METHOD AND APPARATUS TO ATTAIN AND MAINTAIN TARGET ARTERIAL BLOOD GAS CONCENTRATIONS USING RAMP SEQUENCES

Abstract

An apparatus and method for controlling the end tidal partial pressure of a gas X in a subject's lung, and to the use of such an apparatus and method for research, diagnostic and therapeutic purposes, wherein the method consists of: -obtaining input of a series of logistically attainable PetX values for a series of respective breaths: -determining an amount of gas X required to be inspired by the subject in an inspired gas to target the PetX for each of said respective breaths; and controlling a gas delivery device to deliver the amount of gas in a volume of gas delivered to the subject in each of said respective breaths to target the respective PetX for that breath.

Claims

1. to 79. (canceled)

80. An apparatus for controlling an amount of at least one gas X in a subject's lung to attain a targeted end tidal partial pressure of the at least one gas X (PetX.sup.T), the apparatus comprising: (1) a gas delivery device; (2) a control system for controlling the gas delivery device, wherein the control system is adapted to target a PETX.sup.T value with a respective breath [i], the PETX.sup.T value comprising either a PETX.sup.T increment or a PETX.sup.Tdecrement, the control system configured to: a. Obtain input of a logistically attainable PETX.sup.T value for the respective breath [i]; b. Perform a prospective computation of an amount of gas X required to be inspired by the subject in an inspired gas to target the PETX.sup.T for the respective breath [i] the performing comprising: i. Computing a tidal model of the subject's lung including input of the concentration of gas X in the mixed venous blood entering the subject's pulmonary circulation for gas exchange in the respective breath [i] (C.sub.MVX[i]); and ii. Outputting one or more values required to control the amount of gas X in a volume of gas delivered to the subject, based on the tidal model of the subject's lung; and c. Control the amount of gas X in a volume of gas delivered to the subject in the respective breath [i] (F.sub.IX) to target the respective PETX.sup.T for the breath [i].

81. The apparatus of claim 1, wherein computing a tidal model of the subject's lung further includes predicting the C.sub.MVX[i] by compartmental modelling of gas dynamics.

82. The apparatus of claim 1, wherein computing a tidal model of the subject's lung further includes estimating or measuring the value of at least one parameter selected from a group consisting of: functional residual capacity of the subject's lung, anatomic dead space of the subject's lung, metabolic production of gas X in the respective breath [i], metabolic consumption of gas X in the respective breath [i], and tidal volume of the respective breath [i].

83. The apparatus of claim 3, the control system further configured to tune the estimated value of the functional residual capacity over a series of tuning breaths.

84. The apparatus of claim 4 wherein tuning the estimated value of the functional residual capacity comprises: changing the targeted end tidal partial pressure of gas X between a tuning breath [i+x] and a previous tuning breath [i+x−1]; comparing the magnitude of the difference between the targeted end tidal partial pressure of gas X for said tuning breaths [i+x] and [i+x−1] with the magnitude of the difference between the measured end tidal partial pressure of gas X for the same tuning breaths to quantify any discrepancy in relative magnitude; and adjusting the estimated value of the functional residual capacity in proportion to the discrepancy to reduce the discrepancy in any subsequent prospective computing of F.sub./X

85. The apparatus of claim 4 wherein tuning the estimated value of the functional residual capacity comprises: obtaining input of a measured baseline steady state value of P.sub.ETX[i] for computing F.sub.IX at the start of a sequence; selecting a target end tidal partial pressure of gas X (P.sub.ETX[i].sup.T) for at least one tuning breath [i+x] wherein P.sub.ETX[i+x].sup.T differs from P.sub.ETX[i+x−1].sup.T; comparing the magnitude of the difference between the targeted end tidal partial pressure of gas X for said tuning breaths [i+x] and [i+x−1] with the magnitude of the difference between the measured end tidal partial pressure of gas X for the same tuning breaths to quantify any discrepancy in relative magnitude; and adjusting the estimated value of the functional residual capacity in proportion to any discrepancy in magnitude to reduce the discrepancy in a subsequent prospective computation of F.sub./X including in any subsequent corresponding tuning breaths [i+x−1] and [i+x] forming part of an iteration of the sequence.

86. The apparatus of claim 3, the control system further configured to tune the estimated value of metabolic consumption of gas X over a series of tuning breaths.

87. The apparatus of claim 7, wherein tuning the estimated value of the metabolic production or consumption of gas X comprises targeting a sequence of end tidal partial pressure of gas X, the targeting comprising: comparing a targeted end tidal partial pressure of gas X (P.sub.ETX [i+x].sup.T) for the at least one tuning breath [i+x] with a corresponding measured end tidal partial pressure of gas X for the corresponding breath [i+x] to quantify any discrepancy; and adjusting the estimated value of the total metabolic production or consumption of gas X in proportion to any discrepancy to reduce the discrepancy in any subsequent prospective computation of F.sub.IX

88. The apparatus of claim 7, wherein tuning the estimated value of the metabolic production or consumption of gas X comprises targeting a sequence of end tidal partial pressure of gas at least once by: obtaining input of a measured baseline steady state value for P.sub.ETX [i].sup.T for computing F.sub.IX at the start of a sequence; targeting a selected target end tidal partial pressure of gas X (P.sub.ETX [i+x].sup.T) for each of a series of tuning breaths [i+1 . . . i+n], wherein P.sub.ETX [i].sup.T differs from the baseline steady state value for P.sub.ETX[i]; comparing the targeted end tidal partial pressure of gas X (P.sub.ETX[i+x].sup.T for at least one tuning breath [i+x] in which the targeted end tidal gas concentration of gas X has been achieved without drift in a plurality of prior breaths [1+−1, 1+x−2 . . . ] with a corresponding measured end tidal partial pressure of gas X for a corresponding breath [i+x] to quantify any discrepancy and adjusting the estimated value of the total metabolic production or consumption of gas X in proportion to the discrepancy to reduce the discrepancy to reduce the discrepancy in a subsequent prospective computation of F.sub./X including in any subsequent corresponding tuning breath [i+x] forming part of an iteration of the sequence.

89. A computer program product for use in conjunction with a gas delivery device to control an amount of at least one gas X in a subject's lung to attain a target end tidal partial pressure of the at least one gas X (P.sub.ETX.sup.T), the computer program comprising program code for: a. obtaining input of a logistically attainable end tidal partial pressure of gas X (P.sub.ETX.sup.T) for a respective breath [i]; and b. performing a prospective computation to obtain input of an amount of gas X required to be inspired by the subject in an inspired gas to target the P.sub.ETX.sup.Tfor the respective breath [i] (F.sub./X), the performing comprising: i. computing a tidal model of the subject's lung including input of the concentration of gas X in the mixed venous blood entering the subject's pulmonary circulation for gas exchange in the respective breath [i] (C.sub.MVX[i]); and ii. outputting one or more values required to control F.sub.IX, based on tidal model of the subject's lung.

90. A method for controlling an amount of at least one gas X in a subject's lung to attain a targeted end tidal partial pressure of at least one gas X (P.sub.ETX.sup.T), the method comprising: a. obtaining input of a logistically attainable P.sub.ETX.sup.Tvalue for a respective breath [i] comprising either a P.sub.ETX.sup.T increment or a P.sub.ETX.sup.Tdecrement; and b. performing a prospective computation of an amount of gas X required to be inspired by the subject in an inspired gas to target the respective P.sub.ETX.sup.Tfor the respective breath [i] (F.sub./X), the performing comprising: i. computing a tidal model of the subject's lung including input of the concentration of gas X in the mixed venous blood entering the subject's pulmonary circulation for gas exchange in the respective breath [i] (C.sub.MVX[i]); and ii. ii. outputting one or more values required to control the amount of gas X in a volume of gas delivered to the subject, based on the tidal model of the subject's lung.

91. The method of claim 11, wherein computing a tidal model of the subject's lung further includes predicting the C.sub.MVX[i] by compartmental modelling of gas dynamics.

92. The method of claim 11, wherein computing a tidal model of the subject's lung further includes estimating or measuring the value of at least one parameter selected from a group consisting of: functional residual capacity of the subject's lung, anatomic dead space of the subject's lung, metabolic production of gas X in the respective breath [i], metabolic consumption of gas X in the respective breath [i], and tidal volume of the respective breath [i].

93. The method of claim 13, the method further comprising tuning the estimated value functional residual capacity over a series of tuning breaths.

94. The method of claim 14 wherein tuning the estimation of the functional residual capacity comprises: changing the targeted end tidal partial pressure of gas X between a tuning breath [i+x] and a previous tuning breath [i+x−1]; comparing the magnitude of the difference between the targeted end tidal partial pressure of gas X for said tuning breaths [i+x] and [i+x−1] with the magnitude of the difference between the measured end tidal partial pressure of gas X for the same tuning breaths to quantify any discrepancy in relative magnitude; and adjusting the estimated value of the functional residual capacity in proportion to the discrepancy to reduce the discrepancy in any subsequent prospective computing of F.sub./X

95. The method of claim 14 wherein tuning the estimation of the functional residual capacity comprises: obtaining input of a measured baseline steady state value of P.sub.ETX[i] for computing F.sub.IX at the start of a sequence; selecting a target end tidal partial pressure of gas X (P.sub.ETX[i].sup.T) for at least one tuning breath [i+x} wherein P.sub.ETX[i+x].sup.T differs from P.sub.ETX[i+x−1]T; comparing the magnitude of the difference between the targeted end tidal partial pressure of gas X for said tuning breaths [i+x] and [i+x−1] with the magnitude of the difference between the measured end tidal partial pressure of gas X for the same tuning breaths to quantify any discrepancy in relative magnitude; and adjusting the estimated value of the functional residual capacity in proportion to any discrepancy in magnitude to reduce the discrepancy in a subsequent prospective computation of F.sub./X including in any subsequent corresponding tuning breaths [i+x−1] and [i+x] forming part of an iteration of the sequence.

96. The method of claim 13, the method further comprising tuning the estimated value of the metabolic production or consumption of gas X over a series of tuning breaths.

97. The method of claim 17, wherein tuning the estimated value of the metabolic production or consumption of gas X comprises targeting a sequence of end tidal partial pressure of gas X, the targeting comprising: comparing a targeted end tidal partial pressure of gas X (P.sub.ETX [i+x].sup.T) for the at least one tuning breath [i+x] with a corresponding measured end tidal partial pressure of gas X for the corresponding breath [i+x] to quantify any discrepancy; and adjusting the estimated value of the total metabolic production or consumption of gas X in proportion to any discrepancy to reduce the discrepancy in any subsequent prospective computation of F.sub.IX.

98. The method of claim 17, wherein tuning the estimated value of the metabolic production or consumption of gas X comprises targeting a sequence of end tidal partial pressure of gas at least once by: obtaining input of a measured baseline steady state value for P.sub.ETX [i].sup.T for computing F.sub.IX at the start of a sequence; targeting a selected target end tidal partial pressure of gas X (P.sub.ETX [i+x].sup.T) for each of a series of tuning breaths [i+1 . . . i+n], wherein P.sub.ETX [i] .sup.T differs from the baseline steady state value for P.sub.ETX[i]; comparing the targeted end tidal partial pressure of gas X (P.sub.ETX[i+x].sup.T for at least one tuning breath [i+x] in which the targeted end tidal gas concentration of gas X has been achieved without drift in a plurality of prior breaths [1+x−1, 1+x−2 . . . ] with a corresponding measured end tidal partial pressure of gas X for a corresponding breath [i+x] to quantify any discrepancy and adjusting the estimated value of the metabolic production or consumption of gas X in proportion to the discrepancy to reduce the discrepancy to reduce the discrepancy in a subsequent prospective computation of F.sub./X including in any subsequent corresponding tuning breath [i+x] forming part of an iteration of the sequence.

99. The method of claim 13, wherein the gas X is selected from a group consisting of carbon dioxide and oxygen.

Description

BRIEF DESCRIPTION OF THE FIGURES

[0198] The invention will now be described with reference to the figures, in which:

[0199] FIG. 1 is a schematic overview of the movement of blood and the exchange of gases throughout the entire system.

[0200] FIG. 2 is a detailed schematic representation of the movement of blood and the exchange of gases at the tissues.

[0201] FIG. 3 is a detailed schematic representation of the movement of blood and the exchange of gases at the lungs when sequential rebreathing is not employed.

[0202] FIG. 4 is a detailed schematic representation of the movement of blood and the exchange of gases at the lungs when sequential rebreathing is employed.

[0203] FIG. 5 is a schematic diagram of one embodiment of an apparatus according to the invention that can be used to implement an embodiment of a method according to the invention.

[0204] FIG. 6 is a graphic representation of a tuning sequence and observed errors that can be used to tune model parameters.

[0205] FIG. 7 is a Table of abbreviations (Table 1) used in the specification

[0206] FIGS. 8a arid 8b are graphical representations of changes in target end tidal values of CO2 and response—mid-cerebral artery blood flow velocity, for a slow responder and a fast responder as revealed by a ramp sequence.

[0207] FIG. 9 is a graphical representation of blood flow responses to PCO.sub.2 predicted for the model of a brain vascular territory with a partially-stenosed vessel branch and a healthy branch in parallel as revealed by a ramp sequence.

[0208] FIG. 10 is a graphical representation of a bold signal response to PCO.sub.2 as revealed by a ramp sequence and corresponding CVR maps for an axial slice at different PetCO2 ranges for a patient with moya moya disease.

[0209] FIG. 11 is a table showing a partial raw data set for 6 subjects according to Example 1.

DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT

[0210] The invention is described hereafter in terms of one or more optional embodiments of a gas X, namely carbon dioxide and oxygen.

Prospective Modelling

[0211] Mass balance equations of gases in the lung are conventionally derived from a continuous flow model of the pulmonary ventilation. In this model, ventilation is represented as a continuous flow through the lungs, which enters and exits the lungs through separate conduits. As a consequence, for example, the anatomical dead space would not factor into the mass balance other than to reduce the overall ventilatory flow into the alveolar space. In reality, however, ventilation in humans is not continuous, but tidal. Gas does not flow through the lungs, but enters the lungs during a distinct inspiration phase of the breath and exits during a subsequent expiration phase of the breath. In each breath cycle, gas is inspired into the lungs via the airways and expired from the lungs via the same airways through which gas was inspired. One possible implication, for example, is that the first gas inspired into the alveolar space in any breath is residual gas which remains in the anatomical dead space following the previous expiration. Continuous flow models neglect the inspiration of residual gas from the anatomical dead space, and therefore, since accounting for such a factor is generally desirable, do not accurately represent the flux of gases in the lungs.

[0212] As continuous flow models of pulmonary ventilation do not correctly represent the flux of gases in the lungs, the end-tidal partial pressures of gases induced from the inspiration of gas mixtures computed from such a model will, necessarily, deviate from the targets.

[0213] By contrast, according to one aspect of the present invention, a mass balance equation of gases in the lungs is preferably formulated in terms discrete respective breaths [i] including respective discrete volumes corresponding to one or more of the FRC, anatomic dead space, the volume of gas X transferred between the pulmonary circulation and the lung in a respective breath [i] and an individual tidal volume of a respective breath [i]) is adaptable to account, for example, for inspiration of residual gas from the anatomical dead space into the alveolar space in each breath. Inasmuch as a tidal model more faithfully represents the actual flux of gases in the lungs compared with the conventional model, the induced end-tidal partial pressures of gases, to an extent that the model is fully exploited, it will more closely adhere to the targets compared with results achieved using a continuous flow model.

[0214] Moreover, we have found that using a tidal model of pulmonary ventilation, can be synergistically employed with a sequential gas delivery system to facilitate closer adherence to targets in both ventilated and spontaneously breathing subjects without reliance on a negative feedback system.

[0215] According to the present invention, a prospective determination of pulmonary ventilation and gas exchange with the blood can efficiently exploited even in spontaneously breathing subjects where the ventilatory parameters are highly variable and difficult to measure.

[0216] Where mechanical ventilation is employed, a prospective model of pulmonary ventilation and gas exchange with the blood envisages that the subject's ventilatory parameters can be estimated or measured to a level of accuracy sufficient to employ prospective control of the end-tidal partial pressures of one of more gases.

[0217] According to one embodiment of the invention, a technique of inspiratory gas delivery, sequential rebreathing, which, when using a tidal model of the pulmonary ventilation, significantly reduces or eliminates the dependence of the calculation of the inspired gas composition to be delivered in each breath, and therefore the actual end-tidal partial pressures of gases induced, on the subject's ventilatory parameters.

[0218] In parallel to what we have observed from studies with respect to the subject's ventilatory parameters, we have found that when we run a set of standardized tuning sequences, our model of the tissues more accurately reflects the actual dynamics of the gas stored in the subject's tissues.. The model parameters may be refined until the end-tidal partial pressures of gases induced by execution of the tuning sequences sufficiently adhere to the targets without the use of any feedback control.

Sequential Gas Delivery

[0219] Sequential rebreathing is a technique whereby two different gases are inspired in each breath—a controlled gas mixture followed by a “neutral” gas. A controlled gas mixture is any gas that has a controllable composition. Gas inspired in any breath is neutral if it has the same composition as gas expired by the subject in a previous breath. Neutral gas is termed as such since it has substantially the same partial pressures of gases as the blood in the pulmonary capillaries, and hence, upon inspiration into the alveolar space, does not substantially exchange any gas with the pulmonary circulation. Optionally, the rebreathed gas has a composition that is selected to correspond (i.e. have the same gas X concentration as that of) the targeted end tidal gas composition for a respective breath [i]. It will be appreciated that a modified sequential gas delivery circuit in which the subject exhales via a port leading to atmosphere and draws on a second gas formulated by a second gas delivery device (e.g. a gas blender) could be used for this purpose, for example where the second gas is deposited in an open ended reservoir downstream of a sequential gas delivery valve, for example within a conduit of suitable volume as exemplified in FIG. 7 of U.S. Pat. No. 6,799,570.

[0220] Sequential rebreathing is implemented with a sequential gas delivery breathing circuit which controls the sequence and volumes of gases inspired by the subject. A sequential gas delivery circuit may be comprised of active or passive valves and/or a computer or other electronic moans to control the volumes of, and/or switch the composition or source of, the gas inspired by the subject.

[0221] The controlled gas mixture is made available to the sequential gas delivery circuit for inspiration, optionally, at a fixed rate. On each inspiration, the sequential gas delivery circuit ensures the controlled gas mixture is inspired first, for example with active or passive valves that conned the subject's airway to a source of the controlled gas mixture. The supply of the controlled gas mixture is controlled so that it is reliably depleted in each breath.

[0222] Once the supply of the controlled gas mixture is exhausted, the sequential gas delivery circuit provides the balance of the tidal volume from a supply of neutral gas exclusively, for example with active or passive valves that connect the subject airway to the subject's exhaled gas from a previous breath.

[0223] Gas expired in previous breaths, collected in a reservoir, is re-inspired in a subsequent breath. Alternatively, the composition of gas expired by the subject can be measured with a gas analyzer and a gas with equal composition delivered to the subject as neutral gas,

[0224] During inspiration of the neutral gas and expiration, the supply of the controlled gas mixture for the next inspiration accumulates at the rate it is made available to the sequential gas delivery circuit. In this way, the subject inspires only a fixed minute volume of the controlled gas mixture, determined by the rate at which the controlled gas mixture is made available to the sequential gas delivery circuit, independent of the subject's total minute ventilation, and the balance of subject's the minute ventilation is made up of neutral gas.

[0225] Examples of suitable sequential gas delivery circuits are disclosed in US Patent Application No. 20070062534.

[0226] The fixed availability of the controlled gas mixture may be accomplished by delivering a fixed flow rate of the controlled mixture to a physical reservoir from which the subject inspires. Upon exhaustion of the reservoir, the source of inspiratory gas is switched, by active or passive means, to neutral gas from a second gas source, for example a second reservoir, from which the balance of the tidal volume is provided.

[0227] It is assumed that in each breath the volume of the neutral gas inspired at least fills the subject's anatomical dead space. Herein, all of the controlled gas mixture reaches the alveolar space and any of the neutral gas that reaches the alveolar space does not exchange gas with the circulation as it is already in equilibrium with the pulmonary capillary blood.

[0228] Sequential gas delivery circuits may be imperfect in the sense that a subject will inspire what is substantially entirety a controlled gas mixture first. However, upon exhaustion of the supply of the controlled gas mixture, when neutral gas is inspired, an amount of controlled gas mixture is continually inspired along with the neutral gas rather than being accumulated by the sequential gas delivery circuit for the next inspiration (2). The result is that the subject inspires exclusively controlled gas mixture, followed by a blend of neutral gas and controlled gas mixture. As a result of the imperfect switching of gases, a small amount of the controlled gas mixture is inspired at the end of inspiration and enters the anatomical dead space rather than reaching the alveolar space. In practise, the amount of controlled gas mixture lost to the anatomical dead space is small, and therefore, the amount of controlled gas mixture that reaches the alveolar space can still be assumed equal to the rate at which the controlled gas mixture is made available to the sequential gas delivery circuit for inspiration. Therefore, the method described herein can be executed, as described, with imperfect sequential gas delivery circuits.

[0229] A simple implementation of sequential rebreathing using a gas blender and passive sequential gas delivery circuit is described in references cited below (2; 3). Other implementations of sequential gas delivery are described in patents (4-8).

[0230] The contents of all references set forth below are hereby incorporated by reference,

[0231] Various implementations of sequential gas delivery have described by Joseph Fisher et al, in the scientific and patent literature.

[0232] As seen FIG. 1, which shows a high level overview of the movement of blood and the exchange of gases throughout the entire system, the majority of the total blood flow (Q) passes through the pulmonary circulation. Upon transiting the pulmonary capillaries, the partial pressures of gases in the pulmonary blood equilibrate with the partial pressure of gases in the lungs (P.sub.RT[i])—the result is partial pressures of gases in the pulmonary end-capillary blood equal to the end-tidal partial pressures of gases in the lungs. The blood gas contents of this blood (C.sub.p[i]) can then be determined from these partial pressures. The remaining fraction (s) of the total blood flow is shunted past the lungs and flows directly from the mixed-venous circulation into the arterial circulation without undergoing any gas exchange. Therefore, the gas contents of the arterial blood (C.sub.a[i]) are a flow weighted average of the pulmonary end-capillary blood with gas contents equilibrated to that of the lungs, and the shunted blood with gas contents which are equal to the mixed-venous blood entering the pulmonary circulation (C.sub.MV[i]). The arterial blood flows through the tissue capillary beds, where gases are exchanged between the blood and the tissues. There are one or more tissue capillary beds, each of which receives a fraction of the total blood flow (q) and has unique production, consumption, storage, and exchange characteristics for each gas. The gas contents in the venous blood leaving each tissue (C.sub.v[i]) can be determined from these characteristics. The gas contents of the mixed-venous blood leaving the tissues (C.sub.MV(TG)[i]) are given by the flow weighted average of the gas contents in the venous blood leaving each tissue. The mixed-venous blood leaving the tissues enters the pulmonary circulation after the recirculation delay (n.sub.R).

FIG. 2—The Tissues

[0233] As shown in FIG. 2, the total blood flow (Q) enters the tissue capillary beds from the arterial circulation, where the gas contents of the arterial blood (C.sub.a[i]) are modified by gas exchange between the blood and the tissues. To obtain input of the gas contents of the mixed-venous blood, the flow of blood through the tissues is modelled as a system of one or more compartments where each compartment represents a single tissue or group of tissues. Each compartment is assumed to receive a fraction of the total blood flow (q) and has a unique production or consumption (v) of, and storage capacity (d) for, each gas. The content of gases in the venous blood leaving each compartment (C.sub.v[i]) can be determined from the arterial inflow of gases, and the assumed production or consumption, and storage of the gas In the compartment. The blood flows leaving each compartment unite to form the mixed-venous circulation. Therefore, the gas contents of the mixed-venous blood leaving the tissues (C.sub.MV(T)[i]) are given by the flow weighted average of the gas contents in the venous blood leaving each tissue.

[0234] FIG. 3—The Lungs (No Sequential Rebreathing)

[0235] As shown in FIG. 3, gas enters the lungs in two ways—diffusion from the pulmonary circulation and inspiration though the airways. The pulmonary blood flow is equal to the total blood flow (Q) less the fraction (s) of the total blood flow that is shunted past the lungs. The flux rate of gas between the lungs and the pulmonary blood flow in a breath (VB[i]) is, by mass balance, the product of the pulmonary blood flow and the difference between the gas contents of the mixed-venous blood (C.sub.MV[i]) entering the pulmonary circulation and the gas contents of the pulmonary end-capillary blood (C.sub.p[i]) leaving the pulmonary circulation.

[0236] The starting volume of the lungs in any breath Is given by the functional residual capacity (FRC′). This is the gas left over in the lungs at the end of the previous expiration, and contains partial pressures of gases equal to the target end-tidal partial pressures from the previous breath (P.sub.ET[i−1].sup.T). The first part of inspiration draws gas in the anatomical dead space (V.sub.p) from the previous breath into the alveolar space. The partial pressures of gases in this volume are equal to the target end-tidal partial pressures from the previous breath. Subsequently, a volume of a controlled gas mixture (VG.sub.1) with controllable partial pressures of gases P.sub.1[i]) is inspired.

FIG. 4—The Lungs (Sequential Rebreathing)

[0237] As shown in FIG. 4, gas enters the lungs in two ways—diffusion from the pulmonary circulation and inspiration though the airways. The pulmonary blood flow is equal to the total blood flow (Q) less the fraction (s) of the total blood flow that is shunted past the lungs. f he flux rate of gas between the lungs and the pulmonary blood flow in a breath VB[i]) is, by mass balance, the product of the pulmonary blood flow and the difference between the gas contents of the mixed-venous blood (C.sub.MV[i]) entering the pulmonary circulation and the gas contents of the pulmonary end-capillary blood (C.sub.p[i]) leaving the pulmonary circulation.

[0238] The starting volume of the lungs in any breath is given by the functional residual capacity (FRC). This is the gas left over in the lungs at the end of the previous expiration, and contains partial pressures of gases equal to the target end-tidal partial pressures from the previous breath (P.sub.ET[i−1].sup.T). The first part of inspiration draws gas in the anatomical dead space (V.sub.D) from the previous breath into the alveolar space. The partial pressures of gases in this volume are equal to the target end-tidal partial pressures from the previous breath. Subsequently, a volume of a controlled gas mixture (VG.sub.1) with controllable partial pressures of gases (P.sub.1[i]) is inspired. The average volume of the controlled gas mixture inspired into the alveoli in each breath (VG.sub.1) is given by the flow rate of the controlled gas mixture (FG.sub.1) to the sequential gas delivery circuit (SGDC) delivered over one breath period (T.sub.B). The balance of the tidal volume (V.sub.T) is composed of a volume of neutral gas (VG.sub.2). Where a sequential gas delivery circuit is used that provides previously expired gas as neutral gas, this volume contains partial pressures of gases equal to the target end-tidal partial pressures from the previous breath.

FIG. 5—Apparatus

[0239] As shown in FIG. 5, according to one embodiment of an apparatus according to the invention, the apparatus consists of a gas blender (GB), a Hi-OX.sub.SR sequential gas delivery circuit (SGDC), gas analyzers (GA), a pressure transducer (PT), a computer (CPU), an input device (ID), and a display (DX). The gas blender contains three rapid flow controllers which are capable of delivering accurate mixes of three source gases (SG.sub.1, SG.sub.2, SG.sub.3) to the circuit. The gases are delivered to the circuit via a gas delivery tube connecting the outlet of the gas blender to the inlet of the sequential gas delivery circuit. The gas analyzers measure the partial pressures of gases at the airway throughout the breath. The analyzers sample gas for analysis proximal to the subject's airway via a sampling catheter. A small pump is used to draw gases from the subjects airway through the gas analyzers. The pressure transducer is used for measurement of the breath period (T.sub.B) and end-tidal detection, and also connected by a sampling catheter proximal to the subject's airway. The gas analyzers and pressure transducer communicate with the computer via analog or digital electrical signals. The computer runs a software implementation of the end-tidal targeting algorithm and demands the required mixtures from the blender via analog or digital electrical signals. The operator enters the target end-tidal values and subject parameters into the computer via the input device. The display shows the measured and targeted end-tidal gases.

FIG. 6 Tuning

[0240] As illustrated in FIG. 6, with reference to examples of gas X (oxygen and carbon dioxide) parameters representing inputs for computation of F.sub.IX can be tuned so that the measured end-tidal partial pressures of O2 (P.sub.RTO2[i].sup.M) and the measured end-tidal partial pressures of CO2 (P.sub.FTCO2[i].sup.M) during any sequence more closely reflect the target end-tidal partial pressures of O2 (P.sub.ETO2[i].sup.T) and the target end-tidal partial pressures of CO2 (P.sub.ETCO2[i].sup.T). To tune the system parameters, standardized tuning sequences are run and the measured results compared to the targets. The difference between measured end-tidal partial pressures and the target end-tidal partial pressures in the standardized tuning sequences can be used to refine the estimates of some physiological parameters.

[0241] The tuning sequence optionally sets the target end-tidal partial pressure of O2 (P.sub.FTO2[i].sup.T) at 5 mmHg above the baseline end-tidal partial pressure of O2 (P.sub.ETO2.sub.0.sup.M) throughout the sequence, and executes a 5 mmHg step-change in the end-tidal partial pressure of CO2 (P.sub.ETCO2[i].sup.T) from 5 mmHg above the baseline end-tidal partial pressure of CO2 (P.sub.ETCO2.sub.0.sup.M) to 10 mmHg above the baseline end-tidal partial pressure of CO2 in breath 30 (i30) of the sequence.

[0242] Embodiments of mass balance equations: [0243] No SGD:

[00002]$F_{1}X\left[i\right]=\frac{\begin{array}{c}{P}_{\mathrm{ET}}{X\left[i\right]}^T.Math.\left(\mathrm{FRC}+V_T\right)-P_{\mathrm{ET}}{X\left[i-1\right]}^T.Math.\left(\mathrm{FRC}+V_D\right)-\\ \mathrm{PB}.Math.Q.Math.\left(1-s\right).Math.T_B.Math.\left(C_{\mathrm{MV}}X\left[i\right]-C_{p}X\left[i\right]\right)\end{array}}{\left(V_T-V_D\right).Math.\mathrm{PB}}$ [0244] SGD:

[00003]$F_{1}X\left[i\right]=\frac{\begin{array}{c}\left(P_{\mathrm{ET}}{X\left[i\right]}^T-P_{\mathrm{ET}}{X\left[i-1\right]}^T\right).Math.\left(\mathrm{FRC}+V_T\right)+P_{\mathrm{ET}}{X\left[i-1\right]}^T.Math.\\ \left({\mathrm{FG}}_1.Math.T_B\right)-\mathrm{PB}.Math.Q.Math.\left(1-s\right).Math.T_B.Math.\left(C_{\mathrm{MV}}X\left[i\right]-C_{p}X\left[i\right]\right)\end{array}}{{\mathrm{FG}}_1.Math.T_B.Math.\mathrm{PB}}$

[0245] Abbreviations and terms are in FIG. 7.

Physiological Inputs

[0246] This section describes how to obtain measurements or estimates of all the physiological inputs required to execute a prospective end-tidal targeting sequence.

[0247] Subject weight, height, age, and sex:

[0248] Subject weight (IV), height (if), age (A), and sex (G) can be obtained from a subject interview, an interview with a family member, from an attending physician, or from medical records. Weight and height can also be measured.

Bicarbonate:

[0249] The bicarbonate concentration ([HCO.sub.3]) can be obtained from a blood gas measurement. If a blood gas measurement is not available or possible, it can be estimated as the middle of the normal range—24 mmol/L (9; 10).

Temperature:

[0250] Body temperature (T) can be obtained from a recent invasive or non-invasive measurement. If a measurement is not available or possible, it can be estimated as the middle of the normal range—37 C (11; 12).

Haemoglobin Concentration:

[0251] The haemoglobin concentration (Hb) can be obtained from a blood gas measurement. If a blood gas measurement is not available or possible, it can be estimated as the middle of the normal range for the subject's sex (G): [0252] 15 g/dL for males [0253] 13 g/dL for females (10; 13)

Shunt Fraction:

[0254] The intrapulmonary shunt fraction (s) can be measured using a variety of invasive and non-invasive techniques (14-17). If measurement is not available or possible, it can be estimated as the middle of the normal range—0.05 (18; 19).

Cardiac Output:

[0255] The cardiac output (Q) can be measured using a variety of invasive and non-invasive techniques (20-23). If measurement is not available or possible, it can be estimated from the subject's weight (W) according to the relationship:

Q=10.Math.(0.066.Math.W+1.4)   (24)

Breath Period:

[0256] The breath period (T.sub.B) can be measured using a pressure transducer (PT) or flow transducer (FT) proximal to the subject's airway. Alternatively, the subject can be coached to breathe at a predetermined rate using a metronome or other prompter. If the subject is mechanically ventilated, this parameter can be determined from the ventilator settings or ventilator operator.

Recirculation Time:

[0257] The number of breaths for recirculation to occur (n.sub.R) can be measured using a variety of invasive and non-invasive techniques (25-27). If measurement is not available or possible, it can be estimated from the breath period (T.sub.B) and an average recirculation time (0.3 min) (28) according to the relationship:

n.sub.R=0.3/T.sub.B

Metabolic O2 Consumption:

[0258] The overall metabolic O2 consumption (VO2) can be measured using a metabolic cart. If measurement is not available or possible, it can be estimated from the subject's weight (W), height (H), age (A), and sex (G) according to the relationship:

[00004]$\begin{array}{cc}VO2=\frac{10.Math.W+625.Math.H-5.Math.A+5}{6.8832}\mathrm{for}\mathrm{males}& \left(29\right)\\ VO2=\frac{10.Math.W+625.Math.H-5.Math.A-161}{6.8832}\mathrm{for}\mathrm{females}& \end{array}$

Metabolic CO2 Production:

[0259] The overall metabolic CO2 production (VCO2) can be measured using a metabolic cart. If measurement is not available or possible, it can be estimated from the overall metabolic 02 consumption (VO2) and average respiratory exchange ratio (0.8 ml CO2/ml O2) (30) according to the relationship:

VCO2=0.8.Math.VO2

Functional Residual Capacity:

[0260] The functional residual capacity (FRC) can be measured using a variety of respiratory manoeuvres (31). If measurement is not available or possible, it can be estimated from the subjects height (H), age (A), and sex (G) according to the relationship:

FRC=(2.34.Math.H+0.01.Math.A−1,09).Math.1000 for males

FRC=(2.24.Math.H+0.001.Math.A−1. 00).Math.1000 for females   (32)

Anatomical Dead Space:

[0261] The anatomical dead space (V.sub.D) can be measured using a variety of respiratory manoeuvres (33-35). If measurement is not available or possible, it can be estimated from the subject's weight (W) and sex (G) according to the relationship:

V.sub.D=1.765.Math.W+32.16 for males

V.sub.D=1.913.Math.W+21.267 for females   (36)

[0262] Rate at which the controlled gas mixture is made available for inspiration when using a sequential gas delivery circuit (SGDC)

[0263] When using a sequential gas delivery circuit (SGDC), the rate at which the controlled gas mixture is made available for inspiration (FG.sub.1) should be set so that the volume of the neutral gas inspired in each breath (VG.sub.2) is greater than or equal to the anatomical dead space (V.sub.D). The subject can be coached to increase their ventilation and/or the availability of the controlled gas mixture decreased until a sufficient volume of the neutral gas is observed to be inspired in each breath.

Tidal Volume:

[0264] The tidal volume (V) can be measured using a flow transducer (FT) proximal to the subject's airway. If measurement is not available or possible, in spontaneous breathers when using a sequential gas delivery circuit (SGDC), it can be estimated from the rate at which the controlled gas mixture (G.sub.1) is made available for inspiration (FG.sub.1), the breath period (T.sub.B), and the anatomical dead space (V.sub.D) according to the empirical relationship:

If FG.sub.115000: V.sub.T=(0.75.Math.FG.sub.1+3750).Math.T.sub.B+V.sub.D

else: V.sub.TFG.sub.1T.sub.R+V.sub.D

[0265] Alternatively, the subject can be coached or trained to breathe to a defined volume using a prompter which measures the cumulative inspired volume and prompts the subject to stop inspiration when the defined volume has been inspired. If the subject is mechanically ventilated, this parameter can be determined from the ventilator settings or ventilator operator.

Target Sequence Input

[0266] The operator enters a target sequence of n breaths consisting of a target end-tidal partial pressures of O2 (P.sub.ETO2[i].sup.T) and a target end-tidal partial pressure of CO2 (P.sub.ETCO2[i].sup.T) for every breath (i) of the sequence.

[0267] Calculation of the inspired gas composition to Induce target end-tidal values

[0268] The partial pressure of O2 in the controlled gas mixture (P.sub.1O2[i]) and the partial pressure of CO2 in the controlled gas mixture (P.sub.1CO2[i]) required to induce the sequence of target end-tidal partial pressures of O2 (P.sub.ETO2[i].sup.T) and target end-tidal partial pressures of CO2 (P.sub.ETCO2[i].sup.T) can be calculated by executing the steps outlined in sections 6-15 for every breath of the sequence (i, i=1 . . . n).

[0269] Calculate the Oand CO2 partial pressures of pulmonary end-capillary blood

[0270] When sequential rebreathing is employed (2; 37; 38), we assume that the partial pressure of O2 in pulmonary end-capillary blood (P.sub.pO2[i]) is equal to the target end-tidal partial pressure of O2 (P.sub.ETO2[i].sup.T), and the partial pressure of CO2 in pulmonary end-capillary blood (P.sub.pCO2[i]) is equal to the target end-tidal partial pressure of CO2 (P.sub.ETCO2[i ].sup.T) (39).

P.sub.pO2[i]=P.sub.ETO2[i].sup.T

P.sub.pCO2[i]=P.sub.ETCO2[i].sup.T

[0271] Various other formulas have been proposed to derive blood gas partial pressures from end-tidal partial pressures. For example, see (40; 41). Any of these relationships can be used in place of the above equalities.

Calculate the pH Pulmonary End-Capillary Blood

[0272] The pH of the pulmonary end-capillary blood (pH[i]) can be calculated from the Henderson-Hasselbalch equation using the blood bicarbonate concentration ([HCO.sub.3]), the blood CO2 partial pressure (P.sub.pCO2[i]), and the solubility of CO2 in blood (0.03 mmol/L/mmHg) (9).

[00005]$\mathrm{pH}\left[i\right]=6.1+\log \left(\frac{\left[{\mathrm{HCO}}_3\right]}{0.03.Math.P_p\mathrm{CO}2\left[i\right]}\right)$

Calculate the O2 Saturation of Pulmonary End-Capillary Blood

[0273] The O2 saturation of pulmonary end-capillary blood (S.sub.pO2[i]) can be calculated from experimental equations using the body temperature (T), the blood pH (pH[i]), the blood CO2 partial pressure (P.sub.pCO2[i]), and the blood O2 partial pressure (P.sub.pO2[i]) (42).

[00006]$S_{p}O2\left[i\right]=100.Math.\frac{-8532.2289.Math.z+2121.401.Math.z^2-67.073989.Math.z^3+z^4}{\begin{array}{c}935960.87-31346.258.Math.z+2396.1674.Math.\\ z^2-67.104406.Math.z^3+z^4\end{array}}$$\mathrm{where}$$z=P_{p}O2\left[i\right].Math.{10}^{0.024\left(37-r\right)+0.4.Math.\left(pH\left[i\right]-7.4\right)+0.06.Math.\left(\log 4C-\log P_p\mathrm{CO}2\left[i\right]\right)}$

Calculate the O2 Content of Pulmonary End-Capillary Blood

[0274] The OL2 content of pulmonary end-capillary blood (C.sub.pO2[i]) can be calculated from the O2 saturation of the blood (S.sub.pO2[i]), the blood haemoglobin concentration (Hb), the O2 carrying capacity of haemoglobin (1.36 ml/g), and the solubility of O2 in blood (0.003 ml/dL/mmHg) (43).

[00007]$C_{p}O2\left[i\right]=1.36.Math.\mathrm{Hb}.Math.\frac{S_{F}O2\left[i\right]}{100}+0.003.Math.P_{p}O2\left[i\right]$

[0275] Alternative derivations of pH, O2 saturation, and O2 content are reviewed in detail in (44).

Calculate the CO2 Content of Pulmonary End-Capillary Blood

[0276] The CO2 content of pulmonary end-capillary blood (C.sub.pCO2[i]) can be calculated from the blood haemoglobin concentration (Hb), the O2 saturation of the blood (S.sub.pO2[i]), the blood pH (pH[i]), and the blood CO2 partial pressure (P.sub.pCO2[i]) (45).

[00008]$C_p\mathrm{CO}2\left[i\right]-\left(1.0-\frac{0.02924.Math.\mathrm{Hb}}{\left(2.244-0.422.Math.\left(\frac{\mathrm{Sp}O2\left[i\right]}{100}\right)\right).Math.\left(8.740-\mathrm{pH}\left[i\right]\right)}\right).Math.C_{\mathrm{pl}}$

where: C.sub.pi=0.0301.Math.P.sub.pCO2[i].Math.(1+10.sup.pH[i]−6.0).Math.2.226

[0277] See also (46-48) for alternative calculations of CO2 content.

Calculate the O2 and CO2 Content of Arterial Blood

[0278] The arterial blood is a mixture of the pulmonary end-capillary blood and the blood shunted past the lungs. The percentage of the cardiac output (Q) that is shunted past the lungs is given by the intrapulmonary shunt fraction (s).

[0279] The content of O2 in the arterial blood (C.sub.aO2[i]) is a weighted average of the O2 content of the pulmonary end-capillary blood (C.sub.pO2[i]) and the O2 content of the blood which is shunted directly from the mixed venous circulation (C.sub.MVO2[i]).

C.sub.aO2[i]=(1−s).Math.C.sub.pO2[i]1 s−C .sub.MVO2[i]

[0280] The content of CO2 in the arterial blood (C.sub.aCO2[i]) is a weighted average of the CO2 content of the pulmonary end-capillary blood (C.sub.pCO2[i]) and the CO2 content of the blood which is shunted directly from the mixed-venous circulation (C.sub.MVCO2[i]).

C.sub.aCO2[i]=(1−s).Math.C.sub.pCO2 +s.Math.C.sub.MVCO2[i]

Calculate the O2 Content of the Mixed-Venous Blood

[0281] Before returning to the venous circulation, the arterial blood passes through the tissue capillary beds where O2 is consumed and exchanged. This system can be modelled as a compartmental system where each compartment (j) represents a single tissue or group of tissues. Each compartment is assigned a storage capacity for O2 (dO2.sub.j). Each compartment is also modelled as being responsible fora fraction (vo2.sub.j) of the overall metabolic O2 consumption (VO2), and receiving a fraction (q.sub.j) of the total cardiac output (Q). The content of O2 in the venous blood leaving a compartment (C.sub.vO2.sub.j[i]) is equal to the content of O2 in the compartment. Assuming an O2 model with n.sub.O2 compartments, the O2 content of the venous blood leaving each compartment can be calculated from the O2 content in the compartment during the previous breath (C.sub.vO2.sub.j[i−1]), the compartment parameters, and the period of the breath (T.sub.B).

[0282] For j=1 . . . n.sub.O2

[00009]$C_{V}O{2}_j\left[i\right]=C_{V}O{2}_j\left[i-1\right]+\frac{100.Math.T_B}{dO{2}_j}.Math.\left(q_j.Math.Q.Math.\left(C_{a}O2\left[i\right]-C_{V}O{2}_j\left[i-1\right]\right)-\mathrm{vo}{2}_j.Math.VO2\right)$

[0283] The values for a one compartment model (n.sub.O2=1) are given below. The model assumes a single compartment with a storage capacity for O2 (dO2.sub.k) proportional to the subjects weight (W) (49).

TABLE-US-00001 J q.sub.J dO2.sub.J vo2.sub.J 1 1 (1500/70) .Math. W 1

[0284] The mixed-venous O2 content leaving the tissues (C.sub.MV(T)O2[i]) is the sum of the O2 content leaving each compartment (C.sub.vO2.sub.j[i]) weighted by the fraction of the cardiac output (q.sub.j) received by the compartment.

[00010]$C_{\mathrm{MV}\left(T\right)}O2\left[i\right]=\underset{j=1}{\overset{{\hspace{0.17em}}^{n}O2}{.Math.}}{q}_j.Math.C_{V}O{2}_j\left[i\right]$

[0285] Alternatively, since the storage capacity of O2 in the tissues of the body is small, the O2 content of the mixed-venous blood leaving the tissues (C.sub.MV(T)O2[i]) can be assumed to be equal to the arterial inflow of O2 to the tissues (Q.Math.C.sub.4O2.sub.j[i]) less the overall metabolic O2 consumption of the tissues (VO2) distributed over the cardiac output (Q).

[00011]$C_{\mathrm{MV}\left(T\right)}O{2}_j\left[i\right]=\frac{Q.Math.C_{a}O2\left[i\right]-VO2}{Q}$

[0286] The O2 content of the mixed-venous blood entering the pulmonary circulation (C.sub.MVO2[i]) is equal to the O2 content of the mixed-venous blood leaving the tissues delayed by the recirculation time (C.sub.MV(T)O2[i−n.sub.R])

C.sub.MVO2[i]=C.sub.MV(T)O2[i−n.sub.R]

[0287] Other O2 model parameters are available from (49; 50).

Calculate the CO2 Content of the Mixed-Venous Blood

[0288] Before returning to the venous circulation, the arterial blood passes through the tissue capillary beds where CO2 is produced and exchanged. This system can be modelled as a compartmental system where each compartment (k) represents a single tissue or group of tissues. Each compartment is assigned a storage capacity for CO2 (dCO2.sub.k). Each compartment is also modelled as being responsible for a fraction (vco2.sub.k) of the overall metabolic CO2 production (VCO2), and receiving a fraction (q.sub.k)of the total cardiac output (Q). The content of CO2 in the venous blood leaving a compartment (C.sub.vCO2.sub.k[i]) is equal to the content of CO2 in the compartment. Assuming a CO2 model with n.sub.CO2, compartments, the CO2 content of the venous blood leaving each compartment can be calculated from the CO2 content in the compartment during the previous breath (C.sub.vCO2.sub.j[i−1]), the compartment parameters, and the period of the breath (T.sub.B).

[0289] For k=1 . . . n.sub.CO2

[00012]$C_V\mathrm{CO}{2}_k\left[i\right]-C_V\mathrm{CO}{2}_k\left[i-1\right]+\frac{100.Math.T_B}{d\mathrm{CO}{2}_k}.Math.\left(\mathrm{vco}{2}_k.Math.V\mathrm{CO}2-q_k.Math.Q.Math.\left(C_V\mathrm{CO}{2}_k\left[i-1\right]-C_a\mathrm{CO}2\left[i\right]\right)\right)$

[0290] The values for a five compartment model n.sub.CO2−5) are given below (51). The model assumes each compartment has a storage capacity for CO2 (dCO2.sub.k) proportional to the subjects weight (W).

TABLE-US-00002 k q.sub.k dCO2.sub.k vco2.sub.k 1 0.04 (225/70) .Math. W 0.11 2 0.14 (902/70) .Math. W 0.28 3 0.16 (9980/70) .Math. W 0.17 4 0.15 (113900/70) .Math. W 0.15 5 0.51 (3310/70) .Math. W 0.29

[0291] The values for a one compartment model (N.sub.CO2=1) are given below. The model assumes a single compartment with a storage capacity for CO2 (dCO2.sub.k) proportional to the subjects weight (W). The storage capacity for the single compartment is calculated as the average of the storage capacity for each compartment of the multi-compartment model weighted by the fraction of the cardiac output assigned to the compartment.

TABLE-US-00003 k q.sub.k dCO2.sub.k vco2.sub.k 1 1 (20505/70) .Math. W 1

[0292] The mixed-venous CO2 content leaving the tissues (C.sub.MV(T)CO2[i]) is the sum of the CO2 content leaving each compartment (C.sub.vCO2.sub.k[i]) weighted by the fraction of the cardiac output (q.sub.k) received by the compartment.

[00013]$C_{\mathrm{MV}\left(T\right)}\mathrm{CO}2\left[i\right]=\underset{k=1}{\overset{{\hspace{0.17em}}^n\mathrm{CO}2}{.Math.}}{q}_k.Math.C_V\mathrm{CO}{2}_k\left[i\right]$

[0293] The CO2 content of the mixed-venous blood entering the pulmonary circulation (C.sub.MVCO2[i]) is equal to the CO2 content of the mixed-venous blood leaving the tissues delayed by the recirculation time (C.sub.MV(T)CO2[i−n.sub.k])

C.sub.MVCO2[i]=C.sub.MV(T)CO2[i−n.sub.R]

[0294] Other CO2 model parameters are available from (49; 52).

Calculate PIO2 and PICO2 to Deliver with No Sequential Gas Delivery Circuit

[0295] On each inspiration, a tidal volume (V.sub.T) of gas is inspired into the alveoli. When the subject is not connected to a sequential gas delivery circuit, gas is inspired in the following order: a) the gas in the anatomical dead space (V.sub.D) is re-inspired with a partial pressure of O2 equal to the target end-tidal partial pressure of O2 from the previous breath (P.sub.ETO2[i].sup.T) and a partial pressure of CO2 equal to the target end-tidal partial pressure of CO2 from the previous breath (P.sub.ETCO2[i].sup.T): b) a volume of controlled gas mixture (VG.sub.1) with controllable partial pressure of O2 (P.sub.1O2[i]) and controllable partial pressure of CO2 (P.sub.1CO2[i]). This inspired gas mixes with the volume of gas in the functional residual capacity (FRC) with a partial pressure of O2 and CO2 equal to the target end-tidal partial pressures from the previous breath.

[0296] A volume of O2 is transferred between the alveolar space and the pulmonary circulation (VB.sub.P2[i]). The rate of O2 transfer between the alveolar space and the pulmonary circulation depends on the product of the cardiac output (Q) less the intrapulmonary shunt fraction (s), and the difference between the mixed-venous O2 content entering the pulmonary circulation (C.sub.MVO2[i]) and the pulmonary end-capillary O2 content (C.sub.pO2[i]) leaving the pulmonary circulation. This transfer occurs over the breath period (T.sub.B).

VB.sub.O2[i]−Q.Math.(1−s).Math.T.sub.B.Math.(C.sub.MVO2[i]−C.sub.pO2[i])

[0297] A volume of CO2 is transferred between the alveolar space and the pulmonary circulation (VB.sub.CO2[i]). The rate of CO2 transfer between the alveolar space and the pulmonary circulation depends on the product of the cardiac output (Q) less the intrapulmonary shunt fraction (s), and the difference between the mixed-venous CO2 content entering the pulmonary circulation (C.sub.MVCO2[i]) and the pulmonary end-capillary CO2 content (C.sub.pCO2[i]) leaving the pulmonary circulation. This transfer occurs over the breath period (T.sub.B).

VB.sub.CO2[i]=Q.Math.(1−s)T.sub.B.Math.(C.sub.MVCO2[i]−C.sub.pCO2[i])

[0298] The average volume of the controlled gas mixture inspired into the alveoli in each breath (VG.sub.1) is given by the tidal volume (V.sub.T) less the anatomical dead space (V.sub.D).

VG.sub.1=V.sub.T−V.sub.D

[0299] The end-tidal partial pressure O2 (P.sub.ETO2[i].sup.T) is simply the total volume of O2 in the alveolar space, divided by the total volume of the alveolar space. The end-tidal partial pressure CO2 (P.sub.ETCO2[i].sup.T) is simply the total volume of CO2 in the alveolar space, divided by the total volume of the alveolar space.

[00014]$P_{\mathrm{ET}}O{2\left[i\right]}^T=\frac{\left(\begin{array}{c}\stackrel{\stackrel{O2\mathrm{in}\mathrm{FRC}}{︷}}{P_{\mathrm{ET}}O{2\left[i-1\right]}^T.Math.\mathrm{FRC}}+\stackrel{\stackrel{\begin{array}{c}O2\mathrm{re}\text{-}\mathrm{inspired}\\ \mathrm{from}{V}_D\end{array}}{︷}}{P_{\mathrm{ET}}O{2\left[i-1\right]}^T.Math.V_D}+\stackrel{\stackrel{\begin{array}{c}O2\mathrm{in}\mathrm{con}-\\ \mathrm{trolled}\mathrm{gas}\\ \mathrm{mixture}\end{array}}{︷}}{\begin{array}{c}{P}_{I}O2\left[i\right].Math.\\ \left(V_T-V_D\right)\end{array}}+\\ \stackrel{\stackrel{O2\mathrm{transfered}\mathrm{into}\mathrm{lung}\mathrm{from}\mathrm{the}\mathrm{circulation}\left({\mathrm{VB}}_{O2}\right)}{︷}}{\mathrm{PB}.Math.Q.Math.\left(1-s\right).Math.T_B.Math.\left(C_{\mathrm{MV}}O2\left[i\right]-C_{p}O2\left[i\right]\right)}\end{array}\right)}{\underset{\underset{\mathrm{Total}\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{alveolar}\mathrm{space}}{︸}}{V_T+\mathrm{FRC}}}$$P_{\mathrm{ET}}CO{2\left[i\right]}^T=\frac{(\begin{array}{c}\stackrel{\stackrel{\mathrm{CO}2\mathrm{in}\mathrm{FRC}}{︷}}{P_{\mathrm{ET}}\mathrm{CO}{2\left[i-1\right]}^T.Math.\mathrm{FRC}}+\stackrel{\stackrel{\begin{array}{c}\mathrm{CO}2\mathrm{re}\text{-}\mathrm{inspired}\\ \mathrm{from}{V}_D\end{array}}{︷}}{P_{\mathrm{ET}}\mathrm{CO}{2\left[i-1\right]}^T.Math.V_D}+\stackrel{\stackrel{\begin{array}{c}\mathrm{CO}2\mathrm{in}\mathrm{con}-\\ \mathrm{trolled}\mathrm{gas}\\ \mathrm{mixture}\end{array}}{︷}}{\begin{array}{c}{P}_I\mathrm{CO}2\left[i\right].Math.\\ \left(V_T-V_D\right)\end{array}}+\\ \stackrel{\stackrel{\mathrm{CO}2\mathrm{transfered}\mathrm{into}\mathrm{lung}\mathrm{from}\mathrm{the}\mathrm{circulation}\left({\mathrm{VB}}_{\mathrm{CO}2}\right)}{︷}}{\mathrm{PB}.Math.Q.Math.\left(1-s\right).Math.T_B.Math.\left(C_{\mathrm{MV}}\mathrm{CO}2\left[i\right]-C_p\mathrm{CO}2\left[i\right]\right)}\end{array})}{\underset{\underset{\mathrm{Total}\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{alveolar}\mathrm{space}}{︸}}{V_T+\mathrm{FRC}}}$

[0300] Since all of these volumes and partial pressures are either known, or can be estimated, the partial pressure of O2 in the controlled gas mixture (P.sub.1O2[i]) and the partial pressure of CO2 in the controlled gas mixture (P.sub.1CO2[i]) can be set to induce target end-tidal partial pressures.

[0301] In some cases, some of the terms (braced terms in the numerator of the above equations) contributing to the target end-tidal partial pressure of O2 (P.sub.ETO2[i].sup.T) or the target end-tidal partial pressure of CO2 (P.sub.ETCO2[i].sup.T) may be neglected. For example, in most cases, the O2 or CO2 re-inspired from the anatomical dead space (V.sub.D) is small compared to the O2 or CO2 in the other volumes that contribute to the end-tidal partial pressures. In a case where the volume of O.sub.2 or CO.sub.2 in the controlled gas mixture is very large, for example when trying to induce a large increase in the target end-tidal partial pressures, the O.sub.2 or CO.sub.2 transferred into the lung from the circulation may be comparatively small and neglected. Neglecting any terms of the mass balance equations will decrease computational complexity at the expense of the accuracy of the induced end-tidal partial pressures of gases.

[0302] After re-arranging the above equations for the partial pressure of O2 in the controlled gas mixture and the partial pressure of CO2 in the controlled gas mixture, simplification, and grouping of terms:

[00015]$P_{I}O2\left[i\right]=\frac{\begin{array}{c}{P}_{\mathrm{ET}}O{2\left[i\right]}^T.Math.\left(\mathrm{FRC}+V_T\right)-P_{\mathrm{ET}}O{2\left[i-1\right]}^T.Math.\left(\mathrm{FRC}+V_D\right)-\\ \mathrm{PB}.Math.Q.Math.\left(1-s\right).Math.T_B.Math.\left(C_{\mathrm{MV}}O2\left[i\right]-C_{p}O2\left[i\right]\right)\end{array}}{V_T-V_D}$$P_I\mathrm{CO}2\left[i\right]=\frac{\begin{array}{c}{P}_{\mathrm{ET}}\mathrm{CO}{2\left[i\right]}^T.Math.\left(\mathrm{FRC}+V_T\right)-P_{\mathrm{ET}}\mathrm{CO}{2\left[i-1\right]}^T.Math.\\ \left(\mathrm{FRC}+V_D\right)-\mathrm{PB}.Math.Q.Math.\left(1-s\right).Math.T_B.Math.\left(C_{\mathrm{MV}}\mathrm{CO}2\left[i\right]-C_{p}C\right)\end{array}}{V_T-V_D}$

[0303] These equations can be used to calculate the partial pressure of O2 in the controlled gas mixture (P.sub.1O2[i]) and the partial pressure of CO2 in the controlled gas mixture (P.sub.1CO2[i]) required to Induce a target end-tidal partial pressure of O2 (P.sub.ETO2[i]) and target end-tidal partial pressure of CO2 (P.sub.prCO2[i].sup.T) where the target end-tidal partial pressure of O2 from the previous breath (P.sub.ETO2[i−1].sup.T), the target end-tidal partial pressure of CO2 from the previous breath (P.sub.ETCO2[i−1].sup.T), the functional residual capacity (FRC), the anatomical dead space (V.sub.D), tidal volume (V.sub.T), the breath period (T.sub.B), cardiac output (Q), intrapulmonary shunt fraction (s), mixed-venous content of O2 entering the pulmonary circulation (C.sub.MVO2[i]), mixed-venous content of CO2 entering the pulmonary circulation (C.sub.MVCO2[i]), pulmonary end-capillary content of O2 (C.sub.pO2[i]), and pulmonary end-capillary content of CO2 (C.sub.pCO2[i]) are either known, calculated, estimated, measured, or predicted.

[0304] Notice that the partial pressure of O2 in the controlled gas mixture (P.sub.1O2[i]) and the partial pressure of CO2 in the controlled gas mixture (P.sub.1CO2[i]) required to induce a target end-tidal partial pressure of O2 (P.sub.ETO2[i].sup.T) or a target end-tidal partial pressure of CO2 (P.sub.ETCO2[i].sup.T) depends strongly on the tidal volume (V.sub.T), anatomical dead space ( V.sub.D) and the functional residual capacity (FRC).

[0305] It is often useful in practise to maintain the end-tidal partial pressures of gases steady for a predefined number of breaths or period of time. This is a special case of inducing target end-tidal partial pressures of gases where the target end-tidal partial pressure of a gas in a breath is equal to the target end-tidal partial pressure of said gas from the previous breath.

P.sub.ETO2[i].sup.T=P.sub.ETO2[i−1].sup.T OR

P.sub.ETCO2[i].sup.T=P.sub.ETCO2[i−1].sup.T

[0306] Herein, the above general equations for calculating the composition of the controlled gas mixture reduce to the following:

[00016]$P_{I}O2\left[i\right]=\frac{\begin{array}{c}{P}_{\mathrm{ET}}O{2\left[i\right]}^T.Math.\left(V_T-V_D\right)-\mathrm{PB}.Math.Q.Math.\\ \left(1-s\right).Math.T_B.Math.\left(C_{\mathrm{MV}}O2\left[i\right]-C_{p}O2\left[i\right]\right)\end{array}}{V_T-V_D}$$P_I\mathrm{CO}2\left[i\right]=\frac{\begin{array}{c}{P}_{\mathrm{ET}}\mathrm{CO}{2\left[i\right]}^T.Math.\left(V_T-V_D\right)-\mathrm{PB}.Math.Q.Math.\\ \left(1-s\right).Math.T_B.Math.\left(C_{\mathrm{MV}}\mathrm{CO}2\left[i\right]-C_p\mathrm{CO}2\left[i\right]\right)\end{array}}{V_T-V_D}$

[0307] Notice, these equations still require the estimation, measurement, or determination of many of the subject's ventilatory or pulmonary parameters, namely, tidal volume (V.sub.T), functional residual capacity (FRC), breath period (T.sub.B), and anatomical dead space (V.sub.D). Therefore, in the absence of sequential rebreathing, the calculation of the partial pressure of O.sub.2 in the controlled gas mixture (P.sub.1O2[i]) and the partial pressure of CO2 in the controlled gas mixture (P.sub.1CO2[i]) required to induce a target end-tidal partial pressure of O.sub.2 (P.sub.ETO2[i].sup.T) and a target end-tidal partial pressure of CO.sub.2 (P.sub.ETCO2[i].sup.T) is highly dependant on the subjects ventilatory and pulmonary parameters. However, some of these parameters, namely functional residual capacity (FRC) and the anatomical dead space (V.sub.D), can be measured or estimated prior to execution of the targeting sequence, and can be reasonably assumed not to change over the course of the experiment. Other parameters, namely tidal volume (V.sub.T) and breath period (T.sub.B), while normally highly variable, are very well controlled and stable in mechanically ventilated subjects.

[0308] This method, therefore, is optional, especially where a simpler approach is preferred, and the subjects ventilation can be reasonably controlled or predicted.

[0309] It will be recognized that the volumes and partial pressures required to calculate the partial pressure of O.sub.2 in the controlled gas mixture (P.sub.1O2[i]) and the partial pressure of CO.sub.2 in the controlled gas mixture (P.sub.1CO2[i]) may need to be corrected for differences In temperature or presence of water vapour between the lung and the conditions under which they are measured, estimated, or delivered. The corrections applied will depend on the conditions under which these volumes and partial pressures are measured, estimated, or delivered. All volumes and partial pressures should be corrected to body temperature and pressure saturated conditions. A person skilled in the art will be comfortable with these corrections.

[0310] A person skilled in the art will also recognize the equivalence between partial pressures and fractional concentrations.sub.— Any terms expressed as partial pressures can be converted to fractional concentrations and vice versa, For example, the partial pressure of O2 in the controlled gas mixture (P.sub.1O2[i]) and the partial pressure of CO2 in the controlled gas mixture (P.sub.1CO2[i]) may be converted a fractional concentration of O2 in the controlled gas mixture (F.sub.1O2[i]) and a fractional concentration of CO2 in the controlled gas mixture (F.sub.1CO2[i]).

[00017]$F_{I}O2\left[i\right]=\frac{P_{I}O2\left[i\right]}{\mathrm{PB}}$$F_I\mathrm{CO}2\left[i\right]=\frac{P_I\mathrm{CO}2\left[i\right]}{\mathrm{PB}}$

Calculate PIO2 and PICO2 to Deliver to a Sequential Gas Delivery Circuit

[0311] On each inspiration, a tidal volume (V.sub.T)of gas is inspired Into the alveoli. When the subject is connected to a sequential gas delivery circuit (SGDC) that collects previously expired gas in a reservoir for later inspiration as neutral gas (ex. Hi-Ox.sub.SR), gas is inspired in the following order a) the gas in the anatomical dead space (V.sub.D) is re-inspired with a partial pressure of O2 equal to the target end-tidal partial pressure of O2 from the previous breath (P.sub.ETO2[i].sup.T) and a partial pressure of CO2 equal to the target end-tidal partial pressure of CO.sub.2 from the previous breath (P.sub.ETCO2[i−1].sup.T); b) a volume of controlled gas mixture (VG.sub.1) with controllable partial pressure of O.sub.2 (P.sub.1O2[i]) and controllable partial pressure of CO2 (P.sub.1CO2[i]): c) a volume of neutral gas (VG.sub.2) with a partial pressure of O2 and CO2 equal to the target end-tidal partial pressures from the previous breath. This inspired gas mixes with the volume of gas in the functional residual capacity (FRC) with a partial pressure of O2 and CO2 equal to the target end-tidal partial pressures from the previous breath.

[0312] A volume of O2 is transferred between the alveolar space and the pulmonary circulation (VB.sub.n2[i]). The rate of O2 transfer between the alveolar space and the pulmonary circulation depends on the product of the cardiac output (Q) less the intrapulmonary shunt fraction (s), and the difference between the mixed-venous O2 content entering the pulmonary circulation C.sub.MVO2[i]) and the pulmonary end-capillary O2 content (C.sub.pO2[i]) leaving the pulmonary circulation. This transfer occurs over the breath period (T.sub.B).

VB.sub.O2[i]=Q.Math.(1−s).Math.T.sub.B.Math.(C.sub.MVO2[i]−C.sub.pO2[i])

[0313] A volume of CO2 is transferred between the alveolar space and the pulmonary circulation (VB.sub.CO02[i]). The rate of CO2 transfer between the alveolar space and the pulmonary circulation depends on the product of the cardiac output (Q) less the intrapulmonary shunt fraction (s), and the difference between the mixed-venous CO2 content entering the pulmonary circulation (C.sub.MVCO2[i]) and the pulmonary end-capillary CO2 content (C.sub.pC2[i]) leaving the pulmonary circulation. This transfer occurs over the breath period (T.sub.B).

VB.sub.CO2[i]=Q.Math.(1−s).Math.T.sub.B.Math.(C.sub.MVCO2[i]−C.sub.pCO2[i])

[0314] Assuming a neutral gas at least fills the subjects anatomical dead space (V.sub.D), the average volume of the controlled gas mixture inspired into the alveoli in each breath (VG.sub.1) is given by the rate at which the controlled gas mixture is made available for inspiration (FG.sub.1) delivered over a single breath period (T.sub.B):

VG.sub.1=FG.sub.1.Math.T.sub.B

[0315] The average volume of neutral gas that is inspired into the alveoli in each breath is given by the tidal volume ( V.sub.T) less the volume of inspired controlled gas mixture (VG.sub.1) and the volume of gas that remains in the anatomical dead space (V.sub.D):

VG.sub.2=V.sub.T−V.sub.D−FG.sub.1.Math.T.sub.B

[0316] The end-tidal partial pressure O2 (P.sub.ETO2[i].sup.T) is simply the total volume of O2 in the alveolar space, divided by the total volume of the alveolar space. The end-tidal partial pressure CO2 ( P.sub.FTCO2[i].sup.T) is simply the total volume of CO2 in the alveolar space, divided by the total volume of the alveolar space.

[00018]$P_{\mathrm{ET}}O{2\left[i\right]}^T=\frac{\left(\underset{\underset{P_{\mathrm{ET}}O{2\left[i-1\right]}^T.Math.\mathrm{FRC}}{︷}}{O2\mathrm{in}\mathrm{FRC}}\underset{+}{}\underset{P_{\mathrm{ET}}O{2\left[i-1\right]}^T.Math.V_D}{\underset{︷}{O2\text{rc-inspired}\mathrm{from}{V}_D}}\underset{+}{}\underset{P_{1}O2\left[i\right].Math.\left({\mathrm{FG}}_1.Math.T_B\right)}{\underset{︷}{O2\mathrm{in}\mathrm{controlled}\mathrm{gas}\mathrm{mixture}}}\underset{+}{}\underset{\underset{P_{\mathrm{ET}}O{2\left[i-1\right]}^T.Math.(V_T-V_D-{\mathrm{FG}}_1.Math.}{︷}}{O2\mathrm{in}\mathrm{neutral}\mathrm{gas}}\underset{+}{}\underset{\underset{\mathrm{PB}.Math.Q.Math.\left(1-s\right).Math.T_B.Math.\left(C_{\mathrm{MV}}\mathrm{O2}\left[i\right]-C_p\right)2\left[i\right]}{︷}}{O2\mathrm{transfered}\mathrm{into}\mathrm{lung}\mathrm{from}\mathrm{the}\mathrm{circulation}}\right)}{\underset{\underset{\mathrm{Total}\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{alveolar}\mathrm{space}}{︸}}{V_T+\mathrm{FRC}}}$

[0317] Since all of these volumes and partial pressures are either known, or can be estimated, the partial pressure of O2 in the controlled gas mixture (P.sub.1O2[i]) and the partial pressure of CO2 in the controlled gas mixture (P.sub.1CO2[i]) can be set to induce target end-tidal partial pressures.

[0318] In some cases, some of the terms (braced terms in the numerator of the above equations) contributing to the target end-tidal partial pressure of O2 (P.sub.ETO2[i].sup.T) or the target end-tidal partial pressure of CO2 (P.sub.ETCO2[i].sup.T) may be neglected. For example, in most cases, the O.sub.2 or CO.sub.2 re-inspired from the anatomical dead space (V.sub.D) is small compared to the O.sub.2 or CO.sub.2 in the other volumes that contribute to the end-tidal partial pressures. In the case where the volume of O2 or CO2 in the controlled gas mixture is very large, for example when trying to induce a large increase in the target end-tidal partial pressures, the O2 or CO2 transferred into the lung from the circulation may be comparatively small and neglected. Neglecting any terms of the mass balance equations will decrease computational complexity at the expense of the accuracy of the induced end-tidal partial pressures of gases.

[0319] After re-arranging the above equations for the partial pressure of O2 in the controlled gas mixture and the partial pressure of CO2 in the controlled gas mixture, simplification, and grouping of terms:

[00019]$P_{I}O2\left[i\right]=\frac{\left(P_{\mathrm{ET}}O{2\left[i\right]}^T-P_{{}_{\mathrm{ET}}}{\mathrm{O2}\left[i-1\right]}^T\right).Math.\left(\mathrm{FRC}+V_T\right)+P_{\mathrm{ET}}O{2\left[i-1\right]}^T.Math.\left({\mathrm{FG}}_1.Math.T_B\right)-\mathrm{PB}.Math.Q.Math.\left(1-s\right).Math.T_B.Math.\left(C_{\mathrm{MV}}O2\left[i\right]-C_{p}O2\left[i\right]\right)}{{\mathrm{FG}}_1.Math.T_B}$$P_I\mathrm{CO}2\left[i\right]=\frac{\left(P_{\mathrm{ET}}O{2\left[i\right]}^T-P_{{}_{\mathrm{ET}}}\mathrm{CO}{2\left[i-1\right]}^T\right).Math.\left(\mathrm{FRC}+V_T\right)+P_{\mathrm{ET}}\mathrm{CO}{2\left[i-1\right]}^T.Math.\left({\mathrm{FG}}_1.Math.T_B\right)-\mathrm{PB}.Math.Q.Math.\left(1-s\right).Math.T_B.Math.(C_{MV}\mathrm{CO}2\left[i\right]-C_{p}C}{{\mathrm{FG}}_1.Math.T_B}$

[0320] The above equations can be used to calculate the partial pressure of O2 in the controlled gas mixture (P.sub.1O2[i]) and the partial pressure of CO2 in the controlled gas mixture (P.sub.1CO2[i]) required to induce a target end-tidal target partial pressure of O2 (P.sub.ETO2[i].sup.T) and a target end-tidal partial pressure of CO2 (P.sub.ETCO2[i].sup.T) where the target end-tidal partial pressure of O2 from the previous breath (P.sub.ETO2[i−1].sup.T), the target end-tidal partial pressure of CO2 from the previous breath (P.sub.ETCO2[i−1].sup.T, the functional residual capacity (FRC), tidal volume (V.sub.T), rate at which the controlled gas mixture Is made available for inspiration (FG.sub.1), the breath period (T.sub.B), cardiac output (Q), intrapulmonary shunt fraction (s), recirculation time (n.sub.R), mixed-venous content of O2 entering the pulmonary circulation (C.sub.MVO2[i]), mixed-venous content of CO2 entering the pulmonary circulation (C.sub.MVCO2[i]), pulmonary end-capillary content of O2 (C.sub.PO2[i]), and pulmonary end-capillary content of CO.sub.PCO2[i]) are either known, calculated, estimated, measured, or predicted.

[0321] Notice that where this form sequential rebreathing is employed, the anatomical dead space (V.sub.n) does not factor into the above equations and end-tidal targeting is independent of its measurement or estimation. Notice also that the tidal volume (V.sub.T) appears only in summation with the functional residual capacity (FRC), Since the tidal volume is, in general, small compared to the functional residual capacity (V.sub.T≤0.1..Math.FRC), errors in measurement or estimation of the tidal volume have little effect on inducing target end-tidal partial pressures of gases. In fact, the above equations can be used with the tidal volume term omitted completely with little effect on results.

[0322] It is often useful in practise to maintain the end-tidal partial pressures of gases steady for a predefined number of breaths or period of time. This is a special case of inducing target end-tidal partial pressures of gases where the target end-tidal partial pressure of a gas in a breath is equal to the target end-tidal partial pressure of said gas from the previous breath.

P.sub.ETO2[i].sup.T=P.sub.ETP2[i−1].sup.T OR

P.sub.ETCO2[i].sup.T=P.sub.ETCO2[i].sup.T

[0323] Herein, the above general equations for calculating the composition of the controlled gas mixture reduce to the following:

[00020]$P_{I}O2\left[i\right]=\frac{P_{\mathrm{ET}}O{2\left[i\right]}^T.Math.{\mathrm{FG}}_1-\mathrm{PB}.Math.Q.Math.\left(1-s\right).Math.\left(C_{\mathrm{MV}}O2\left[i\right]-C_{p}O2\left[i\right]\right)}{{\mathrm{FG}}_1}$$P_I\mathrm{CO}2\left[i\right]=\frac{P_{\mathrm{ET}}\mathrm{CO}{2\left[i\right]}^T.Math.{\mathrm{FG}}_1-\mathrm{PB}.Math.Q.Math.\left(1-s\right).Math.(C_{MV}\mathrm{CO}2\left[i\right]-C_p\mathrm{CO}2\left[i\right]}{{\mathrm{FG}}_1}$

[0324] Notice, these equations do not require the estimation, measurement, or determination of any of the subject's ventilatory or pulmonary parameters, namely, tidal volume (V.sub.T), functional residual capacity (FRC), breath period (T.sub.B), or anatomical dead space (V.sub.D).

[0325] The reduced or eliminated sensitivity of the equations to the subject's ventilatory parameters makes this method useful in practise with spontaneously breathing subjects. It is, however, not limited to spontaneously breathing subjects, and may also be used in mechanically ventilated subjects.

[0326] A person skilled in the art will recognize that the volumes and partial pressures required to calculate the partial pressure of O2 in the controlled gas mixture (P.sub.1O2[i]) and the partial pressure of CO2 in the controlled gas mixture (P.sub.1CO2[i]) may need to be corrected for differences in temperature or presence of water vapour between the lung and the conditions under which they are measured, estimated, or delivered. The corrections applied will depend on the conditions under which these volumes and partial pressures are measured, estimated, or delivered. All volumes and partial pressures should be corrected to body temperature and pressure saturated conditions. A person skilled in the art will be comfortable with these corrections.

[0327] A person skilled in the art will also recognize the equivalence between partial pressures and fractional concentrations. Any terms expressed as partial pressures can be converted to fractional concentrations and vice-versa. For example, the partial pressure of O2 in the controlled gas mixture (P.sub.1O2[i])and the partial pressure of CO2 in the controlled gas mixture (P.sub.1CO2[i]) may be converted a fractional concentration of O2 in the controlled gas mixture (F.sub.1CO2[i]) and a fractional concentration of CO2 in the controlled gas mixture (F.sub.1CO2[i]).

[00021]$F_{I}O2\left[i\right]-\frac{P_{I}O2\left[i\right]}{\mathrm{PB}}$$F_I\mathrm{CO}2\left[i\right]=\frac{P_I\mathrm{CO}2\left[i\right]}{\mathrm{PB}}$

[0328] Determine if targets are logistically feasible

[0329] In practise, many different Implementations of gas delivery devices and sequential gas delivery circuits may be used. In general, it is logistically feasible to induce the target end-tidal partial pressures for the current breath (P.sub.ETO2[i].sup.T, P.sub.ETCO2[].sup.T) if: [0330] 1) The required partial pressures of gases in the controlled gas mixture are physically realizable: [0331] a) 0≤P.sub.1O2[i]≤PB [0332] b) 0≤P.sub.1CO2[i]≤PB [0333] c) P.sub.1O2[i]+P.sub.1CO2[i]<PB [0334] 2) The gas delivery device is capable of delivering a controlled mixture of the desired composition at the required flow rate

[0335] Where sequential rebreathing is carried out with a Hi-Ox.sub.SR sequential gas delivery circuit and a gas blender:

[0336] Assuming 11.sub.SB source gases (SG.sub.1, SG.sub.n.sub.G) are blended to deliver the required mixture to the Hi-Ox.sub.SR sequential gas delivery circuit (SGDC). Each gas (m) contains a known fractional concentration of O2 (fo2.sub.m) and a known fractional concentration of CO2 (fco2.sub.m). The flow rate of each gas (FSG.sub.m[i]) required to deliver the total desired flow rate of the controlled gas (FG.sub.1) with the required partial pressure of O2 (P.sub.1O2[i]) and the required partial pressure of CO2 (P.sub.1CO2[i]) can be determined by solving the following set of equations:

[00022]$\underset{m=1}{\overset{n_{\mathrm{SG}}}{.Math.}}{\mathrm{FSG}}_m\left[i\right]={\mathrm{FG}}_1$$\underset{m=1}{\overset{n_{SG}}{.Math.}}\mathrm{fo}{2}_m.Math.{\mathrm{FSG}}_m\left[i\right]=\frac{P_{I}O2\left[i\right]}{PB}.Math.{\mathrm{FG}}_1$$\underset{m=1}{\overset{n_{SG}}{.Math.}}\mathrm{fco}{2}_m.Math.{\mathrm{FSG}}_m\left[i\right]=\frac{P_I\mathrm{CO}2\left[i\right]}{\mathrm{PB}}.Math.{\mathrm{FG}}_1$

[0337] The target end-tidal partial pressures for the current breath (P.sub.ETO2[i].sup.T, P.sub.ETCO2[i].sup.T) are logistically feasible if: [0338] 1) 0≤PO2[i]≤PB [0339] 2) 0≤P.sub.1CO2[i]≤PB [0340] 3) P.sub.1O2[i]+P.sub.1CO2[i]≤PB [0341] 4) There exists a solution to the above system of equations, and [0342] 5) FSG.sub.m[i]≥0∀m [0343] 6) The gas blender is capable of delivering a controlled mixture of the desired composition at the required flow rate

[0344] It is therefore required that n.sub.SG≥3. It is computationally optimal to have n.sub.SG=3.

[0345] One possible set of gases is: [0346] SG.sub.1: fco2,.sub.1=0, fo2.sub.1=1 [0347] SG.sub.2: fco.2.sub.2=1, fo2.sub.2=0 [0348] SG3 fco2.sub.3=0, fo2.sub.3=0

[0349] It may enhance the safety of the system to use gases with a minimal concentration of O2 and maximum concentration of CO2. In this case, a possible set of gases is: [0350] SG.sub.1: fco2.sub.1=0, fo2.sub.1=0.1 [0351] SG.sub.2: fco2.sub.2=0.4, fo2.sub.2=0.1 [0352] SG.sub.3, fco2.sub.3=0, fo2.sub.3=1

[0353] The balance of the source gases when not entirely composed of O2 and CO2 can be made up of any gas or combination of gases, which may vary depending on the context. The balance of the source gases is most often made up of N2 because it is physiologically inert.

[0354] Adjusting parameters to make logistically infeasible targets logistically feasible:

[0355] It may occur that inducing a target end-tidal partial pressure of O2 (P.sub.ETO2[i].sup.T) or a target end-tidal partial pressure of CO2 (P.sub.ETCO2[i].sup.T) in a given breath is not logistically feasible. This may occur because the partial pressure of O2 in the controlled gas mixture (P.sub.1O2[i]) or the partial pressure of CO2 in the controlled gas mixture (P.sub.1CO2[o]) required to induce the target end-tidal partial pressure of O2 or the target end-tidal partial pressure of CO2 is either not physically realizable, or there does not exist a blend of the current source gases (SG.sub.1, SG.sub.n.sub.G) resulting in the required tho partial pressure of O2 in the controlled gas mixture and the required partial pressure of CO2 in the controlled gas mixture. If the composition of the controlled gas mixture is not physically realizable for a given set of targets, the targets may be modified and/or the rate at which the controlled gas mixture is made available to the circuit (FG.sub.1)modified, or where applicable, the tidal volume ( V.sub.T) modified, until the composition is physically realizable. If the composition of the controlled gas mixture is physically realizable for a given set of targets, but no combination of the source gases results in the required composition, the targets may be modified and/or the rate at which the controlled gas mixture is made available to the circuit modified, or where applicable, the tidal volume (V.sub.T) modified, and/or different source gases used.

[0356] If P.sub.1O2[i]<0—The target end-tidal partial pressure of O2 (P.sub.ETO2[i].sup.T) in not logistically feasible because the partial pressure of O2 in the controlled gas mixture (P.sub.1O2[i]) required to induce the target end-tidal partial pressure of O2 is not physically realizable, To make induction of the target logistically feasible, increase the target end-tidal partial pressure of O2. Alternatively, where sequential rebreathing is used, the rate at which the controlled gas mixture is made available to the circuit (FG.sub.1) may be modified. Where sequential rebreathing is not used, the tidal volume (V.sub.T) may be modified.

[0357] If P.sub.1O2[i]>PB—The target end-tidal partial pressure of O2 (P.sub.ETO2[i].sup.T) is not logistically feasible because the partial pressure of O2 in the controlled gas mixture (P.sub.1O2[i]) required to induce the target end-tidal partial pressure of O2 is not physically realizable. To make induction of the target logistically feasible, decrease the target end-tidal partial pressure of O2. Alternatively, where sequential rebreathing is used, the rate at which the controlled gas mixture is made available to the circuit (FG.sub.1) may be modified. Where sequential rebreathing Is not used, the tidal volume (V.sub.T) may be modified.

[0358] If P.sub.1CO2[i]<0—The target end-tidal partial pressure of CO2 (P.sub.ETCO2[i].sup.T) is not logistically feasible because the partial pressure of CO2 in the controlled gas mixture (P.sub.1CO2[i]) required to induce the target end-tidal partial pressure of CO2 is not physically realizable. To make induction of the target logistically feasible, decrease the target end-tidal partial pressure of CO2. Alternatively, where sequential rebreathing is used, the rate at which the controlled gas mixture is made available to the circuit (FG.sub.1) may be modified. Where sequential rebreathing is not used, the tidal volume (V.sub.T) may be modified.

[0359] If P.sub.1CO2[i]>PB—The target end-tidal partial pressure of CO2 (P.sub.ETCO2[i].sup.T) is not logistically feasible because the partial pressure of CO2 in the controlled gas mixture (P.sub.1CO2[i])required to induce the target end-tidal partial pressure of CO2 is not physically realizable. To make Induction of the target logistically feasible, decrease the target end-tidal partial pressure of CO2. Alternatively, where sequential rebreathing is used, the rate at which the controlled gas mixture is made available to the circuit (FG.sub.1) may be modified. Where sequential rebreathing is not used, the tidal volume (V.sub.T) may be modified.

[0360] If P.sub.1O2[i]+P.sub.1CO2[i]>PB—The combination of the target end-tidal partial pressure of O2 (P.sub.ETO2[i].sup.T) and the target end-tidal partial pressure of CO2 (P.sub.ETCO2[i].sup.T) is not logistically feasible because the combination of the partial pressure of O2 in the controlled gas mixture P.sub.1O2[i]) and the partial pressure of CO2 in the controlled gas mixture (P.sub.1CO2[i]) required to induce the targets is not physically realizable. To make induction of the targets logistically feasible, decrease the target end-tidal partial pressure of O2 and/or the target end-tidal partial pressure of CO2. Alternatively, where sequential rebreathing is used, the rate at which the controlled gas mixture is made available to the circuit (FG.sub.1) may be modified. Where sequential rebreathing is not used, the tidal volume (V.sub.T) may be modified.

[0361] If there does not exist a solution to the above system of equations, or there exists a solution for which FSG.sub.m[i]<0 for any m, then the current source gases (SG.sub.1, SG.sub.m.sub.G) cannot be blended to create the controlled gas mixture. Different source gases must be used to induce the end-tidal target of O2 (P.sub.ETO2[i].sup.T) and the end-tidal target of CO2 (P.sub.ETCO2[i].sup.T), or the desired targets must be changed. Alternatively, it may be possible to modify the rate at which the controlled gas mixture is made available to the circuit (FG.sub.1) until the partial pressure of O2 in the controlled gas mixture (P.sub.1O2[i]) and the partial pressure of CO2 in the controlled gas mixture (P.sub.1CO2[i]) required to induce the targets are realizable with the current source gases.

[0362] Often, the rate at which the controlled gas mixture is made available to the circuit (FG.sub.1) is modified to make a target end-tidal partial pressure of O2 (P.sub.ETO2[i].sup.T) or a target end-tidal partial pressure of CO2 (P.sub.ETCO2[i].sup.T) logistically feasible to induce. However, the rate at which the controlled gas mixture is made available to the circuit should not be increased to a rate beyond which the subject fails to consistently exhaust the supply of the controlled gas mixture in each breath. This maximal rate varies between subjects. However, it is not necessary that the rate at which the controlled gas mixture is made available to the circuit be the same in every breath. Therefore, the rate at which the controlled gas mixture is made available to the circuit may be set to some basal value for most breaths, and only increased in particular breaths in which the inducing the target end-tidal partial pressures is not logistically feasible at the basal rate of flow. The basal rate at which the controlled gas mixture is made available to the circuit should be a rate at which the subject can comfortably, without undo ventilatory effort, exhaust the supply of the controlled gas mixture in each breath. The maximal rate at which the controlled gas mixture is made available to the circuit should be the maximum rate at which the subject can consistently exhaust the supply of the controlled gas mixture in each breath with a maximal ventilatory effort. The subject may be prompted to increase their ventilatory effort In breaths where the rate at which the controlled gas mixture is made available to the circuit is increased.

Initializing the System

[0363] Let the index [0] represent the value of a variable for all breaths before the start of the sequence (all values of i≤0). To initialize the system, the subject is allowed to breathe freely, without intervention, until the measured end-tidal partial pressure of O2 (P.sub.ETCO2.sup.M) and the 5measured end tidal partial pressure of CO2 (P.sub.ETCO2.sup.M) are stable—these are taken as the baseline partial pressure of O2 (P.sub.ETO2.sub.0.sup.M) and the baseline partial pressure of CO2 (P.sub.ETCO2.sub.0).The measured end-tidal partial pressures are considered stable when there is less than ±5 mmHg change in the measured end-tidal partial pressure of O2 and less than ±2 mmHg change in the measured end-tidal partial pressure of CO2 over 3 consecutive breaths. The rest of the variables are Initialized by assuming the whole system has equilibrated to a steady state at the baseline end-tidal partial pressures.

[0364] Assume that end-tidal partial pressures are equal to the baseline measurements: [0365] P.sub.ETO2[0].sup.T=P.sub.ETO2.sub.0.sup.M [0366] P.sub.ETCO2[0].sup.T=P.sub.ETCO2.sub.0.sup.M

[0367] Assume pulmonary end-capillary partial pressures are equal to end-tidal partial pressures: [0368] P.sub.pO2[0]=P.sub.ETO2[0].sup.T [0369] P.sub.pC O2[0]=P.sub.ETCO 2[0].sup.T

[0370] Calculate O2 blood contents assuming steady state:

[0371] Pulmonary end-capillary O2 saturation:

[00023]$\mathrm{pH}\left[0\right]=6.1+\log \left(\frac{\left[{\mathrm{HCO}}_3\right]}{0.03.Math.P_P\mathrm{CO}2\left[0\right]}\right)$$S_{p}O2\left[0\right]=100.Math.\frac{{\left(-8532.2289.Math.z^{1}2121.401.Math.z^2-67.073989.Math.z^3+z\right)}^4}{935960.87-31346.258.Math.z+2396.1674.Math.z^1-67.104406.Math.z^3+z^4}$$\mathrm{where}z=P_{P}O2\left[0\right].Math.{10}^{0.024.Math.\left(37-T\right)+0.4.Math.(p11\left[0\right]-7.4.Math.+0.06.Math.\left(\log 40-{\mathrm{logP}}_P\mathrm{CO}2\left[0\right]\right)}$

[0372] Pulmonary end-capillary O2 content

[00024]$C_{p}O2\left[0\right]=1\mathrm{.36}.Math.\mathrm{Hb}.Math.\frac{S_{p}O2\left[0\right]}{100}+0.003.Math.P_{p}O2\left[0\right]$

[0373] Mixed-venous O2 content:

[00025]$C_{\mathrm{MV}\left(T\right)}O2\left[0\right]=C_{p}O2\left[0\right]-\frac{\mathrm{VO}2}{\left(1-s\right).Math.Q}$$C_{\mathrm{MV}}O2\left[0\right]=C_{\mathrm{MV}\left(T\right)}O2\left[0\right]$

[0374] Arterial O2 content:

[0375] C.sub.aO[0]=(1−s).Math.C.sub.pO2[0]+s.Math.C.sub.MVO2[0]

[0376] O2 content of each compartment In the model

[0377] For j=1 . . . n.sub.O2

[00026]$C_{V}O{2}_j\left[0\right]=C_{4}O2\left[0\right]-\frac{\mathrm{vo}{2}_j.Math.\mathrm{VO}2}{q_1.Math.Q}$

[0378] Calculate CO2 blood contents assuming steady state:

[0379] Pulmonary end-capillary CO2 content

[00027]$C_p\mathrm{CO}2\left[0\right]=\left(1.0-\frac{0.02924.Math.\mathrm{Hb}}{\left(2.244-0\mathrm{.422}.Math.\left(\frac{\mathrm{Sp}O2\left[0\right]}{100}\right)\right).Math.\left(8.740-\mathrm{pH}\left[0\right]\right)}\right).Math.C_{\mathrm{pl}}$$C_{\mathrm{pi}}=0.0301.Math.P_p\mathrm{CO}2\left[0\right].Math.\left(1+{10}^{\mathrm{pH}\left[0\right]-6.10}\right).Math.2.226$

[0380] Mixed-venous CO2 content

[00028]$C_{\mathrm{MV}\left(T\right)}\mathrm{CO2}\left[0\right]=C_p\mathrm{CO2}\left[0\right]+\frac{\mathrm{VCO2}}{\left(1-s\right).Math.Q}$$C_{\mathrm{MV}}\mathrm{CO}2\left[0\right]=C_{\mathrm{MV}\left(T\right)}\mathrm{CO}2\left[0\right]$

[0381] Arterial CO2 content

[0382] C.sub.aCO2[0]=(1−s).Math.C.sub.pCO2[0]+.Math.C.sub.MVCO2[0]

[0383] CO2 content of each compartment In the model:

[0384] For k=1 . . . n.sub.CO2

[00029]$C_V{\mathrm{CO}2}_k\left[0\right]=C_a\mathrm{CO}2\left[0\right]+\frac{\mathrm{vco}{2}_k.Math.\mathrm{VCO}2}{q_k.Math.Q}$

[0385] Tuning the system

[0386] The parameters of the system can be tuned so that the measured end-tidal partial pressures of O2 (P.sub.ETO2[i].sup.M) and the measured end-tidal partial pressures of CO2 (P.sub.ETCO2[i].sup.M) during any sequence more closely reflect the target end-tidal partial pressures of O2 (P.sub.ETO2[i].sup.T) and target end-tidal partial pressures of CO2 (P.sub.ETCO 2[i].sup.T). To tune the system parameters, standardized tuning sequences are run and the measured results compared to the targets. The difference between measured end-tidal partial pressures and the target end-tidal partial pressures in the standardized tuning sequences can be used to refine the estimates of some physiological parameters.

[0387] Example tuning sequence:

[0388] The tuning sequence sets the target end-tidal partial pressure of O2 (P.sub.ETO 2[i].sup.T) at 5 mmHg above the baseline end-tidal partial pressure of O2 (P.sub.ETO2.sub.0.sup.M) throughout the sequence, and executes a 5 mmHg step-change in the end-tidal partial pressure of CO2 (P.sub.ETCO2[i].sup.T) from 5 mmHg above the baseline end-tidal partial pressure of CO2 (P.sub.ETCO2.sub.0.sup.M) to 10 mmHg above the baseline end-tidal partial pressure of CO2 in breath 30 (i=30) of the sequence. [0389] P.sub.ETO2[i].sup.T=P.sub.ETO2.sub.0.sup.M+5 i=1..60 [0390] P.sub.ETCO2[i].sup.T=P.sub.ETCO2.sub.0.sup.M+5 i=1..29 [0391] P.sub.ETCO2[i].sup.T=P.sub.ETCO2.sub.0.sup.M+10 i=30..60

[0392] The estimate of the functional residual capacity (FRC) can be refined as a function of the difference between the actual step change induced in the end-tidal CO2(P.sub.ETCO2[30].sub.M−P.sub.ETCO2[29].sup.M) and the target step-change (P.sub.ETCO2[30].sup.T−P.sub.ETCO2[29].sup.T=5) in breath 30 (i−30).

FRC=FRC.sub.0+α((P.sub.ETCO2[30].sup.M−P.sub.ETCO2[29 ].sup.M)−P.sub.ETCO[30].sup.T−P.sub.ETCO2[29].sup.T)) α=200 ml/mmHg

[0393] In general, the correction factor (a) can range from 50-500 ml/mmHg. Lower values of the correction factor will produce a more accurate estimate of the functional residual capacity (FRC) while requiring more tuning iterations. Higher values will reduce the number of tuning iterations but may cause the refined estimate of the parameter to oscillate around the optimal value.

[0394] The estimate of the overall metabolic O2 consumption (VO2) can be refined as a function of the difference between the target end-tidal partial pressure of O2 (P.sub.ETO2[60].sup.T) and the measured end-tidal partial pressure of O2 (P.sub.ETO2[60].sup.M) in breath 60 (i=60). [0395] VO2=VO2.sub.0−β(P.sub.ETO2[60].sup.M−P.sub.ETO)2[60].sup.T) β=10 ml//min/mmHg

[0396] In general, the correction factor (β) can range from 5-200 ml/min/mmHg. Lower values of the correction factor will produce a more accurate estimate of the overall metabolic O2 consumption (VO2) while requiring more tuning iterations. Higher values will reduce the number of tuning iterations but may cause the refined estimate of the parameter to oscillate around the optimal value.

[0397] The estimate of the overall metabolic CO2 production (VCO2) can be refined as a function of the difference between the target end-tidal partial pressure of CO2 (P.sub.ETCO2[29].sup.T) and the measured end-tidal partial pressure of CO2 (P.sub.ETCO2[29].sup.M) in breath 29 (i=29). [0398] VCO2=VCO2.sub.0+γ(P.sub.ETCO2[29].sup.M−P.sub.ETCO2[29].sup.T) γ=10 ml/min/mmHg

[0399] Alternatively. the estimate of the overall metabolic CO2 production (VCO2) can be refined as a function of the difference between the target end-tidal partial pressure of CO2 (P.sub.ETCO2[60].sup.T) and the measured end-tidal partial pressure of CO2 (P.sub.ETCO2[60].sup.M) in breath 60 (i=60) VCO2=VCO2.sub.0+γ(P.sub.ETCO2[60].sup.M−P.sub.ETCO2[60].sup.T) γ=10 ml/min/mmHg

[0400] In general, the correction factor (y) can range from 5-200 ml/min/mmHg. Lower values of the correction factor will produce a more accurate estimate of the overall metabolic CO2 production (VCO2) while requiring more tuning iterations. Higher values will reduce the number of tuning iterations but may cause the refined estimate of the parameter to oscillate around the optimal value.

[0401] General requirements of a tuning sequence:

[0402] In breaths where the target end-tidal partial pressures of gases are transitioning between values, the estimate of the functional residual capacity (FRC) determines the magnitude of the change induced in the actual end-tidal tidal partial pressures of gases. The estimate of the overall metabolic O2 consumption (VO2) influences the induced/measured end-tidal partial pressure of O2 (P.sub.ETO2[i].sup.M) in steady state. Similarly, the estimate of the overall metabolic CO2 production (VCO2) influences the induced/measured end-tidal partial pressure of CO2 (P.sub.ETCO2[i].sup.M) in steady state.

[0403] It therefore follows that a difference between the measured change in the end-tidal partial pressure of O2 (P.sub.ETO2[i].sup.M−P.sub.ETO2[i].sup.M) and the targeted change in the end-tidal partial pressure of O2 (P.sub.ETO2[i].sup.T−P.sub.ETO2[i].sup.T) in breaths where the target end-tidal partial pressure of O2 Is not equal to the target end-tidal partial pressure of O2 from the previous breath (P.sub.ETO2[i ].sup.T≠P.sub.ETO2[i−1), or a difference between the measured change in the end-tidal partial pressure of CO2 (P.sub.ETCO2[i].sup.M−P.sub.ETCO2[i−1].sup.M) and the targeted change in the end-tidal partial pressure of CO2 (P.sub.ETCO2[i].sup.T−P.sub.ETCO2υi−1].sup.T) in breaths where the target end-tidal partial pressure of CO2 is not equal to the target end-tidal partial pressure of CO2 from the previous breath (P.sub.ETCO2[i].sup.T≠P.sub.ETCO2[i−1].sup.T), reflect errors in the estimate of the functional residual capacity (FRC).

[0404] Conversely, differences between the target end-tidal partial pressure of O2 (P.sub.ETO2[i].sup.T) and the measured end-tidal tidal partial pressure of O2 (P.sub.ETO2[i].sup.M) in breaths at the end of a long (20 breath) period of constant target end-tidal partial pressures of O2 (P.sub.ETO2[i].sup.T=P.sub.ETO2[i−1].sup.T) reflect errors in the overall metabolic O2 consumption (VO2). It is assumed that the measured end-tidal partial pressures of O2 will have stabilized (less than ±5 mmHg change in the measured end-tidal partial pressure of O2 over 3 consecutive breaths), although not necessarily at the target end-tidal partial pressure of O2, after 20 breaths of targeting the same end-tidal partial pressures of O2.sub.— If, however, the measured end-tidal partial pressure of O2 has not stabilized after 20 breaths of targeting the same end-tidal partial pressures of O2, a longer duration of targeting the same end-tidal partial pressure of O2 should be used for tuning the overall metabolic consumption of O2.

[0405] Differences between the target end-tidal partial pressure of CO2 (P.sub.ETCO2[i].sup.T) and the measured end-tidal tidal partial pressure of CO2 (P.sub.ETCO2[i].sup.M) in breaths at the end of a long (20 breath) period of constant target end-tidal partial pressures of CO2 (P.sub.ETCO2[i].sup.T=P.sub.ETCO2[i−1].sup.T) reflect errors in the overall metabolic CO2 production (VCO2). It is assumed that the measured end-tidal partial pressures of CO2 will have stabilized (less than ±2 mmHg change in the measured end-tidal partial pressure of CO2 over 3 consecutive breaths), although not necessarily at the target end-tidal partial pressure of CO2, after 20 breaths of targeting the same end-tidal partial pressures of CO2. If, however, the measured end-tidal partial pressure of CO2 has not stabilized after 20 breaths of targeting the same end-tidal partial pressures of CO2, a longer duration of targeting the same end-tidal partial pressure of CO2 should be used for tuning the overall metabolic production of CO2.

[0406] The tuning sequence described above is only an example of one sequence that can be used to tune the estimates of the physiological parameters.

[0407] The functional residual capacity (FRC) can be tuned by observing the difference between the measured change in the end-tidal partial pressure of O2 (P.sub.ETO2[i].sup.M−P.sub.ETO2[i].sup.m) and the targeted change in the end-tidal partial pressure of O2 (P.sub.ETO2[i].sup.T−P.sub.ETO2[i−1].sup.T) in breaths where the target end-tidal partial pressure of O2 is not equal to the target end-tidal partial pressure of O2 from the previous breath (P.sub.ETO2[i].sup.T≠P.sub.ETO2[i−1].sup.T), or a difference between the measured change in the end-tidal partial pressure of CO2 (P.sub.ETCO2[i].sup.M−P.sub.ETCO2[i−1].sup.M) and the targeted change in the end-tidal partial pressure of CO2 (P.sub.ETCO2[i].sup.T−P.sub.ETCO2[i−1].sup.T) in breaths where the target end-tidal partial pressure of CO2 is not equal to the target end-tidal partial pressure of CO2 from the previous breath (P.sub.ETCO2[i].sup.T≠P.sub.ETCO2[i−1].sup.T). Therefore, any sequence that targets the induction of a change in the end-tidal partial pressure of O2, or a change in the end-tidal partial pressure of CO2, can be used to tune the estimate of the functional residual capacity.

[0408] The overall metabolic consumption of O2 (VO2) can be tuned by observing the difference between the target end-tidal partial pressure of O2 (P.sub.ETO2[i].sup.T) and the measured end-tidal tidal partial pressure of O2 (P.sub.ETO2[i].sup.M) in breaths at the end of a long (20 breath) period of constant target end-tidal partial pressures of O2 (P.sub.ETO2[i].sup.T=P.sub.ETO2[i].sup.T). It is assumed that the measured end-tidal partial pressures of O2 will have stabilized (less than t5 mmHg change in the measured end-tidal partial pressure of O2 over 3 consecutive breaths), although not necessarily at the target end-tidal partial pressures of O2, after 20 breaths of targeting the same end-tidal partial pressures of O2. If, however, the measured end-tidal partial pressure of O2 has not stabilized after 20 breaths of targeting the same end-tidal partial pressures of O2, a longer duration of targeting the same end-tidal partial pressure of O2 should be used for tuning the overall metabolic consumption of O2Therefore, any sequence that targets to maintain the end-tidal partial pressure of O2 constant for a sufficiently long duration may be used to tune the estimate of the overall metabolic consumption of O2.

[0409] The overall metabolic production of CO2 (VCO2) can be tuned by observing the difference between the target end-tidal partial pressure of CO2 (P.sub.ETCO2[i].sup.T) and the measured end-tidal tidal partial pressure of CO2 (P.sub.ETCO2[i].sup.M) in breaths at the end of a long (20 breath) period of constant target end-tidal partial pressures of CO2 (P.sub.ETCO2[i].sup.T=P.sub.ETCO2[i−1].sup.T). It is assumed that the measured end-tidal partial pressures of CO2 will have stabilized (less than ±2 mmHg change in the measured end-tidal partial pressure of CO2 over 3 consecutive breaths), although not necessarily at the target end-tidal partial pressure of CO2, after 20 breaths of targeting the same end-tidal partial pressures of CO2. if, however, the measured end-tidal partial pressure of CO2 has not stabilized after 20 breaths of targeting the same end-tidal partial pressures of CO2, a longer duration of targeting the same end-tidal partial pressure of CO2 should be used for tuning the overall metabolic production of CO2. Therefore, any sequence that targets to maintain the end-tidal partial pressure of CO2 constant fora sufficiently long duration may be used to tune the estimate of the overall metabolic production of CO2.

[0410] it is not required that all parameter estimates are tuned in the same sequence. Tuning of all parameters in the example sequence is done only for convenience. Different tuning sequences may be used to tune the estimates of different individual, or groups of, parameters.

[0411] Embodiments of mass balance equations:

[0412] No SGD:

[00030]$F_{I}X\left[i\right]=\frac{P_{\mathrm{ET}}{X\left[i\right]}^T.Math.\left(\mathrm{FRC}.Math.V_T\right)-P_{\mathrm{ET}}{X\left[i-1\right]}^T.Math.\left(\mathrm{FRC}+V_D\right)-\mathrm{PB}.Math.Q.Math.\left(1-s\right).Math.T_B(C_{\mathrm{MV}}X\left[i\right]-C_{p}X\left[i\right]}{\left(V_T-V_D\right).Math.\mathrm{PB}}$

[0413] SGD:

[00031]$F_{I}X\left[i\right]=\frac{(P_{\mathrm{ET}}{X\left[i\right]}^T-P_{\mathrm{ET}}{X\left[i-1\right]}^T.Math.\left(\mathrm{FRC}+V_T\right)+P_{\mathrm{ET}}{X\left[i-1\right]}^T.Math.\left({\mathrm{FG}}_1.Math.T_B\right)-\mathrm{PB}.Math.Q.Math.\left(1-s\right).Math.T_B(C_{\mathrm{MV}}X\left[i\right]-}{{\mathrm{FG}}_1.Math.T_B.Math.\mathrm{PB}}$

[0414] As seen in FIGS. 8a and 8b a ramp sequence reveals the sigmoidal nature of a pattern of a physiological response—mid-cerebral artery blood flow velocity—showing its sigmoidal nature over different time courses depending on whether the subject is a fast or slow responder.

[0415] FIG. 9 blood flow responses to PCO.sub.2 predicted for the model of a brain vascular territory with a partially-stenosed vessel branch and a healthy branch in parallel. Where there is some blood flow resistance upstream from the branches, it causes the partially-stenosed vessel to encroach on its vasodilatory reserve by an auto-regulatory mechanism. A vasodilatory stimulus such as in increase in arterial CO.sub.2 will stimulate all vessels to dilate, but those vessels that have already dilated in response to the increase in upstream resistance have a reduced range of response. The solid red line in FIG. 9 depicts the sigmoidal response of a normal branch. The dotted blue line depicts the response of the partially stenosed vessel branch when coupled in parallel with the normal vessel branch, showing steal in hypercapnia and reverse steal in hypocapnia. The slopes of the straight fines show the predicted CVR values for PCO.sub.2 stimulus ranges 40-45 and 40-60 mmHg. The filled circle marks the resting blood flow et resting PCO.sub.2 and the open circles show the measured responses for a healthy territory (solid circles and line) and a territory perfused via a stenosed vessel (dotted circles and line).

[0416] FIG. 9 illustrates the sigmoidal relationship between regional blood flow and PCO.sub.2 predicts that CVR in a vascular territory with adequate vasodilatory reserve will be greater for increases In PCO.sub.2 from 40 to 45 rnmHg vs. Increases from 40 to 50 mmHg. By contrast, a vascular territory downstream from a hemodynamically significant stenosis may have a positive CVR when the PCO.sub.2 change is in a range where some vasodilatory reserve is preserved, but, with a greater stimulus range such as 40-50 mmHg PCO.sub.2, these vessels reach their vasodilatory limit and the continued vasodilatory capacity In other regions will induce steal.

[0417] The model outlined in FIG. 9 was investigated a comprehensive manner by using it to predict the change in CBF region by region in response to graded changes in PETCO.sub.2 in a patient with steno-occlusive disease.

[0418] FIG. 10 shows an example of the development of steal with hypercapnia, and reverse steal (Robin Hood effect) with hypocapnia [Lassen, 1968 #16325]. Both of these conditions were observed in the same patient, confirming that steal and reverse steal are a function of the changes taking place in the parallel branches of the vascular bed with intact cerebral autoregulation. The CVR map in response to a hypercapnic change in PETCO.sub.2 from 30 to 50 mmHg is shown in FIG. 10A and colour coded with the scale shown. We interpret the blue colour of the right MCA territory as signifying a vascular bed with reduced vasodilatory reserve (presumably as a result of MCA stenosis). The CVR maps for an axial slice at different PETCO.sub.2 ranges for a 18 year old male patient with moya moya disease affecting the right MCA territory are divided as follows (A) CVR map calculated for a hypocapnic PETCO.sub.2 change from 40 to 30 mmHg. (B) CVR map calculated for a hypercapnic PETCO.sub.2 change from 30 to 40 mmHg, (C) CVR map calculated fora hypercapnic PETCO.sub.2 change from 40 to 50 mmHg. (D) CVR map calculated for a hypocapnic PETCO.sub.2 change from 50 to 40 mmHg. (E) CVR map calculated over the full hypercapnic PETCO.sub.2 change from 30 to 50 mmHg. In this subject, inducing a reduction of PETCO.sub.2 from 40 mmHg to 30 mmHg produces a robust constriction in the healthy left brain territory and a decrease in the blood flow and BOLD signal (FIG. 10, CVR A). The CVR is color coded as before, but with the convention that its sign follows the BOLD change, so the CVR map is predominantly blue in the ‘normal’ vascular beds. However, a careful inspection of FIG. 10 (CVR A) shows some yellow and orange colouration in the right MCA territory, indicating areas of increasing blood flow and CVR due to reverse steal, as predicted by the model demonstrated in FIG. 9. With another change in the direction of the stimulus, the hypercapnic increase in PETCO.sub.2 from 30 to 40 mmHg produces a large increase in flow in the healthy left MCA region, but a lesser increase in the compromised right MCA region (FIG. 10, CVR B). Within this range of PETCO.sub.2 hypercapnia, the right MCA territory demonstrates some vasodilatory reserve. Nevertheless, as predicted and illustrated in FIG. 9, further hypercapnia to 50 mmHg results in a greater steal and the CVR values are negative, and the map is coloured blue (FIG. 10, CVR C). Finally, our conceptual model predicts that withdrawal of the vasodilatory stimulus will abolish the steal and induce a reverse steal via the Robin Hood effect. Once again, this result is observed in FIG. 10 (CVR D); this CVR map is virtually the reverse image of the CVR map calculated for the full range of 30 to 50 mmHg change in PETCO.sub.2 (FIG. 10, CVR E). In FIG. 10 the BOLD signal vs. time is presented for the whole brain, an average value of all voxels.

EXAMPLE 1

[0419] An apparatus according to the invention was used to target end tidal gas concentrations of CO.sub.2 and O.sub.2 in 35 subjects. We targeted the following sequence (values attained in brackets): normocapnia (60 seconds a PetCO.sub.2=40 mm Hg, SD=1 mm; PetO.sub.2=100 mm Hg, SD=2 mm), Hypercapnia (60 seconds at PetCO.sub.2=50mm Hg, SD=1 mm; PetO.sub.2=100mm Hg, SD=2mm), normocapnia (100seconds), hypercapnia (180 seconds), and normocapnia (110 seconds). FIG. 11, comprises a partial raw data set for 6 subjects.

[0420] The content of all of the patent and scientific references herein is hereby incorporated by reference. [0421] 1. Robbins P A, Swanson G D, Howson M G. A prediction-correction scheme for forcing alveolar gases along certain time courses. J Appl Physiol 1982 May; 52(5):1353-1357. [cited 2011 Oct.11 ] [0422] 2. Slessarev M, Han J, Mardimae A, Prisman E, Preiss D, Volgyesi G, Ansel C, Duffin J, Fisher J A. Prospective targeting and control of end-tidal CO2 and O2 concentrations. J. Physiol. (Lond.) 2007 June; 581(Pt 3):1207-1219. [cited 2011 Oct. 6] [0423] 3. Banzett R B, Garcia R T, Moosavi S H, Simple contrivance “clamps” end-tidal and despite rapid changes in ventilation. Journal of Applied Physiology 2000 May; 88(5):1597-1600. [cited 2011 Oct. 7 ] [0424] 4. Fisher J. Breathing circuits to facilitate the measurement of cardiac output during . . . [Internet]. [date unknown]; [cited 2011 Oct. 11] Available from: http://www.google.com/patents/about?id=RSqbAAAAEBAJ

[0425] 5. Fisher J. Method of measuring cardiac related parameters non-invasively via the lung . . . [Internet]. [date unknown]; [cited 2011 Oct. 11] Available from: http://www.google.com/patents/about?id=QiqbAAAAEBAJ [0426] 6. Fisher J A. Method And Apparatus For Inducing And Controlling Hypoxia [Internet]. [date unknown]; [cited 2011 Oct. 11] Available from: http://www.google.com/patents/about?id=Cd7HAAAAEBAJ [0427] 7. Slessarev M. Method and Apparatus to Attain and Maintain Target End Tidal Gas Concentrations [Internet], [date unknown]; [cited 2011 Oct.11] Available from: http://www.google.com/patents/about?id=23XGAAAAEBAJ [0428] 8. Stenzier A. High FiO2 oxygen mask with a sequential dilution feature [Internet]. [date unknown]; [cited 2011 Oct. 11] Available from: http://www.google.corm/patents/about?id=v1WIAAAAEBAJ [0429] 9. Bray J, Gregg P A, Macknight A, Mills R, Taylor D. Lecture Notes on Human Physiology. 4th ed. Wiley-Blackwell; 1999. [0430] 10. Kratz A, Lewandrowskl K B. Case records of the Massachusetts General Hospital. Weekly clinicopathological exercises. Normal reference laboratory values. N. Engl. J. Med. 1998 October ; 339(15):1063-1072. [cited 2011 Oct.6] [0431] 11. Sund-Levander M, Forsberg C, Wahren L K. Normal oral, rectal, tympanic and axillary body temperature in adult men and women: a systematic literature review. Scand J Caring Sci 2002 June; 16(2):122-128. [cited 2011 Oct. 6] [0432] 12, Mackowiak P A, Wasserman S S, Levine M M. A critical appraisal of 98.6 degrees F., the upper limit of the normal body temperature, and other legacies of Carl Reinhold August Wunderlich. JAMA 1992 Sep. ; 268(12):1578-1580. [cited 2011 Oct.6 ] [0433] 13. Beutler E, Waalen J. The definition of anemia: what is the lower limit of normal of the blood hemoglobin concentration? Blood 2006 Mar; 107(5):1747-1750. [cited 2011 Oct. 6 ] [0434] 14. Peyton P J, Poustie S J, Robinson G J B, Penny D J, Thompson B. Non-invasive measurement of intrapulmonary shunt during inert gas rebreathing. Physiol Meas 2005 June; 26(3):309-316. [cited 2011 Oct. 6 ] [0435] 15. Peyton P J, Robinson G J B, McCall P R, Thompson B. Noninvasive measurement of intrapulmonaryshunting. J. Cardiothorac. Vasc. Anesth. 2004 February; 18(1):47-52. [cited 2011 Oct.6] [0436] 16. Hope D A, Jenkins B J, Willis N, Maddock H, Mapleson W W. Non-invasive estimation of venous admixture: validation of a new formula. Br J Anaesth 1995 May; 74(5):538-543. [cited 2011 Oct 6 ] [0437] 17. Smith H L, Jones J G. Non-invasive assessment of shunt and ventilation/perfusion ratio in neonates with pulmonary failure. Arch. Dis. Child. Fetal Neonatal Ed. 2001 September; 85(2):F127-132. [cited 2011 Oct. 6] [0438] 18. Finley T N, Lenfant C, Haab P, Paper J. Rahn H. Venous admixture in the pulmonary circulation of anestethetized dogs. J Appl Physiol 1960 May; 15:418-424. [cited 2011 Oct. 5 ] [0439] 19. Krowka M J, Cortese D A. Hepatopulmonary syndrome: an evolving perspective in the era of liver transplantation. Hepatology 1990 January; 11(1):138-142. [cited 2011 Oct. 6 ] [0440] 20. Reuter D A, Goetz A E. Measurement of cardiac output. Anaesthesist 2005 November; 54(11):1135-1151; quiz 1152-1153. [cited 2011 Oct. 6 ] [0441] 21. Ehlers K C, Mylrea K C, Waterson C K, Calkins J M. Cardiac output measurements. A review of current techniques and research. Ann Biomed Eng 1986; 14(3):219-239. [cited 2011 Oct. 6] [0442] 22. Geerts B F, Aarts L P, Jansen J R. Methods in pharmacology: measurement of cardiac output. Br J Clin Pharmacol 2011 March; 71(3):316-330. [cited 2011 Oct. 6] [0443] 23. Pugsley J, Lerner A B. Cardiac output monitoring; is there a gold standard and how do the newer technologies compare? Semin Cardiothorac Vasc Anesth 2010 December; 14(4):274-282. [cited 2011 Oct. 6] [0444] 24. Jegier W, Sekelj P, Auld P A, Simpson R, McGregor M. The relation between cardiac output and body size. Br Heart J 1963 July; 25:425-430. [cited 2011 Oct. 6 ] [0445] 25. Ross D N. Theophyiline-ethylenediamine in the measurement of blood circulation time. Br Heart J 1951 January; 13(1):56-60. [cited 2011 Oct. 6] [0446] 26. Zubieta-Calleja G R, Zubieta-Castillo G, Paulev P-E, Zubieta-Calleja L. Non-invasive measurement of circulation time using pulse oximetry during breath holding in chronic hypoxia. J. Physiol. Pharmacol. 2005 September; 56 Suppl 4:251-256. [cited 2011 Oct. 6] [0447] 27 Sowton E, Bloomfield D, Jones N L, Higgs B E, Campbell E. J. Recirculation time during exercise. Cardiovasc. Res. 1968 October; 2(4):341-345. [cited 2011 Oct. 6] [0448] 28. Chapman C B, Fraser R S. Studies on the effect of exercise on cardiovascular function. I.

[0449] Cardiac output and mean circulation time. Circulation 1954 January; 9(1):57-62. [cited 2011 Oct. 6] [0450] 29. Mifflin M D, St Jeor S T, Hill L A, Scott B J, Daugherty S A, Koh Y O. A new predictive equation for resting energy expenditure in healthy individuals. Am. J, Clin. Nutr. 1990 February; 51(2):241-247. [cited 2011 Oct. 6 ] [0451] 30. Lenfant C. Time-dependent variations of pulmonary gas exchange in normal man at rest. J Appl Physiol 1967 April; 22(4):675-684. [cited 2011 Oct. 6] [0452] 31. Wenger J, Clausen J L, Coates A, Pedersen O F, Brusasco V, Burgos F, Casaburi R, Crapo

[0453] R, Enright P, van der Grinten C P M, Gustafsson P, Hankinson J, Jensen R, Johnson D, Macintyre N, McKay R, Miller M R, Navajas D, Pellegrino R, Viegi G. Standardisation of the measurement of lung volumes. Eur. Respir. J. 2005 September; 26(3):511-522. [cited 2011 Oct. 6] [0454] 32. Stocks J, Quanjer P H. Reference values for residual volume, functional residual capacity and total lung capacity. ATS Workshop on Lung Volume Measurements. Official Statement of The European Respiratory Society. Eur. Respir. J. 1995 March; 8(3):492-506.1[cited 2011 Oct. 6] [0455] 33. Arnold J H, Thompson J E, Arnold L W. Single breath CO2 analysis: description and validation of a method. Crit. Care Med. 1996 January; 24(1):96-102. [cited 2011 Oct 6] [0456] 34. Heller H, Konen-Bergmann M, Schuster K D. An algebraic solution to dead space determination according to Fowler's graphical method. Comput. Biomed, Res. 1999 April; 32(2):161-167. [cited 2011 Oct. 6] [0457] 35. Williams E M, Hamilton R M, Sutton L, Viale J P, Hahn C E. Alveolar and dead space volume measured by oscillations of inspired oxygen in awake adults. Am. J. Respir. Crit. Care Med. 1997 December; 156(6):1834-1839. [cited 2011 Oct.6] [0458] 36. Hart M C, Orzalesi M M, Cook C D. Relation between anatomic respiratory dead space and body size and lung volume. Journal of Applied Physiology 1963 May; 18(3):519-522.[cited 2011 Oct. 6] [0459] 37. Ito S, Mardimae A, Han J, Duffin J, Wells G, Fedorko L, Minkovich L, Katznelson R,

[0460] Meineri M, Arenovich T, Kessler C, Fisher J A. Non-invasive prospective targeting of arterial PCO2 in subjects at rest. J, Physiol. (Loud.) 2008 August; 586(Pt15):3675-3682. [cited 2011 Oct.6] [0461] 38. Somogyi R B, Vesely A E, Preiss D, Prisman E, Volgyesi G, Azami T, Iscoe S, Fisher J A, Sasano H. Precise control of end-tidal carbon dioxide levels using sequential rebreathing circuits. Anaesth Intensive Care 2005 December; 33(6):726-732. [cited 2011 Oct. 6] [0462] 39. Fierstra J, Machina M. Battisti-Charbonney A, Duffin J, Fisher J A, Minkovich L. End-inspiratory rebreathing reduces the end-tidal to arterial PCO2 gradient in mechanically ventilated pigs. Intensive Care Med 2011 September; 37(9):1543-1550. [cited 2011 Oct. 6] [0463] 40. Jones N L, Robertson D G, Kane J W, Campbell E J. Effect of PCO2 level on alveolar-arterial PCO2 difference during rebreathing. J Appl Physiol 1972 June; 32(6):782-787. [cited 2011 Oct. 6] [0464] 41. Raine J M, Bishop J M. A-a difference in O2 tension and physiological dead space in normal man. J Appl Physiol 1963 March; 18:284-288. [cited 2011 Oct. 6] [0465] 42. Kelman G R. Digital computer subroutine for the conversion of oxygen tension into saturation. J Appl Physiol 1966 July; 21(4):1375-1376. [cited 2011 Oct. 6] [0466] 43. Wheeler D S, Wong H R, Shanley T P. Pediatric Critical Care Medicine: Basic Science and Clinical Evidence. 1st ed. Springer; 2007. [0467] 44. Burnett R W, Noonan D C. Calculations and correction factors used in determination of blood pH and blood gases. Gin. Chem. 1974 December; 20(12):1499-1506. [cited 2011 Oct.6] [0468] 45. Loeppky J A, Luft U C, Fletcher E R. Quantitative description of whole blood CO2 dissociation curve and Haldane effect. Respir Physiol1983 February; 51(2):167-181. [cited 2011 Oct. 6] [0469] 46. Douglas A R, Jones N L, Reed J W. Calculation of whole blood CO2 content. J. Appl. Physiol. 1988 July; 65(1):473-477. [cited 2011 Oct. 6]

[0470] 47. Kelman G R. Digital computer procedure for the conversion of PCO2 into blood CO2 content. Respir Physiol 1967August; 3(1):111-115. [cited 2011 Oct. 6] [0471] 48. Olszowka A J, Farhi L E, A system of digital computer subroutines for blood gas calculations. Respir Physiol 1968 March; 4(2):270-280. [cited 2011 Oct. 6] [0472] 49. Chemiack N S, Longobardo G S. Oxygen and carbon dioxide gas stores of the body. Physiol. Rev. 1970 April; 50(2):196-243. [cited 2011 Oct. 6] [0473] 50. Chernlack N S, Longobardo G S, Palermo F P, Heymann M. Dynamics of oxygen stores changes following an alteration in ventilation. J Appl Physiol 1968 June; 24(6):809-816. [cited 2011 Oct. 6] [0474] 51. Farhi L E, Rahn H. Dynamics of changes in carbon dioxide stores. Anesthesiology 1960 December; 21:604-614. [cited 2011 Oct. 6] [0475] 52. Chemiack N S, Longobardo G S, Staw I, Heymann M. Dynamics of carbon dioxide stores changes following an alteration in ventilation. J Appl Physiol 1966 May; 21(3):785-793. [cited 2011 Oct. 6]