal gases and the flow of gas to a sequential gas delivery circuit 5 [00005]${\stackrel{.}{V}}_{g.Math..Math.1}.Math.\frac{310}{293}.Math.\left[\left(\frac{1-{\mathrm{FICO}}_{2,g.Math..Math.1}-{\mathrm{FIO}}_{2,g.Math..Math.1}}{1-{\mathrm{FETCO}}_2-{\mathrm{FETO}}_2}\right).Math.{\mathrm{FETCO}}_2-{\mathrm{FICO}}_{2,g.Math..Math.1}\right]=\stackrel{.}{Q}\left(C.Math.\stackrel{\_}{v}.Math.{\mathrm{CO}}_2-{\mathrm{CaCO}}_2\right)$ Substitution of (4) for {dot over (V)}CO.sub.2 in (1) 6a [00006]$C.Math.\stackrel{\_}{v}.Math.{\mathrm{CO}}_2=\frac{\begin{array}{c}{\stackrel{.}{V}}_{g.Math..Math.1}.Math.\frac{310}{293}.Math.[\left(\frac{1-{\mathrm{FICO}}_{2,g.Math..Math.1}-{\mathrm{FIO}}_{2,g.Math..Math.1}}{1-{\mathrm{FETCO}}_2-{\mathrm{FETO}}_2}\right).Math.\\ {\mathrm{FETCO}}_2-{\mathrm{FICO}}_{2,g.Math..Math.1}]\end{array}}{\stackrel{.}{Q}}+{\mathrm{CaCO}}_2$ Rearrangement of (5) for the mixed-venous CO.sub.2 where the end- tidal gases, the flow of gas to a sequential gas delivery circuit, the arterial CO.sub.2 concentration, and cardiac output are known or estimated 6b [00007]$\stackrel{.}{Q}=\frac{{\stackrel{.}{V}}_{g.Math..Math.1}.Math.\frac{310}{293}.Math.\left[\left(\frac{1-{\mathrm{FICO}}_{2,g.Math..Math.1}-{\mathrm{FIO}}_{2,g.Math..Math.1}}{1-{\mathrm{FETCO}}_2-{\mathrm{FETO}}_2}\right).Math.{\mathrm{FETCO}}_2-{\mathrm{FICO}}_{2,g.Math..Math.1}\right]}{C.Math.\stackrel{\_}{v}.Math.{\mathrm{CO}}_2-{\mathrm{CaCO}}_2}$ Rearrangement of (5) for the cardiac output where the end-tidal gases, the flow of gas to a sequential gas delivery circuit, the arterial CO.sub.2 concentration, and the mixed-venous CO.sub.2 concentration are known or estimated 7a [00008]${\mathrm{FICO}}_{2,g.Math..Math.1}=\frac{\begin{array}{c}{\stackrel{.}{V}}_{g.Math..Math.1}.Math.\frac{310}{293}.Math.{\mathrm{FETCO}}_2.Math.\left({\mathrm{FIO}}_{2,g.Math..Math.1}-1\right)+\\ \stackrel{.}{Q}\left(C.Math.\stackrel{\_}{v}.Math.{\mathrm{CO}}_2-{\mathrm{CaCO}}_2\right).Math.\left(1-{\mathrm{FETO}}_2-{\mathrm{FETCO}}_2\right)\end{array}}{{\stackrel{.}{V}}_{g.Math..Math.1}.Math.\frac{310}{293}.Math.\left({\mathrm{FETO}}_2-1\right)}$ Rearrangement of (5) for the inspired fraction of CO.sub.2 required to maintain end-tidal CO.sub.2 at a steady state where the end-tidal gases, the flow of gas to a sequential gas delivery circuit, the arterial CO.sub.2 concentration, the mixed-venous CO.sub.2 concentration, and cardiac output are known or estimated 7b [00009]${\stackrel{.}{V}}_{g.Math..Math.1}=\frac{\stackrel{.}{Q}\left(C.Math.\stackrel{\_}{v}.Math.{\mathrm{CO}}_2-{\mathrm{CaCO}}_2\right)}{\frac{310}{293}.Math.\left[\left(\frac{1-{\mathrm{FICO}}_{2,g.Math..Math.1}-{\mathrm{FIO}}_{2,g.Math..Math.1}}{1-{\mathrm{FETCO}}_2-{\mathrm{FETO}}_2}\right).Math.{\mathrm{FETCO}}_2-{\mathrm{FICO}}_{2,g.Math..Math.1}\right]}$ Rearrangement of (5) for the G1 gas flow required to maintain end- tidal CO.sub.2 at a steady state where the end-tidal gases, the fractional concentration of CO.sub.2 in the G1 gas, the arterial CO.sub.2 concentration, the mixed-venous CO.sub.2 concentration, and cardiac output are known or estimated 8 [00010]${\mathrm{FICO}}_{2,g.Math..Math.1,B}=\frac{\mathrm{RR}.Math.[\left({\mathrm{FETCO}}_{2,R}+\frac{10}{\mathrm{PB}-47}.Math.\left(\mathrm{FRC}+\frac{{\stackrel{.}{V}}_{g.Math..Math.1}}{\mathrm{RR}}\right)-\mathrm{FRC}.Math.{\mathrm{FETCO}}_{2,R}\right]}{{\stackrel{.}{V}}_{g.Math..Math.1}}$ Can be used to estimate the fractional concentration of CO.sub.2 required in the bolus breath to raise end-tidal CO.sub.2 by about 10 mmHg from baseline 9 |FETCO.sub.2,T,x − FETCO.sub.2,T,x−1| < |FETCO.sub.2,T,x+1 − FETCO.sub.2,T,x| Applied to each breath of the test to detect recirculation of the arterial blood 3a2 {dot over (Q)}.sub.calc = {dot over (Q)}.sub.est + k(FETCO.sub.2,B − FETCO.sub.2,T) k > 0 An alternative to calculate cardiac output from an estimated cardiac output and the drift of end-tidal CO.sub.2 observed during a test executed with said estimate 3b2 CvCO.sub.2,calc = CvCO.sub.2,est − k(FETCO.sub.2,B − FETCO.sub.2,T) k > 0 An alternative to calculate mixed- venous CO.sub.2 from an estimated mixed-venous CO.sub.2 and the drift of end-tidal CO.sub.2 observed during a test executed with said estimate 4-O [00011]$\stackrel{.}{V}.Math.{\mathrm{CO}}_2={\stackrel{.}{V}}_{g.Math..Math.1}.Math.\frac{310}{\underset{\underset{\mathrm{BTPS}}{}}{293}}.Math.\left[{\mathrm{FETCO}}_2-{\mathrm{FICO}}_{2,g.Math..Math.1}\right]$ An alternative, slightly less accurate, measure of minute volume of expired CO.sub.2 than (4) when oxygen monitoring is not present. 5-O [00012]${\stackrel{.}{V}}_{g.Math..Math.1}.Math.\frac{310}{293}.Math.\left[{\mathrm{FETCO}}_2-{\mathrm{FICO}}_{2,g.Math..Math.1}\right]=\stackrel{.}{Q}\left(C.Math.\stackrel{\_}{v}.Math.{\mathrm{CO}}_2-{\mathrm{CaCO}}_2\right)$ Substitution of (4-O) for {dot over (V)}CO.sub.2 in (1) 6a-O [00013]$C.Math.\stackrel{\_}{v}.Math.{\mathrm{CO}}_2=\frac{{\stackrel{.}{V}}_{g.Math..Math.1}.Math.\frac{310}{293}.Math.\left[{\mathrm{FETCO}}_2-{\mathrm{FICO}}_{2,g.Math..Math.1}\right]}{\stackrel{.}{Q}}+{\mathrm{CaCO}}_2$ Rearrangement of (5-O) for the mixed-venous CO.sub.2 where the end- tidal CO.sub.2, the flow of gas to a sequential gas delivery circuit, the arterial CO.sub.2 concentration, and cardiac output are known or estimated 6b-O [00014]$\stackrel{.}{Q}=\frac{{\stackrel{.}{V}}_{g.Math..Math.1}.Math.\frac{310}{293}.Math.\left[{\mathrm{FETCO}}_2-{\mathrm{FICO}}_{2,g.Math..Math.1}\right]}{C.Math.\stackrel{\_}{v}.Math.{\mathrm{CO}}_2-{\mathrm{CaCO}}_2}$ Rearrangement of (5-O) for the cardiac output where the end-tidal CO.sub.2, the flow of gas to a sequential gas delivery circuit, the arterial CO.sub.2 concentration, and the mixed-venous CO.sub.2 concentration are known or estimated 7a-O [00015]${\mathrm{FICO}}_{2,g.Math..Math.1}={\mathrm{FETCO}}_2-\frac{\stackrel{.}{Q}\left(C.Math.\stackrel{\_}{v}.Math.{\mathrm{CO}}_2-{\mathrm{CaCO}}_2\right)}{{\stackrel{.}{V}}_{g.Math..Math.1}.Math.\frac{310}{293}}$ Rearrangement of (5-O) for the inspired fraction of CO.sub.2 required to maintain end-tidal CO.sub.2 at a steady state where the end-tidal CO.sub.2, the flow of gas to a sequential gas delivery circuit, the arterial CO.sub.2 concentration, the mixed-venous CO.sub.2 concentration, and cardiac output are known or estimated 7b-O [00016]${\stackrel{.}{V}}_{g.Math..Math.1}=\frac{\stackrel{.}{Q}\left(C.Math.\stackrel{\_}{v}.Math.{\mathrm{CO}}_2-{\mathrm{CaCO}}_2\right)}{\frac{310}{293}.Math.\left[\left(\frac{1-{\mathrm{FICO}}_{2,g.Math..Math.1}-{\mathrm{FIO}}_{2,g.Math..Math.1}}{1-{\mathrm{FETCO}}_2-{\mathrm{FETO}}_2}\right).Math.{\mathrm{FETCO}}_2-{\mathrm{FICO}}_{2,g.Math..Math.1}\right]}$ Rearrangement of (5-O) for the G1 gas flow required to maintain end-tidal CO.sub.2 at a steady state where the end-tidal CO.sub.2, the fractional concentration of CO.sub.2 in the G1 gas, the arterial CO.sub.2 concentration, the mixed-venous CO.sub.2 concentration, and cardiac output are known or estimated

[0106] The term “reference end tidal concentration” is used to describe a value obtained by measurement which reflects an arterial blood concentration of the test gas preferably obtained prior to a recirculation time, preferably a value or one or more averaged values obtained closest in time to recirculation since this value may most usefully reflect a new steady state value achieved as a result of administering the test gas. In this connection, it is noteworthy that although the differential Fick equation is a steady state equation, using reference end tidal test gas concentrations obtained before a steady is reached does not prevent the adjusted test value for the iterated variable to be refined recursively. Therefore, the “reference end tidal concentration” is preferably at least a “surrogate steady state value” i.e. a value preferably obtained before a recirculation time that equals or sufficiently represents a steady state value to make the iterative process of meeting the test criterion useful in practice. To reduce the number of iterations required to determine pulmonary blood flow, the surrogate steady state value is preferably selected to be one value, or one or more averaged values, determined to be closest to a recirculation time—generally one or more among the last test values obtained prior to a recirculation. Equation 9 may be used at each breath to detect recirculation of the arterial blood.

[0107] The term “refined test value” is used to refer to a value for a iterated variable that is revised relative a previous test value. Since the invention contemplates that more than one iterated variable may be employed and since the iterated variables are mathematically interrelated the term refined test value should be understood to include a value indirectly derived from data related to a prior test value related to another iterated variable.

[0108] The reference to an iterated variable which is determined by pulmonary blood flow and from which pulmonary blood flow can be computed generally refers to a mixed venous test gas concentration. In contrast to carbon dioxide, with respect to test gases such as oxyacetylene, which are not produced or reliably consumed, the mixed venous blood concentration is equal to the arterial concentration at steady state and hence may not provide useful information about the pulmonary blood flow. In this case, the choice of iterated variable for iteration of a test value would be pulmonary blood flow. If pulmonary shunt is known total pulmonary blood flow can also be used to compute total cardiac output.

[0109] The term “gas delivery apparatus” means a device that can be controlled to control the rate of flow of the test gas into the circuit or set the concentration of the test gas into the inspiratory gas, and preferably both, for example a respiratory gas blender known to those skilled in the art, for example a gas blender with rapid flow controllers, optionally a gas blender capable of delivering accurate mixes of three gases into the circuit. The apparatus and gas mixes may of the type described in published WO 2007/02197. The key functionality of the apparatus is understood to serve the role of establishing (by administering test gas containing inspiratory gas) and maintaining a test concentration of test gas. The gas delivery apparatus may be operatively associated with suitable gas analyzers to measure fractional carbon dioxide and oxygen concentrations at the mouth. The apparatus is operatively associated with a control system for controlling the gas delivery apparatus. The control system demands the required output of the gas delivery apparatus to maintain a test concentration of test gas in the manner described above. The control system or the apparatus comprises the necessary controllers for this purpose as described above, for example for controlling rate of flow of inspiratory gas and optionally separate flow controllers for controlling the rate of flow of the sources gases.

[0110] The gas delivery apparatus comprises at least one input port for receiving a source which may be an inspiratory gas containing the test gas, at least one output port for connection to a breathing circuit and a flow controller for controlling the rate of flow of the inspiratory gas.

[0111] The flow controller optionally controls a gas delivery means.

[0112] The term “gas delivery means”, abbreviated refers to specifically to hardware for delivering (e.g. releasing, where the source gas is under pressure) specific volumes of a source gas comprising or consisting of the test gas for inspiration by the patient, preferably a device that is adapted to output volumes of variable incremental size. The gas delivery means may be any known gas delivery device such as a gas injector, or a valve, for example, a proportional flow control valve.

[0113] Optionally, the gas delivery apparatus is a gas blender, for example, an apparatus that comprises a plurality of input ports for connection to a plurality of gas sources in order to blend different gases that make up the test gas containing gas, for example oxygen, air, nitrogen and a test gas. Optionally, carbon dioxide is the test gas. A flow controller optionally controls a proportional solenoid valve operatively associated with each gas source and optionally a separate flow controller and valve is employed to set the rate of flow of the blended gas into a breathing circuit. Input devices are used to set the rate of flow of gas into the breathing circuit and the concentration of the test gas in the gas provided to the subject.

[0114] According to one aspect the invention is directed to a computer program product which implements a method according to the invention. The computer program product comprises a non-transitory computer readable medium encoded with program code for controlling operation of gas delivery device, the program code including code for iteratively generating a series of test values of a iterated variable based on an iterative algorithm as described above in order to maintain a test concentration of test gas. The program code may comprise code for: [0115] A) providing an inspired concentration of a test gas that defines a test concentration of the test gas in the subject's end tidal exhaled gas; [0116] B) using an iterative algorithm to set the gas delivery apparatus to deliver, for at least one series of inspiratory cycles, a test gas that is computed to target the test concentration of the test gas based a test value of the iterated variable; [0117] C) obtaining input comprising measurements of end tidal concentrations of test gas for expiratory cycles corresponding to the at least one series of inspiratory cycles; [0118] D) using at least one measurement obtained in step C) as a reference end tidal concentration value to generate at least one of the following outputs: [0119] (1) the test value satisfies the test criterion; [0120] (2) a refined test value; [0121] wherein the reference end tidal concentration is a surrogate steady state value and the refined test value is ascertainable from the reference end tidal concentration;

[0122] The program code may include code to test a series of test values for the iterated variable based on the following criteria: [0123] If output (1) is not obtained, repeating step (A) to (D) as necessary at least until output (1) is obtained; and [0124] If output (1) is obtained, outputting a value for pulmonary blood flow which, based on the test criterion, sufficiently represents a subject's true pulmonary blood flow.

[0125] As described above, the computer readable medium or computer readable memory has recorded thereon computer executable instructions for carrying out one or more embodiments of the above-identified methods. The invention is not limited by a particular physical memory format on which such instructions are recorded for access by a computer. Non-volatile memory exists in a number of physical forms including non-erasable and erasable types. Hard drives, DVDs/CDs and various types of flash memory may be mentioned. The invention, in one broad aspect, is directed to a non-transitory computer readable medium comprising computer executable instructions for carrying out one or more embodiments of the above-identified method.

[0126] The term “test concentration” means a concentration of a test gas in a subject's arterial blood as reflected in the end tidal concentration of the test gas in the subject's exhaled gas after attaining equilibrium with that arterial concentration of test gas. As described above, this concentration is optionally achieved by arranging for a subject to obtain an inspiratory gas with any suitable concentration of test gas which may be delivered via the gas delivery apparatus or optionally indirectly from a re-breathed gas.

[0127] The term “computer” is used broadly to refer to any device (constituted by one or any suitable combination of components) which may used in conjunction with discrete electronic components to perform the functions contemplated herein, including computing and obtaining input signals and providing output signals, and optionally storing data for computation, for example inputs/outputs to and from electronic components and application specific device components as contemplated herein. The computer may use machine readable instructions or dedicated circuits to perform the functions contemplated herein including without limitation by way of digital and/or analog signal processing capabilities, for example a CPU, for example a dedicated microprocessor embodied in an IC chip which may be integrated with other components, for example in the form of a microcontroller. Key inputs may include input signals from a gas analyzer, any type of input device for inputting inputs as contemplate herein (for example, a knob, dial, keyboard, keypad, mouse, touch screen etc.) input from a computer readable memory etc. Key outputs include output of a control signal to control to a gas delivery mean such as a proportional control valve, for example outputs to a flow controller for controlling key components of gas delivery apparatus.

[0128] It is to be understood that an iterative algorithm may execute computation based on a test mathematical relationship herein and that this relationships may be variously defined with equivalent formula in which terms/parameters are substituted by equivalent expressions that are expressed in other forms or styles e.g. read from a graph etc. Hence the invention is not limited by a reference to particular expressions of a test mathematical relationship or related equations. For example, equation 5 may expressed by equivalent expressions of equation 1 from which it is derived may be obtained by computing {dot over (V)}CO.sub.2 (eq. 4) in a manner other than expressed in equation 4. It is understood that the equations relate back to the Fick equation and differential Fick equation and hence a iterative algorithm expressed as being “based on” the Fick equation” is understood to be encompass equivalent expressions or expansions of the equation with and without correction factors. In contrast to prior methods, in one embodiment of a method according to the invention, which is also primarily described hereafter in connection with using carbon dioxide as an embodiment of a “test gas”, the invention contemplates obtaining steady state values optionally when the subject is at “rest” and those values are stabilized. VCO.sub.2 and CaCO.sub.2 are measured in a first steady state. Rather than waiting for end-tidal CO.sub.2 to exponentially drift up to some second steady-value (which notably is generally not achieved before a recirculation), the present method contemplates giving a bolus of CO.sub.2 to more acutely increase end-tidal CO.sub.2 and calculate the inspired CO.sub.2 required to force a second steady state at the elevated end-tidal CO.sub.2 from a guess at the cardiac output. If the end-tidal CO.sub.2 remains stable, the guess at cardiac output was correct. If the guess at cardiac output was incorrect, much like in the previous art, the end-tidal CO.sub.2 will exponentially drift towards a steady state until recirculation. If we apply the differential Fick formula to our rest state and a second state represented for example by the last test breath before recirculation, it is possible to calculate a value for cardiac output. Much like previous methods, if the last test breath doesn't actually represent steady state (i.e. equilibration did not occur before recirculation), the cardiac output calculated by the differential Fick will be in error. However, it will be closer to the actual cardiac output than an original guess going in, and therefore, represents a refined estimate of the actual cardiac output. If this procedure is executed again, but with the refined estimate of cardiac output calculated from the last iteration, then there will be less drift during the test, the last test breath will better represent steady state, and again, our calculation of cardiac output will be even closer to the actual cardiac output. Repeat as necessary and the cardiac output calculated by this method will converge to the actual cardiac output. Accordingly, in contrast to prior methods there is no need to fit exponentials and extrapolate. In one embodiment, with sequential gas delivery (SGD), it is possible to clamp alveolar ventilation, and therefore measure a very consistent VCO.sub.2 with equation 4 obviating the need for simultaneous flow/CO.sub.2 measurements. To implement the test, an operator can provide a precise reduction in alveolar ventilation that will not be affected by changes in minute ventilation, and can therefore be used in spontaneous breathers and mechanically ventilated subjects.

Iterative NICO Equations

[0129] A method according to the invention will now be described in accordance with a preferred embodiment of the invention in which the test gas is carbon dioxide.

[0130] With the use of sequential gas delivery, alveolar ventilation can be controlled independent of overall minute ventilation. As a result, EQUATION 4 provides an accurate measure of the net minute volume of expired CO.sub.2 calculated from the end-tidal fractional concentrations of CO.sub.2 and O.sub.2 (FETCO.sub.2,FETO.sub.2) without the use of breath collection or flowmetry.

[00017]$\begin{array}{cc}\stackrel{.}{V}.Math.{\mathrm{CO}}_2={\stackrel{.}{V}}_{\mathrm{gl}}.Math.\frac{310}{\underset{\underset{\mathrm{BTPS}}{}}{293}}.Math.\hspace{1em}\left[\left(\underset{\underset{\mathrm{Haldane}}{}}{\frac{1-{\mathrm{FICO}}_{2,\mathrm{gl}}-{\mathrm{FIO}}_{2,\mathrm{gl}}}{1-{\mathrm{FETCO}}_2-{\mathrm{FETO}}_2}}\right).Math.{\mathrm{FETCO}}_2-{\mathrm{FICO}}_{2,\mathrm{gl}}\right]& \mathrm{EQUATION}.Math..Math.4\end{array}$

[0131] The correction term, BTPS, accounts for the expansion of gases in the lung owing to the increase in temperature from standard conditions. The Haldane term applies the Haldane transform to calculate the expired volume when only the inspired volume is known.

[0132] When the amount of CO.sub.2 in the alveolar space is unchanging, EQUATION 4 can be substituted into EQUATION 1. The resulting steady state mass balance equation for the alveolar space is shown in EQUATION 5.

[00018]$\begin{array}{cc}{\stackrel{.}{V}}_{\mathrm{gl}}.Math.\frac{310}{293}.Math.\hspace{1em}\left[\left(\frac{1-{\mathrm{FICO}}_{2,\mathrm{gl}}-{\mathrm{FIO}}_{2,\mathrm{gl}}}{1-{\mathrm{FETCO}}_2-{\mathrm{FETO}}_2}\right).Math.{\mathrm{FETCO}}_2-{\mathrm{FICO}}_{2,\mathrm{gl}}\right]=\stackrel{.}{Q}\left(C.Math.\stackrel{\_}{v}.Math.{\mathrm{CO}}_2-{\mathrm{CaCO}}_2\right)& \mathrm{EQUATION}.Math..Math.5\end{array}$

[0133] Equation 5, based on the differential Fick equation, is a key test mathematical relationship from which other mathematical relationships are derived by solving for a test variable or an apparatus controllable variable.

[0134] The results of solving EQUATION 5 for the mixed-venous concentration of CO.sub.2 and the pulmonary blood flow are shown in EQUATIONS 6.

[00019]$\begin{array}{cc}{\mathrm{Cv}.Math.\mathrm{CO}}_2=\frac{\begin{array}{c}{\stackrel{.}{V}}_{\mathrm{gl}}.Math.\frac{310}{293}.Math.\\ \left[\left(\frac{1-{\mathrm{FICO}}_{2,\mathrm{gl}}-{\mathrm{FIO}}_{2,\mathrm{gl}}}{1-{\mathrm{FETCO}}_2-{\mathrm{FETO}}_2}\right).Math.{\mathrm{FETCO}}_2-{\mathrm{FICO}}_{2,\mathrm{gl}}\right]\end{array}}{\stackrel{.}{Q}}+{\mathrm{CaCO}}_2.Math.& \mathrm{EQUATION}.Math..Math.6.Math.a\\ \stackrel{.}{Q}=\frac{\begin{array}{c}{\stackrel{.}{V}}_{\mathrm{gl}}.Math.\frac{310}{293}.Math.\\ \hspace{1em}\left[\left(\frac{1-{\mathrm{FICO}}_{2,\mathrm{gl}}-{\mathrm{FIO}}_{2,\mathrm{gl}}}{1-{\mathrm{FETCO}}_2-{\mathrm{FETO}}_2}\right).Math.{\mathrm{FETCO}}_2-{\mathrm{FICO}}_{2,\mathrm{gl}}\right]\end{array}}{C.Math.\stackrel{\_}{v}.Math.{\mathrm{CO}}_2-{\mathrm{CaCO}}_2}& \mathrm{EQUATION}.Math..Math.6.Math.b\end{array}$

[0135] Similarly, the results of solving EQUATION 5 for the fractional concentration of CO.sub.2 in the G1 gas and the flow rate of G1 gas are shown in EQUATIONS 7.

[00020]$\begin{array}{cc}{\mathrm{FICO}}_{2,\mathrm{gl}}=\frac{\begin{array}{c}{\stackrel{.}{V}}_{\mathrm{gl}}.Math.\frac{310}{293}.Math.{\mathrm{FETCO}}_2.Math.\left({\mathrm{FIO}}_{2,\mathrm{gl}}-1\right)+\\ \stackrel{.}{Q}\left(C.Math.\stackrel{\_}{v}.Math.{\mathrm{CO}}_2-{\mathrm{CaCO}}_2\right).Math.\left(1-{\mathrm{FETO}}_2-{\mathrm{FETCO}}_2\right)\end{array}}{{\stackrel{.}{V}}_{\mathrm{gl}}.Math.\frac{310}{293}.Math.\left({\mathrm{FETO}}_2-1\right)}& \mathrm{EQUATION}.Math..Math.7.Math.a\\ .Math.{\stackrel{.}{V}}_{\mathrm{gl}}=\frac{\stackrel{.}{Q}\left(C.Math.\stackrel{\_}{v}.Math.{\mathrm{CO}}_2-{\mathrm{CaCO}}_2\right)}{\frac{310}{293}.Math.\left[\begin{array}{c}\left(\frac{1-{\mathrm{FICO}}_{2..Math.\mathrm{gl}}-{\mathrm{FIO}}_{2,\mathrm{gl}}}{1-{\mathrm{FETCO}}_2-{\mathrm{FETO}}_2}\right).Math.\\ {\mathrm{FETCO}}_2-{\mathrm{FICO}}_{2,\mathrm{gl}}\end{array}\right]}& \mathrm{EQUATION}.Math..Math.7.Math.b\end{array}$

The Iterative NICO Method

[0136] The partial pressure of CO.sub.2 in the arterial blood is assumed to be equal to the end-tidal partial pressure of CO.sub.2 and then converted to a concentration via the CO.sub.2 dissociation curve of oxygenated whole blood [3,4]. This requires haemoglobin concentration ([HB]). [HB] is preferably obtained from a blood gas analysis. If blood gas analysis is not possible, [HB] can be measured transcutaneously. Alternatively, [HB] can be obtained from the normal published ranges for age/sex. End-tidal fractional concentrations can be converted to partial pressures by multiplying the fractional concentrations by barometric pressure (PB) less the partial pressure of water vapour.

[0137] The amount of CO.sub.2 in the lung is entirely determined by the alveolar ventilation and the diffusion of CO.sub.2 between the circulation and the alveolar space. If the pulmonary blood flow or the mixed-venous concentration of CO.sub.2 is known, the other can be calculated from the steady state minute volume of expired CO.sub.2 and arterial CO.sub.2 concentration (EQUATIONS 6a,b). Therefore, the transfer rate of CO.sub.2 between the circulation and the alveolar space can be determined for any value of end-tidal CO.sub.2 as long as the pulmonary blood flow and mixed-venous concentration of CO.sub.2 remains unchanged. Correspondingly, following an acute change in end-tidal CO.sub.2 from a previously steady value, if the alveolar ventilation can be controlled or measured, a temporary steady state at the new end-tidal CO.sub.2 (referred to as a test concentration) can be maintained by delivering the inspired fraction of CO.sub.2 and/or alveolar ventilation required to exactly offset the influx from the circulation (EQUATIONS 7). This steady state can be maintained until the mixed-venous CO.sub.2 changes due to recirculation of the affected arterial blood.

[0138] Our algorithm recursively exploits this observation to measure the pulmonary blood flow. According to one embodiment, throughout each iteration, the alveolar ventilation (={dot over (V)}.sub.g1) is set with a sequential gas delivery circuit. The fraction of O.sub.2 in the G1 gas (FIO.sub.2,g1) is not important, but should be held constant at a level sufficient to maintain arterial oxygen saturation. The end-tidal gases are measured by continuous real-time analysis of the expired gas.

[0139] In the baseline phase, the fractional concentration of CO.sub.2 in the G1 gas (FICO.sub.2,g1,R) is set and held constant. Although not necessary, FICO.sub.2,g1,R is usually zero. The G1 gas flow during the rest phase ({dot over (V)}.sub.g1,R) is usually set to about 80% of the subjects total measured or estimated minute ventilation. In general, {dot over (V)}.sub.g1,R should be low enough to permit rebreathing which at least fills the subject's anatomical dead space, but high enough to prevent hypercapnia. The baseline phase can be ended when end-tidal CO.sub.2 is stable. Stability of end-tidal CO.sub.2 can be determined by the standard-deviation of end-tidal CO.sub.2 measured over five breaths being within ±2 mmHg, or if the difference between the largest and smallest end-tidal CO.sub.2 measured over the last 5 breaths is within ±2 mmHg, or if the slope of the linear regression line passing through the end-tidal CO.sub.2 of the last five breaths is less than ±0.5 mmHg/breath. Alternatively, the baseline period can be ended after predefined time has elapsed and/or predefined number of breaths has occurred.

[0140] At the end of the baseline phase, the end-tidal CO.sub.2 during the baseline phase (FETCO.sub.2,R) is converted to an arterial concentration (CaCO.sub.2,R). The end-tidal CO.sub.2 from the last breath of the baseline phase can be used as FETCO.sub.2,R. Alternatively, FETCO.sub.2,R can be the average of a number of breaths at the end of the baseline phase. The baseline minute volume of expired CO.sub.2 ({dot over (V)}CO.sub.2,R) is calculated from EQUATION 4, using the average end-tidal O.sub.2 (FETO.sub.2,R) measured during the baseline phase, {dot over (V)}.sub.g1,R, FICO.sub.2,g1,R, FIO.sub.2,g1, and FETCO.sub.2,R. A test value for an iterated variable, e.g. mixed-venous concentration of CO.sub.2 is estimated from EQUATION 6a using an estimate of the pulmonary blood flow ({dot over (Q)}.sub.est), {dot over (V)}.sub.g1,R, FICO.sub.2,g1,R, FIO.sub.2,g1, FETCO.sub.2,R, FETO.sub.2,R, and CaCO.sub.2,R. Alternatively, a test value for pulmonary blood flow (a preferred iterated variable for convenience) is estimated starting from an estimate of the mixed-venous concentration of CO.sub.2 (CvCO.sub.2,est) using EQUATION 6b with {dot over (V)}.sub.g1,R, FICO.sub.2,g1,R, FIO.sub.2,g1, FETCO.sub.2,R, FETO.sub.2,R, and CaCO.sub.2,R.

[0141] To transition from the baseline phase to the test phase, the inspired fraction of CO.sub.2 in the G1 gas is increased substantially for one bolus breath, inducing a sharp increase in the end-tidal CO.sub.2. The bolus breath may optimally increase end-tidal CO.sub.2 by approximately 10 mmHg to provide sufficient measurement resolution and minimize discomfort to the patient. The inspired fraction of CO.sub.2 in the bolus breath (FICO.sub.2,g1,B) required to elevate end-tidal CO.sub.2 by approximately 10 mmHg can be calculated using an approximation of the subject's functional residual capacity (FRC), respiratory rate (RR), {dot over (V)}.sub.g1,R, and FETCO.sub.2,R using EQUATION 8. The FRC can be estimated or obtained from normal published ranges for the age, weight, and sex of the subject. Respiratory rate can be measured or estimated. For most adults, FICO.sub.2,g1,B of 15-20% should provide an adequate increase in end-tidal CO.sub.2.

[00021]$\begin{array}{cc}{\mathrm{FICO}}_{2,g.Math..Math.1,B}=\frac{\mathrm{RR}.Math.\left[\begin{array}{c}\left({\mathrm{FETCO}}_{2,R}+\frac{10}{\mathrm{PB}-47}\right).Math.\left(\mathrm{FRC}+\frac{{\stackrel{.}{V}}_{g.Math.1}}{\mathrm{RR}}\right)-\\ \mathrm{FRC}.Math.{\mathrm{FETCO}}_{2,R}\end{array}\right]}{\left({\stackrel{.}{V}}_{g.Math..Math.1,R}\right)}& \mathrm{EQUATION}.Math..Math.8\end{array}$

[0142] The elevated end-tidal CO.sub.2 (FETCO.sub.2,B), and corresponding arterial CO.sub.2 (CaCO.sub.2,B) measured in the exhalation immediately following inspiration of the bolus are recorded. This recorded value represents the test concentration of CO2 sought to be maintained in the test phase. Subsequently, a value for an apparatus controllable variable preferably selected from the inspired fraction of CO.sub.2 (FICO.sub.2,g1,T) and G1 flow rate ({dot over (V)}.sub.g1,T) during the test phase are set to try and maintain end-tidal CO.sub.2 at FETCO.sub.2,B.Math.{dot over (V)}.sub.g1,T can be chosen arbitrarily, but in general, {dot over (V)}.sub.g1,T should be low enough to permit rebreathing which at least fills the subject's anatomical dead space. A test mathematical relationship solving for FICO2,gl (EQUATION 7a), with {dot over (Q)}.sub.est, CvCO.sub.2,est, {dot over (V)}.sub.g1,T, FIO.sub.2,g1, FETCO.sub.2,B, FETO.sub.2,R, and CaCO.sub.2,B, can be used to calculate FICO.sub.2,g1,T presumed to force a second steady state of end-tidal CO.sub.2 at FETCO.sub.2,B. Alternatively, FICO.sub.2,g1,T can be set arbitrarily within the limitations of the hardware and the test mathematical relationship solves for Vg1 (EQUATION 7b), with {dot over (Q)}.sub.est, CvCO.sub.2,est, FICO.sub.2,g1,T, FIO.sub.2,g1, FETCO.sub.2,B, FETO.sub.2,R, and CaCO.sub.2,B, can be used to calculate {dot over (V)}.sub.g1,T presumed to force a second steady state of end-tidal CO.sub.2 at FETCO.sub.2,B. This {dot over (V)}.sub.g1,T and FICO.sub.2,g1,T is delivered until recirculation is detected (described later), or for a predefined length of time presumed to be less than the recirculation time, or a predefined number of breaths presumed to occur before recirculation.

[0143] At the end of the test phase, the end-tidal CO.sub.2 during the test phase (FETCO.sub.2,T) is converted to an arterial concentration (CaCO.sub.2,T). The end-tidal CO.sub.2 from the last breath of the test phase can be used as a reference end tidal concentration (FETCO2,T). Alternatively, FETCO.sub.2,T can be the average of values obtained for a number of breaths at the end of the test phase. The minute volume of expired CO.sub.2 during the test phase ({dot over (V)}CO.sub.2,T) is calculated from EQUATION 4, using the average end-tidal O.sub.2 (FETO.sub.2,T) measured during the test phase, {dot over (V)}.sub.g1,T, FICO.sub.2,g1,T, FIO.sub.2,t1, and FETCO.sub.2,T. Refined test values for pulmonary blood flow and mixed-venous CO.sub.2 are recalculated ({dot over (Q)}.sub.calc,CvCO.sub.2calc) from EQUATIONS 3a1,b1 using {dot over (V)}CO.sub.2,R, CaCO.sub.2,R, {dot over (V)}CO.sub.2,T, and CaCO.sub.2,T or EQUATIONS 3a2,b2 using {dot over (Q)}.sub.est, CvCO.sub.2,est, FETCO.sub.2,B, and FETCO.sub.2,T. Subsequently, the system is returned to the baseline state.

[0144] This manoeuvre is repeated within successively refined test values for the test variable utilizing either the calculated pulmonary blood flow of each test as the estimated pulmonary blood flow in the next iteration, or the calculated mixed-venous CO.sub.2 concentration as the estimated mixed-venous CO.sub.2 concentration in the next iteration.

Selecting the Apparatus Controllable Variable and its Values:

[0145] Although {dot over (V)}.sub.g1,R can be chosen arbitrarily, in general, {dot over (V)}.sub.g1,R should be low enough to permit rebreathing which at least fills the subject's anatomical dead space, but high enough to prevent hypercapnia. Although FICO.sub.2,g1,R can be chosen arbitrarily, in general, there is not often a reason to deliver CO.sub.2 in the baseline phase, and FICO.sub.2,g1,R is generally set to zero. Although either {dot over (V)}.sub.g1,T or FICO.sub.2,g1,T can be set arbitrarily and the other value for the apparatus controllable variable calculated from EQUATIONS 7a,b, it is simplest to set {dot over (V)}.sub.g1,T equal to {dot over (V)}.sub.g1,R during the test phase and calculate FICO.sub.2,g1,T from EQUATION 7a.

No O.SUB.2

[0146] It is pertinent to note that knowledge of inspired and end-tidal O.sub.2 is only required to implement the Haldane transform (EQUATION 4) which gives a measure of expired volumes when only inspired volumes are known. In practise, the expired volumes are not significantly different than inspired volumes. Where an oxygen analyzer is not present, the iterative algorithm method described herein can be executed with a small loss in accuracy using equations ending with (—O). (e.g. 7a-0, 7b-0, etc.)

Initiation and Convergence and Termination

[0147] The initial test value for the iterated variable, be it pulmonary blood flow or mixed-venous CO.sub.2, is taken as the middle of the normal published range for the age, height, weight, and sex of the subject. Alternatively, the initial pulmonary blood flow or mixed-venous CO.sub.2 estimate can be arbitrary. Alternatively, the test value for pulmonary blood flow can be estimated as 0.07 L/min/kg of subject body weight. Alternatively, the initial pulmonary blood flow or mixed-venous CO.sub.2 estimate can be obtained from a pervious execution of the recursive algorithm. Alternatively, the initial test value for pulmonary blood flow or mixed-venous CO.sub.2 can be obtained from another measurement technique (thermodilution, mixed-venous blood gases). Alternatively, the mixed-venous partial pressure of CO.sub.2 can be estimated as 6 mmHg above the resting end-tidal CO.sub.2 and converted to a concentration via the CO.sub.2 dissociation curve.

[0148] If the test value for pulmonary blood flow does not satisfy the test criterion, the predicted transfer rate of CO.sub.2 between the circulation and the alveolar space will also be in error. However, the minute volume of expired of CO.sub.2 in the test phase will exponentially equilibrate with the flux across the blood-alveolar interface. As a result, the pulmonary blood flow calculated in each test will be refined and better reflect the actual pulmonary blood flow ({dot over (Q)}.sub.act) than the ingoing test value. Because the iterative algorithm is implemented recursively, and the estimated test value for the iterative variable is refined after each iteration to reflect the previously calculated test values, the algorithm converges to the actual physiological parameters of the subject.

[0149] The rate at which the calculated parameters converge to the actual parameters depends on how fast the end-tidal CO.sub.2 approaches equilibrium in the test phase. The derivative of an exponential function is largest at the start and vanishes with time. Therefore, a substantial refinement in the estimated parameters occurs in the breaths before recirculation. As a result, the calculated parameters at the end of each test are significantly more accurate than the previous estimates.

[0150] Testing is optionally terminated when the difference in pulmonary blood flow calculated between subsequent tests differs in magnitude less than a user-definable threshold. Optionally, the algorithm can be continued indefinitely. Optionally, the algorithm can be executed for a predefined number of iterations. All of these options satisfy a test criterion.

Detection of Recirculation

[0151] The pulmonary recirculation time varies between individuals, and within the same individual in different hemodynamic states. Indeed, the reported interval before recirculation occurs differs significantly amongst investigators.

[0152] We detect the occurrence of recirculation by analysis of the time course of the end-tidal CO.sub.2 during the test phase. Prior to recirculation, the end-tidal CO.sub.2 approaches a steady value exponentially—the absolute difference between consecutive end-tidal measurements decreases as the test proceeds. Recirculation causes a deviation from this asymptotic approach, detectable as an increase in the difference between consecutive end-tidal CO.sub.2 measurements. Accordingly, in our method, the test proceeds as long as the magnitude of the difference between consecutive end-tidal CO.sub.2 measurements is decreasing.

[0153] More specifically, let FETCO.sub.2,T,x be the end-tidal CO.sub.2 of a breath during the test phase, and FETCO.sub.2,T,x−1 and FETCO.sub.2,T,x+1 be the breaths immediate before and after. The last breath before recirculation is the first test breath for which:

|FETCO.sub.2,T,x−FETCO.sub.2,T,x−1|<|FETCO.sub.2,T,x+1−FETCO.sub.2,T,x|  EQUATION 9

Apparatus

[0154] According to one embodiment of a gas delivery system, the system apparatus is shown in FIG. 1. It consists of a gas blender 22, a sequential gas delivery circuit 26, gas analyzers for oxygen 16 and carbon dioxide 18, a pressure transducer 14, a computer 8 including software 10 (which is optionally embodied a computer program product) that works the gas blender 22 to request gas flows and with the gas analyzers 16 and 18, pressure transducer 14 and input devices for measured or estimated physiological parameters 36 and algorithm settings 34 to obtain inputs as contemplated herein. The gas blender 22 may be connected to three pressurized gas tanks 32. The gas blender optionally contains three rapid flow controllers (not shown) capable of delivering accurate mixes of three source gases, optionally comprised of CO.sub.2, O.sub.2, and N.sub.2 to the circuit. The concentrations of CO.sub.2, O.sub.2, and N.sub.2 in the source gases must be such that they can produce the blends required to carry out the algorithm. Pure CO.sub.2, O.sub.2, and N.sub.2 are one option. The gas analyzers 18 and 16 measure the fractional concentrations of CO.sub.2 and O.sub.2 at the mouth throughout the breath. The pressure transducer 14 is used for end-tidal detection. The computer runs a software implementation of a pulmonary blood flow measurement algorithm and demands the required mixtures from the blender 22. The monitor may display the real-time capnograph, oxigraph, pulmonary blood flow, and mixed-venous concentration of CO.sub.2.

{dot over (Q)}.sub.calc={dot over (Q)}.sub.est+k(FETCO.sub.2,B−FETCO.sub.2,T) k>0  EQUATION 3a2

CvCO.sub.2,calc=CvCO.sub.2,est−k(FETCO.sub.2,B−FETCO.sub.2,T) k>0  EQUATION 3b2

DESCRIPTION OF FIGURES

[0155] FIG. 4

[0156] 1 The initial pulmonary blood flow or mixed-venous CO.sub.2 estimate is taken as the middle of the normal published range for the age, height, weight, and sex of the subject. Alternatively, the initial pulmonary blood flow or mixed-venous CO.sub.2 estimate can be arbitrary. Alternatively, pulmonary blood flow can be estimated as 0.07 L/min/kg of subject body weight. Alternatively, the initial pulmonary blood flow or mixed-venous CO.sub.2 estimate can be obtained from a pervious execution of the recursive algorithm. Alternatively, the initial pulmonary blood flow or mixed-venous CO.sub.2 estimate can be obtained from another measurement technique (thermodilution, mixed-venous blood gases). Alternatively, the mixed-venous partial pressure of CO.sub.2 can be estimated as 6 mmHg above the resting end-tidal CO.sub.2 and converted to a concentration via the CO.sub.2 dissociation curve.

[0157] 2 In the baseline phase, the fractional concentration of CO.sub.2 in the G1 gas (FICO.sub.2,g1,R) is set and held constant. Although not necessary, FICO.sub.2,g1,R is usually zero. The G1 gas flow during the rest phase ({dot over (V)}.sub.g1,R) is usually set to about 80% of the subjects total measured or estimated minute ventilation. In general, {dot over (V)}.sub.g1,R should be low enough to permit rebreathing which at least fills the subject's anatomical dead space, but high enough to prevent hypercapnia.

[0158] 3 The baseline phase can be ended when end-tidal CO.sub.2 is stable. Stability of end-tidal CO.sub.2 can be determined by the standard-deviation of end-tidal CO.sub.2 measured over five breaths being within ±2 mmHg, or if the difference between the largest and smallest end-tidal CO.sub.2 measured over the last 5 breaths is within ±2 mmHg, or if the slope of the linear regression line passing through the end-tidal CO.sub.2 of the last five breaths is less than ±0.5 mmHg/breath. Alternatively, the baseline period can be ended after predefined time has elapsed and/or predefined number of breaths has occurred.

[0159] 4 At the end of the baseline phase, the end-tidal CO.sub.2 during the baseline phase (FETCO.sub.2,R) is converted to an arterial concentration (CaCO.sub.2,R). The end-tidal CO.sub.2 from the last breath of the baseline phase can be used as FETCO.sub.2,R. Alternatively, FETCO.sub.2,R can be the average of a number of breaths at the end of the baseline phase.

[0160] 5 The baseline minute volume of expired CO.sub.2 ({dot over (V)}CO.sub.2,R) is calculated from EQUATION 4, using the average end-tidal O.sub.2 (FETO.sub.2,R) measured during the baseline phase, {dot over (V)}.sub.g1,R, FICO.sub.2,g1,R, FIO.sub.2,g1, and FETCO.sub.2,R.

[0161] 6 The mixed-venous concentration of CO.sub.2 is estimated from EQUATION 6a using an estimate of the pulmonary blood flow ({dot over (Q)}.sub.est) {dot over (V)}.sub.g1,R, FICO.sub.2,g1,R, FIO.sub.2,g1, FETCO.sub.2,R, FETO.sub.2,R, and CaCO.sub.2,R. Alternatively, the pulmonary blood flow is estimated starting from an estimate of the mixed-venous concentration of CO.sub.2 (CvCO.sub.2,est) using EQUATION 6b with {dot over (V)}.sub.g1,R, FICO.sub.2,g1,R FIO.sub.2,g1, FETCO.sub.2,R FETO.sub.2,R, and CaCO.sub.2,R.

[0162] 7 To transition from the baseline phase to the test phase, the inspired fraction of CO.sub.2 in the G1 gas is increased substantially for one bolus breath, inducing a sharp increase in the end-tidal CO.sub.2. In one embodiment, the bolus breath increases end-tidal CO.sub.2 by approximately 10 mmHg to provide sufficient measurement resolution and minimize discomfort to the patient. The inspired fraction of CO.sub.2 in the bolus breath (FICO.sub.2,g1,B) required to elevate end-tidal CO.sub.2 by approximately 10 mmHg can be calculated using an approximation of the subject's functional residual capacity (FRC), respiratory rate (RR), {dot over (V)}.sub.g1,R, and FETCO.sub.2,R using EQUATION 8. The FRC can be estimated or obtained from normal published ranges for the age, weight, and sex of the subject. Respiratory rate can be measured or estimated. For most adults, FICO.sub.2,g1,B of 15-20% should provide an adequate increase in end-tidal CO.sub.2.

[00022]$\begin{array}{cc}{\mathrm{FICO}}_{2,g.Math..Math.1,B}=\frac{\mathrm{RR}.Math.\left[\begin{array}{c}\left({\mathrm{FETCO}}_{2,R}+\frac{10}{\mathrm{PB}-47}\right)\\ \left(\mathrm{FRC}+\frac{{\stackrel{.}{V}}_{\mathrm{gl}}}{\mathrm{RR}}\right)-\mathrm{FRC}.Math.{\mathrm{FETCO}}_{2,R}\end{array}\right]}{{\stackrel{.}{V}}_{g.Math..Math.1,R}}& \mathrm{EQUATION}.Math..Math.8\end{array}$

[0163] 8 The elevated end-tidal CO.sub.2 (FETCO.sub.2,B), and corresponding arterial CO.sub.2 (CaCO.sub.2,B) measured in the exhalation immediately following inspiration of the bolus are recorded. This recorded value represents the test concentration of CO.sub.2 sought to be maintained in the test phase.

[0164] 9 Subsequently, the inspired fraction of CO.sub.2 (FICO.sub.2,g1,T) and G1 flow rate ({dot over (V)}.sub.g1,T) during the test phase are set to try and maintain end-tidal CO.sub.2 at FETCO.sub.2,B. {dot over (V)}.sub.g1,T can be chosen arbitrarily, but in general, {dot over (V)}.sub.g1,T should be low enough to permit rebreathing which at least fills the subject's anatomical dead space. EQUATION 7a, with {dot over (Q)}.sub.est, CvCO.sub.2,est, {dot over (V)}.sub.g1,T, FIO.sub.2,g1, FETCO.sub.2,B, FETO.sub.2,R, and CaCO.sub.2,B, can be used to calculate FICO.sub.2,g1,T presumed to force a second steady state of end-tidal CO.sub.2 at FETCO.sub.2,B. Alternatively, FICO.sub.2,g1,T can be set arbitrarily within the limitations of the hardware and EQUATION 7b, with {dot over (Q)}.sub.est, CvCO.sub.2,est, FICO.sub.2,g1,T, FIO.sub.2,g1, FETCO.sub.2,B, FETO.sub.2,R, and CaCO.sub.2,B, can be used to calculate {dot over (V)}.sub.g1,T presumed to force a second steady state of end-tidal CO.sub.2 at FETCO.sub.2,B.

[0165] 10 This {dot over (V)}.sub.g1,T and FICO.sub.2,g1,T is delivered until recirculation is detected (described later), or for a predefined length of time presumed to be less than the recirculation time, or a predefined number of breaths presumed to occur before recirculation.

[0166] 11 At the end of the test phase, the end-tidal CO.sub.2 during the test phase (FETCO.sub.2,T) is converted to an arterial concentration (CaCO.sub.2,T). The end-tidal CO.sub.2 from the last breath of the test phase can be used as FETCO.sub.2,T. Alternatively, FETCO.sub.2,T can be the average of a number of breaths at the end of the test phase.

[0167] 12 The minute volume of expired CO.sub.2 during the test phase ({dot over (V)}CO.sub.2,T) is calculated from EQUATION 4, using the average end-tidal O.sub.2 (FETO.sub.2,T) measured during the test phase, {dot over (V)}.sub.g1,T, FICO.sub.2,g1,T, FIO.sub.2,g1, and FETCO.sub.2,T. Pulmonary blood flow and mixed-venous CO.sub.2 are recalculated ({dot over (Q)}.sub.calc,CvCO.sub.2calc) from EQUATIONS 3a1,b1 using {dot over (V)}CO.sub.2,R, CaCO.sub.2,R, {dot over (V)}CO.sub.2,T, and CaCO.sub.2,T or EQUATIONS 3a2,b2 using {dot over (Q)}.sub.est, CvCO.sub.2,est, FETCO.sub.2,B, and FETCO.sub.2,T. Subsequently, the system is returned to the baseline state.

[0168] This manoeuvre is repeated utilizing either the calculated pulmonary blood flow of each test as the estimated pulmonary blood flow in the next iteration, or the calculated mixed-venous CO.sub.2 concentration as the estimated mixed-venous CO.sub.2 concentration in the next iteration.

[0169] 13 Testing is terminated when the difference in pulmonary blood flow calculated between subsequent tests differs in magnitude less than a user-definable threshold. Optionally, the algorithm can be continued indefinitely. Optionally, the algorithm can be executed for a predefined number of iterations.

FIG. 1

[0170] According to one embodiment of a gas delivery system, the system apparatus is shown in FIG. 1. It consists of a gas blender 22, a sequential gas delivery circuit 26, gas analyzers for oxygen 16 and carbon dioxide 18, a pressure transducer 14, a computer 8 including software 10 (which is optionally embodied a computer program product) that works the gas blender 22 to request gas flows and with the gas analyzers 16 and 18, pressure transducer 14 and input devices for measured or estimated physiological parameters 36 and algorithm settings 34 to obtain inputs as contemplated herein. The gas blender 22 may be connected to three pressurized gas tanks 32. The gas blender optionally contains three rapid flow controllers (not shown) capable of delivering accurate mixes of three source gases, optionally comprised of CO.sub.2, O.sub.2, and N.sub.2 to the circuit. The concentrations of CO.sub.2, O.sub.2, and N.sub.2 in the source gases must be such that they can produce the blends required to carry out the algorithm. Pure CO.sub.2, O.sub.2, and N.sub.2 are one option. The gas analyzers 18 and 16 measure the fractional concentrations of CO.sub.2 and O.sub.2 at the mouth throughout the breath. The pressure transducer 14 is used for end-tidal detection. The computer runs a software implementation of a pulmonary blood flow measurement algorithm and demands the required mixtures from the blender 22. The monitor may display the real-time capnograph, oxigraph, pulmonary blood flow, and mixed-venous concentration of CO.sub.2.

[0171] Other inputs to the algorithm include an initial estimate of pulmonary blood flow or mixed-venous CO.sub.2 36, and termination criteria for the algorithm 34.

FIG. 5

Panel A

[0172] In FIG. 5a (Panel A), three iterations of the recursive algorithm showing convergence of the calculated pulmonary blood flow to the actual pulmonary blood flow starting from an incorrect estimate. As shown, if the estimated pulmonary blood flow is incorrect, the predicted transfer rate of CO.sub.2 between the circulation and the alveolar space will also be in error. However, the minute volume of expired of CO.sub.2 in the test phase will exponentially equilibrate with the flux across the blood-alveolar interface. As a result, the pulmonary blood flow calculated in each test will better reflect the actual pulmonary blood flow ({dot over (Q)}.sub.act) than the ingoing estimate. Because this procedure is implemented recursively, and the estimated parameters updated after each iteration to reflect the previously calculated values, the algorithm converges to the actual physiological parameters of the subject.

[0173] The rate at which the calculated parameters converge to the actual parameters depends on how fast the end-tidal CO.sub.2 approaches equilibrium in the test phase. The derivative of an exponential function is largest at the start and vanishes with time. Therefore, a substantial refinement in the estimated parameters occurs in the breaths before recirculation. As a result, the calculated parameters at the end of each test are significantly more accurate than the previous estimates.

Panel B

[0174] FIG. 5B (Panel B) shows that (a) if the estimate of pulmonary blood flow is higher than the actual pulmonary blood flow, the end-tidal CO.sub.2 in the test phase drifts exponentially upwards; (b) if the estimate of pulmonary blood flow is lower than the actual pulmonary blood flow, the end-tidal CO.sub.2 in the test phase drifts exponentially downwards; (c) if the estimate of pulmonary blood flow is approximately equal to than the actual pulmonary blood flow, the end-tidal CO.sub.2 in the test phase remains constant. It also shows how recirculation may be detected by analysis of the time course of the end-tidal CO.sub.2 during the test phase. Prior to recirculation, the end-tidal CO.sub.2 approaches a steady value exponentially—the absolute difference between consecutive end-tidal measurements decreases as the test proceeds. Recirculation causes a deviation from this asymptotic approach, detectable as an increase in the difference between consecutive end-tidal CO.sub.2 measurements. Mathematically, this is shown in equation 9.

REFERENCES

[0175] [1] Geerts B F, Aarts L P, Jansen J R. Methods in pharmacology: measurement of cardiac output. Br J Clin Pharmacol. 2011 March; 71(3):316-30. [0176] [2] Fick A. Ueber die Messung des Blutquantums in den Herzventrikeln. Sitzungsberichte der Physiologisch-Medizinosche Gesellschaft zuWuerzburg 1870; 2: 16. [0177] [3] Douglas A R, Jones N L, Reed J W. Calculation of whole blood CO2 content. J Appl Physiol. 1988 July; 65(1):473-7. [0178] [4] Kelman R G. Digital computer procedure for the conversion of PCO2 into blood content. Respir Physiol 3: 111-115, 1967. [0179] [5] DEFARES J G. Determination of PvCO2 from the exponential CO2 rise during rebreathing. J Appl Physiol. 1958 September; 13(2):159-64. [0180] [6] COLLIER C R. Determination of mixed venous CO2 tensions by rebreathing. J Appl Physiol. 1956 July; 9(1):25-9. [0181] [7] Gedeon, A., Forslund, L., Hedenstierna, G., Romano, E. (1980). A new method for noninvasive bedside determination of pulmonary blood flow. Med Biol Eng Comput 18(4), 411-8. [0182] [8] Jaffe M B. Partial CO2 rebreathing cardiac output—operating principles of the NICO system. J Clin Monit Comput. 1999 August; 15(6):387-401. [0183] [9] Tachibana K, Imanaka H, Takeuchi M, Takauchi Y, Miyano H, Nishimura M. [0184] Noninvasive cardiac output measurement using partial carbon dioxide rebreathing is less accurate at settings of reduced minute ventilation and when spontaneous breathing is present. Anesthesiology. 2003 April; 98(4):830-7. [0185] [10] Yem J S, Tang Y, Turner M J, Baker A B. Sources of error in noninvasive pulmonary blood flow measurements by partial rebreathing: a computer model study. Anesthesiology. 2003 April; 98(4):881-7. [0186] [11] Somogyi R B, Vesely A E, Preiss D, Prisman E, Volgyesi G, Azami T, et al. Precise control of end-tidal carbon dioxide levels using sequential rebreathing circuits. Anaesth Intensive Care 2005 December; 33(6):726-32.