APPARATUS TO ATTAIN AND MAINTAIN TARGET END TIDAL PARTIAL PRESSURE OF A GAS

20170361042 · 2017-12-21

Inventors

Cpc classification

International classification

Abstract

A processor obtains input of a logistically attainable end tidal partial pressure of gas X (PetX[i].sup.T) for one or more respective breaths [i] and input of a prospective computation of an amount of gas X required to be inspired by the subject in an inspired gas to target the PetX[i].sup.T for a respective breath [i] using inputs required to utilize a mass balance relationship, wherein one or more values required to control the amount of gas X in a volume of gas delivered to the subject is output from an expression of the mass balance relationship. The mass balance relationship is expressed in a form which takes into account (prospectively), for a respective breath [i], the amount of gas X in the capillaries surrounding the alveoli and the amount of gas X in the alveoli, optionally based on a model of the lung which accounts for those sub-volumes of gas in the lung which substantially affect the alveolar gas X concentration affecting mass transfer.

Claims

1. A method of controlling a gas delivery device to target or attain a target end tidal partial pressure of gas X in a subject, wherein a signal processor operatively associated with a gas delivery device controls the amount of gas X contained in a volume of inspiratory gas delivered to a subject in a respective breath [i], using inputs and outputs processed by the signal processor for a respective breath [i], the method comprising: (a) Obtaining input of one or more values sufficient to compute the concentration of gas X in the mixed venous blood entering the subject's pulmonary circulation for gas exchange in one or more respective breaths [i] (C.sub.MVX[i]); (b) Obtaining input of a logistically attainable end tidal partial pressure of gas X (PetX[i].sup.T) for a respective breath [i]; (c) Utilizing a prospective computation to determine an amount of gas X required to be inspired by the subject to target the PetX[i].sup.T for a respective breath [i], the prospective computation using inputs sufficient to compute a mass balance equation for a respective breath [i], the inputs including values, for a respective breath [i], from which C.sub.MVX[i] and the concentration of gas X in the subject's lung affecting mass transfer can be determined, wherein one or more values required to control the amount of gas X in a volume of gas delivered to the subject is output from the mass balance equation; and (d) Outputting control signals to the gas delivery device to control the amount gas X in a volume of gas delivered to the subject in a respective breath [i] to target the respective PetX[i].sup.T based on the prospective computation.

2. A method according to claim 1, wherein the mass balance equation is formulated in terms of discrete respective breaths [i] taking into account one or more discrete volumes corresponding to a subject's FRC, anatomic dead space, a volume of gas transferred between the subject's lung and pulmonary circulation in the respective breath [i] and an individual tidal volume of the respective breath [i].

3. A method according to claim 1, wherein the inspired gas comprises a first inspired gas and a second inspired gas, wherein the first inspired gas is delivered in the first part of a respective breath [i] followed by the second inspired gas for the remainder of the respective breath [i], the volume of the first inspired gas preferably selected so that intake of the second inspired gas at least fills the entirety of the anatomic dead space.

4. A method according to claim 1, wherein a concentration of gas X (F.sub.IX) in the first inspired gas is computed from the mass balance equation to target or attain a PetX[i].sup.T in a respective breath [i].

5. A method according to claim 1, wherein the mass balance equation is solved for F.sub.IX.

6. A method according to claim 1, comprising the step of obtaining inputs required to compute F.sub.IX prospectively to target PetX[i].sup.T for a respective breath [i], wherein F.sub.IX is computed using a mass balance equation which comprises terms corresponding to all or an application-specific subset of the terms in: $\begin{matrix} F_{I} .Math. X [i] = \frac{\begin{matrix} (P_{ET} .Math. {X [i]}^{T} - P_{ET} .Math. {X [i - 1]}^{T}) .Math. (FRC + V_{T}) + P_{ET} .Math. {X [i - 1]}^{T} .Math. \\ ({FG}_{1} .Math. T_{B}) - PB .Math. Q .Math. (1 - s) .Math. T_{B} .Math. (C_{MV} .Math. X [i] - C_{p} .Math. X [i]) \end{matrix}}{{FG}_{1} .Math. T_{B} .Math. PB} & eq . .Math. 1 \\ .Math. or \\ F_{I} .Math. X [i] = \frac{\begin{matrix} P_{ET} .Math. {X [i]}^{T} .Math. (FRC + V_{T}) - P_{ET} .Math. {X [i - 1]}^{T} .Math. (FRC + V_{D}) - \\ PB .Math. Q .Math. (1 - s) .Math. T_{B} .Math. (C_{MV} .Math. X [i] - C_{p} .Math. X [i]) \end{matrix}}{(V_{T} - V_{D}) .Math. PB} & eq . .Math. 2 \end{matrix}$

7. A method according to claim 6, wherein F.sub.IX is computed prospectively from a mass balance equation expressed in terms which correspond to all or an application-specific subset of the terms in equation 1 and the first inspired gas has a concentration of gas X which corresponds to F.sub.IX for the respective breath [i].

8. A method according to claim 1, wherein the gas inspired by the subject in each respective breath [i] comprises a first inspired gas and a second inspired neutral gas, wherein the first inspired gas is delivered in the first part of a respective breath [i] followed by a second inspired neutral gas for the remainder of the respective breath [i], the volume of the first inspired gas selected so that intake of the second inspired neutral gas at least fills the entirety of the anatomic dead space; wherein F.sub.IX is computed prospectively using a mass balance equation which comprises all or a functional subset of the terms in equation 1 and wherein the first inspired gas has a concentration of gas X which corresponds to F.sub.IX for the respective breath [i].

9. A method according to claim 1, comprising ascertaining the volume of inspired gas entering the subject's alveoli by fixing a tidal volume of an inspired gas containing gas X using a ventilator and subtracting a volume of gas corresponding to an estimated or measured value for the subject's anatomic dead space volume.

10. A method according to claim 1, wherein the gas inspired by the subject is inspired via a sequential gas delivery circuit; and wherein the rate of flow of gas into the sequential gas delivery circuit is used to compute the volume of inspired gas entering the subject's alveoli in a respective breath [i].

11. A method according to claim 1, further comprising tuning one or more parameters required for computation of F.sub.IX including at least one parameter selected from the group consisting of the subject's functional residual capacity (FRC) and the subject's total metabolic production or consumption of gas X.

12. A method according to claim 11, wherein FRC is tuned in a series of tuning breaths by: (a) changing the targeted end tidal concentration of gas X between a tuning breath [i+x] and a previous tuning breath [i+x−1]; (b) comparing the magnitude of the difference between the targeted end tidal concentration of gas X for said tuning breaths [i+x] and [i+x−1] with the magnitude of the difference between the measured end tidal concentration of gas X for the same tuning breaths to quantify any discrepancy in relative magnitude; and (c) adjusting the value of FRC in proportion to the discrepancy to reduce the discrepancy in any subsequent prospective computation of F.sub.IX.

13. A method according to claim 11, wherein the total metabolic production or consumption of gas X is tuned in a series of tuning breaths by comparing a targeted end tidal concentration of gas X (PetX[i+x].sup.T) for the at least one tuning breath [i+x] with a corresponding measured end tidal concentration of gas X for the corresponding breath [i+x] to quantify any discrepancy and adjusting the 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.

14. A method according to claim 13, wherein FRC is tuned in a series of tuning breaths in which a sequence of end tidal concentrations of gas X is targeted at least once by: (a) obtaining input of a measured baseline steady state value for PetX[i] for computing F.sub.IX at start of a sequence; (b) selecting a target end tidal concentration of gas X (PetX[i].sup.T) for at least one tuning breath [i+x] wherein PetX[i+x].sup.T differs from PetX[i+x−1].sup.T; and (c) comparing the magnitude of the difference between the targeted end tidal concentration of gas X for said tuning breaths [i+x] and [i+x−1] with the magnitude of the difference between the measured end tidal concentration of gas X for the same tuning breaths to quantify any discrepancy in relative magnitude; (d) adjusting the value of FRC in proportion to any discrepancy in magnitude to reduce the discrepancy in a subsequent prospective computation of F.sub.IX including in any subsequent corresponding tuning breaths [i+x−1] and [i+x] forming part of an iteration of the sequence.

15. A method according to claim 12, wherein the total metabolic consumption or production of gas X is tuned in a series of tuning breaths in which a sequence of end tidal concentrations of gas X is targeted at least once by: (a) obtaining input of a measured baseline steady state value for PetX[i] for computing F.sub.IX at start of a sequence; (b) targeting a selected target end tidal concentration of gas X (PetX[i].sup.T) for each of a series of tuning breaths [i+1 . . . i+n], wherein PetX[i].sup.T differs from the baseline steady state value for PetX[i]; (c) comparing the targeted end tidal concentration of gas X (PetX[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 concentration of gas X for a corresponding breath [i+x] to quantify any discrepancy and adjusting the value of the total metabolic consumption or production of gas X in proportion to the discrepancy to reduce the discrepancy in a subsequent prospective computation of F.sub.IX including in any subsequent corresponding tuning breath [i+x] forming part of an iteration of the sequence.

16. A method according to claim 1, wherein input of a concentration of gas X in the mixed venous blood entering the subject's pulmonary circulation for gas exchange in a respective breath [i] (C.sub.MVX[i]) is determined by a compartmental model of gas dynamics.

17. A method according to claim 14, wherein the compartmental model of gas dynamics accounts for the total and compartmental metabolic production or consumption of gas X, the total and compartmental storage capacity for gas X and the total cardiac output and compartmental contribution to total cardiac output.

18. A method according to claim 1, wherein gas X is carbon dioxide.

19. 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, comprising: (1) a gas delivery device; (2) a control system for controlling the gas delivery device, the control system configured for: (a) Obtaining input of a concentration of gas X in the mixed venous blood entering the subject's pulmonary circulation for gas exchange in one or more respective breaths [i] (C.sub.MVX[i]); (b) Obtaining input of a logistically attainable end tidal partial pressure of gas X (PetX[i].sup.T) for a respective breath [i]; (c) Obtaining input of a prospective computation of an amount of gas X required to be inspired by the subject in an inspired gas to target the PetX[i].sup.T for a respective breath [i] using inputs required to compute a mass balance equation including C.sub.MVX[i], wherein one or more values required to control the amount of gas X in the volume of gas delivered to the subject is output from the mass balance equation; and (d) Controlling the amount of gas X in the volume of gas delivered to the subject in a respective breath [i] to target the respective PetX[i].sup.T based on the prospective computation.

20. An apparatus according to claim 19, wherein the mass balance equation is computed based on a tidal model of the lung.

21. An apparatus according to claim 19, wherein the mass balance equation is computed in terms of discrete respective breaths [i] including one or more discrete volumes comprising or corresponding to a subject's FRC, anatomic dead space, a volume of gas transferred between the subject's lung and pulmonary circulation in the respective breath [i] and an individual tidal volume of the respective breath [i].

22. An apparatus according to claim 19, wherein the inspired gas comprises a first inspired gas and a second inspired gas, wherein the first inspired gas is delivered in a first part of a respective breath [i] followed by the second inspired gas for a remainder of the respective breath [i], a volume of the first inspired gas selected so that intake of the second inspired gas at least fills the entirety of the anatomic dead space; and wherein for a respective breath [i], the volume of the first inspired gas and a concentration of gas X in the second inspired gas are selected to attain PetX[i].sup.T; and wherein for a respective breath [i], the concentration of gas X in the second inspired gas corresponds to PetX[i].sup.T for a respective breath [i].

23. An apparatus according to claim 19, comprising the step of obtaining inputs required to compute an F.sub.IX to target PetX[i].sup.T for a respective breath [i], wherein F.sub.IX is computed using a mass balance equation which comprises terms corresponding to all or an application-specific subset of the terms in: $\begin{matrix} F_{I} .Math. X [i] = \frac{\begin{matrix} (P_{ET} .Math. {X [i]}^{T} - P_{ET} .Math. {X [i - 1]}^{T}) .Math. (FRC + V_{T}) + P_{ET} .Math. {X [i - 1]}^{T} .Math. \\ ({FG}_{1} .Math. T_{B}) - PB .Math. Q .Math. (1 - s) .Math. T_{B} .Math. (C_{MV} .Math. X [i] - C_{p} .Math. X [i]) \end{matrix}}{{FG}_{1} .Math. T_{B} .Math. PB} & eq . .Math. 1 \\ .Math. or \\ F_{I} .Math. X [i] = \frac{\begin{matrix} P_{ET} .Math. {X [i]}^{T} .Math. (FRC + V_{T}) - P_{ET} .Math. {X [i - 1]}^{T} .Math. (FRC + V_{D}) - \\ PB .Math. Q .Math. (1 - s) .Math. T_{B} .Math. (C_{MV} .Math. X [i] - C_{p} .Math. X [i]) \end{matrix}}{(V_{T} - V_{D}) .Math. PB} & eq . .Math. 2 \end{matrix}$

24. An apparatus according to claim 19, wherein the control system is implemented by a computer.

25. An apparatus according to claim 24, wherein the computer provides output signals to one or more rapid flow controllers.

26. An apparatus according to claim 24, wherein the computer receives input from a gas analyzer and an input device adapted for providing input of one or more logistically attainable target end tidal concentration of gas X (PetX[i].sup.T) for a series of respective breaths [i].

27. An apparatus according to claim 19, wherein the control system, in each respective breath [i], controls the delivery of at least a first inspired gas and wherein delivery of the first inspired gas is coordinated with delivery a second inspired neutral gas, such that a selected volume of the first inspired gas is delivered in a first part of a respective breath [i] followed by the second inspired neutral gas for a remainder of the respective breath [i].

Description

BRIEF DESCRIPTION OF THE FIGURES

[0170] The invention will now be described with reference to the figures, in which:

[0171] FIG. 1 is a schematic overview of the movement of blood and the exchange of gases throughout the entire system.

[0172] FIG. 2 is a detailed schematic representation of the movement of blood and the exchange of gases at the tissues.

[0173] 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.

[0174] 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.

[0175] 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.

[0176] FIG. 6 is a graphic representation of a tuning sequence and observed errors that can be used to tune model parameters.

[0177] FIG. 7 is a Table of abbreviations (Table 1) used in the specification.

[0178] FIG. 8, is a representative raw data sample excerpted from the study of 35 subjects referred to in Example 1, showing a targeting sequence wherein normocapnia (40 mm Hg targeted three times) and hypercapnia (50 mm Hg targeted twice) were sequentially targeted in 6 study subjects.

DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT

[0179] The invention is described hereafter in terms of one or more optional embodiments of a gas X, namely carbon dioxide and oxygen.

Prospective Modelling

[0180] 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.

[0181] 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.

[0182] 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.

[0183] 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.

[0184] 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.

[0185] 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.

[0186] 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.

[0187] 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

[0188] 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.

[0189] 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 means to control the volumes of, and/or switch the composition or source of, the gas inspired by the subject.

[0190] 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 connect 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.

[0191] 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.

[0192] 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.

[0193] 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.

[0194] Examples of suitable sequential gas delivery circuits are disclosed in US Patent Application No. 20070062534. An example of a gas delivery device suitable for delivering a first inspired gas or composing a neutral gas is a volumetric type delivery device described in published PCT Application No. WO2012/139204.

[0195] 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.

[0196] 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.

[0197] Sequential gas delivery circuits may be imperfect in the sense that a subject will inspire what is substantially entirely 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.

[0198] 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).

[0199] The contents of all references set forth below are hereby incorporated by reference.

[0200] Various implementations of sequential gas delivery have described by Joseph Fisher et al. in the scientific and patent literature.

[0201] 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.ET[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(T)[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

[0202] 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.

FIG. 3—The Lungs (No Sequential Rebreathing)

[0203] 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.

[0204] 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.I[i]) is inspired.

FIG. 4—The Lungs (Sequential Rebreathing)

[0205] 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. 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.

[0206] 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].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.I[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

[0207] 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 subject's 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

[0208] 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.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 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.

[0209] The tuning sequence optionally sets the target end-tidal partial pressure of O2 (P.sub.ETO2[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.

[0210] Embodiments of mass balance equations:

[00002] $No .Math. .Math. SGD .Math. : .Math. .Math. F_{l} .Math. X [i] = \frac{\begin{matrix} P_{ET} .Math. {X [i]}^{T} .Math. (FRC + V_{T}) - P_{ET} .Math. {X [i - 1]}^{T} .Math. (FRC + V_{D}) - \\ PB .Math. Q .Math. (1 - s) .Math. T_{B} .Math. (C_{MV} .Math. X [i] - C_{p} .Math. X [i]) \end{matrix}}{(V_{T} - V_{D}) .Math. PB}$ $SGD .Math. : .Math. .Math. F_{l} .Math. X [i] = \frac{\begin{matrix} (P_{ET} .Math. {X [i]}^{T} - P_{ET} .Math. {X [i - 1]}^{T}) .Math. (FRC + V_{T}) - P_{ET} .Math. {X [i - 1]}^{T} .Math. .Math. \\ ({FG}_{1} .Math. T_{B}) - PB .Math. Q .Math. (1 - s) .Math. T_{B} .Math. (C_{MV} .Math. X [i] - C_{p} .Math. X [i]) \end{matrix}}{{FG}_{1} .Math. T_{B} .Math. PB}$ $Abbreviations .Math. .Math. and .Math. .Math. terms .Math. .Math. are .Math. .Math. repeated .Math. .Math. in .Math. .Math. FIG . .Math. 7.$

Physiological Inputs

[0211] This section describes how to obtain measurements or estimates of all the physiological inputs required to execute a prospective end-tidal targeting sequence.

Subject Weight, Height, Age, and Sex:

[0212] Subject weight (W), height (H), 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:

[0213] 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:

[0214] 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:

[0215] 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):

15 g/dL for males
13 g/dL for females (10; 13)

Shunt Fraction:

[0216] 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:

[0217] 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:

[0218] 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:

[0219] 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:

[0220] 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:

[00003] $\begin{matrix} VO .Math. .Math. 2 = \frac{10 .Math. W + 625 .Math. H - 5 .Math. A + 5}{6.8832} .Math. .Math. for .Math. .Math. males .Math. .Math. VO .Math. .Math. 2 = \frac{10 .Math. W + 625 .Math. H - 5 .Math. A - 161}{6.8832} .Math. .Math. for .Math. .Math. females & (29) \end{matrix}$

Metabolic CO2 Production:

[0221] 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 O2 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:

[0222] The functional residual capacity (FRC) can be measured using a variety of respiratory maneuvers (31). If measurement is not available or possible, it can be estimated from the subject's 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:

[0223] The anatomical dead space (V.sub.D) can be measured using a variety of respiratory maneuvers (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)

Rate at which the Controlled Gas Mixture is Made Available for Inspiration when Using a Sequential Gas Delivery Circuit (SGDC)

[0224] 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:

[0225] The tidal volume (V.sub.T) 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.1<15000:V.sub.T=(0.75.Math.FG.sub.1+3750).Math.T.sub.B+V.sub.D

else:V.sub.T=FG.sub.1.Math.T.sub.B+V.sub.D

[0226] 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

[0227] 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.

Calculation of the Inspired Gas Composition to Induce Target End-Tidal Values

[0228] The partial pressure of O2 in the controlled gas mixture (P.sub.IO2[i]) and the partial pressure of CO2 in the controlled gas mixture (P.sub.ICO2[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).

Calculate the O2 and CO2 Partial Pressures of Pulmonary End-Capillary Blood

[0229] 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

[0230] 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

[0231] 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).

[00004] $pH [i] = 6.1 + \log (\frac{[{HCO}_{3}]}{0.03 .Math. P_{p} .Math. CO .Math. .Math. 2 [i]})$

Calculate the O2 Saturation of Pulmonary End-Capillary Blood

[0232] 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).

[00005] $S_{p} .Math. O .Math. .Math. 2 [i] = 100 .Math. \frac{- 8532.2289 .Math. z + 2121.401 .Math. z^{2} - 67.073989 .Math. z^{3} + z^{4}}{\begin{matrix} 935960.87 - 31346.258 .Math. z + 2396.1674 .Math. z^{2} - \\ 67.104406 .Math. z^{3} + z^{4} \end{matrix}}$ $where .Math. .Math. z = P_{p} .Math. O .Math. .Math. 2 [i] .Math. 10^{0.024 .Math. (37 - T) + 0.4 .Math. (pH [i] - 7.4) + 0.06 .Math. (\log .Math. .Math. 40 - \log .Math. .Math. P_{p} .Math. CO .Math. .Math. 2 [i])}$

Calculate the O2 Content of Pulmonary End-Capillary Blood

[0233] The O2 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).

[00006] $C_{p} .Math. O .Math. .Math. 2 [i] = 1.36 .Math. Hb .Math. \frac{S_{p} .Math. O .Math. .Math. 2 [i]}{100} + 0.003 .Math. P_{p} .Math. O .Math. .Math. 2 [i]$

[0234] Alternative derivations of pH, O2 saturation, and O2 content are reviewed in detail in (44).

Calculate the CO2 Content of Pulmonary End-Capillary Blood

[0235] 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).

[00007] $C_{p} .Math. CO .Math. .Math. 2 [i] = (1.0 - \frac{0.02924 .Math. Hb}{(2.244 - 0.422 .Math. (\frac{Sp .Math. .Math. O2 [i]}{100})) .Math. (8.740 - p .Math. .Math. H [i])}) .Math. C_{pl}$ $where .Math. : .Math. .Math. C_{pl} = 0.0301 .Math. P_{p} .Math. CO .Math. .Math. 2 [i] .Math. (1 + 10^{pH [i] - 6.10}) .Math. 2.226$

[0236] See also (46-48) for alternative calculations of CO2 content.

Calculate the O2 and CO2 Content of Arterial Blood

[0237] 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).

[0238] 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]+s.Math.C.sub.MVO2[i]

[0239] 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

[0240] 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 for a 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).

[00008] $.Math. For .Math. .Math. j = 1 .Math. .Math. .Math. .Math. .Math. n_{O .Math. .Math. 2}$ $C_{V} .Math. O .Math. .Math. 2 [i] = C_{V} .Math. O .Math. .Math. 2 [i - 1] + \frac{100 .Math. T_{B}}{d .Math. .Math. O .Math. .Math. 2_{j}} .Math. (q_{j} .Math. Q .Math. (C_{a} .Math. O .Math. .Math. 2 [i] - C_{V} .Math. O .Math. .Math. 2_{j} [i - 1]) - vo .Math. .Math. 2_{j} .Math. VO .Math. .Math. 2)$

[0241] 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

[0242] 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.

[00009] $C_{MV (T)} .Math. O .Math. .Math. 2 [i] = {.Math.}_{j = 1}^{n_{O .Math. .Math. 2}} .Math. .Math. q_{j} .Math. C_{V} .Math. O .Math. .Math. 2_{j} [i]$

[0243] 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.aO2.sub.j[i]) less the overall metabolic O2 consumption of the tissues (VO2) distributed over the cardiac output (Q).

[00010] $C_{MV (T)} .Math. O .Math. .Math. 2 [i] = \frac{Q .Math. C_{a} .Math. O .Math. .Math. 2 [i] - VO .Math. .Math. 2}{Q}$

[0244] 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]

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

Calculate the CO2 Content of the Mixed-Venous Blood

[0245] 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).

[00011] $.Math. For .Math. .Math. k = 1 .Math. .Math. .Math. .Math. .Math. n_{CO .Math. .Math. 2}$ $C_{V} .Math. CO .Math. .Math. 2_{k} [i] = C_{V} .Math. CO .Math. .Math. 2_{k} [i - 1] + \frac{100 .Math. T_{B}}{d .Math. .Math. CO .Math. .Math. 2_{k}} .Math. (vco .Math. .Math. 2_{k} .Math. VCO .Math. .Math. 2 - q_{k} .Math. Q .Math. (C_{V} .Math. CO .Math. .Math. 2_{k} [i - 1] - C_{a} .Math. CO .Math. .Math. 2 [i]))$

[0246] 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

[0247] 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

[0248] 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.

[00012] $C_{MV (T)} .Math. CO .Math. .Math. 2 [i] = {.Math.}_{k = 1}^{n_{CO .Math. .Math. 2}} .Math. .Math. q_{k} .Math. C_{V} .Math. CO .Math. .Math. 2_{k} [i]$

[0249] 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.R])

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

[0250] Other CO2 model parameters are available from (49; 52).

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

[0251] 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−1].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−1].sup.T); b) a volume of controlled gas mixture (VG.sub.1) with controllable partial pressure of O2 (P.sub.IO2[i]) and controllable partial pressure of CO2 (P.sub.ICO2[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.

[0252] A volume of O2 is transferred between the alveolar space and the pulmonary circulation (VB.sub.O2[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])

[0253] 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).Math.T.sub.B.Math.(C.sub.MVCO2[i]−C.sub.pCO2[i])

[0254] 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

[0255] 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.

[00013] $P_{ET} .Math. O .Math. .Math. {2 [i]}^{T} = \frac{(\begin{matrix} \overset{\overset{O .Math. .Math. 2 .Math. .Math. in .Math. .Math. FRC}{}}{P_{ET} .Math. O .Math. .Math. {2 [i - 1]}^{T} .Math. FRC} + \overset{\overset{O .Math. .Math. 2 .Math. .Math. re .Math. - .Math. inspired .Math. .Math. from .Math. .Math. V_{D}}{}}{P_{ET} .Math. O .Math. .Math. {2 [i - 1]}^{T} .Math. V_{D}} + \\ \begin{matrix} \overset{\overset{O .Math. .Math. 2 .Math. .Math. in .Math. .Math. controlled .Math. .Math. gas .Math. .Math. mixture}{}}{P_{I} .Math. O .Math. .Math. 2 [i] .Math. (V_{T} - V_{D})} + \\ \overset{\overset{O .Math. .Math. 2 .Math. .Math. transfered .Math. .Math. into .Math. .Math. lung .Math. .Math. from .Math. .Math. the .Math. .Math. circulation .Math. .Math. ({VB}_{O .Math. .Math. 2})}{}}{PB .Math. Q .Math. (1 - s) .Math. T_{B} .Math. (C_{MV} .Math. O .Math. .Math. 2 [i] - C_{p} .Math. O .Math. .Math. 2 [i])} \end{matrix} \end{matrix})}{\underset{\underset{Total .Math. .Math. volume .Math. .Math. of .Math. .Math. the .Math. .Math. alveolar .Math. .Math. space}{}}{V_{T} + FRC}}$ $P_{ET} .Math. CO .Math. .Math. {2 [i]}^{T} = \frac{(\begin{matrix} \overset{\overset{CO .Math. .Math. 2 .Math. .Math. in .Math. .Math. FRC}{}}{P_{ET} .Math. CO .Math. .Math. {2 [i - 1]}^{T} .Math. FRC} + \overset{\overset{CO .Math. .Math. 2 .Math. .Math. re .Math. - .Math. inspired .Math. .Math. from .Math. .Math. V_{D}}{}}{P_{ET} .Math. CO .Math. .Math. {2 [i - 1]}^{T} .Math. V_{D}} + \\ \begin{matrix} \overset{\overset{CO .Math. .Math. 2 .Math. .Math. in .Math. .Math. controlled .Math. .Math. gas .Math. .Math. mixture}{}}{P_{I} .Math. CO .Math. .Math. 2 [i] .Math. (V_{T} - V_{D})} + \\ \overset{\overset{CO .Math. .Math. 2 .Math. .Math. transfered .Math. .Math. into .Math. .Math. lung .Math. .Math. from .Math. .Math. the .Math. .Math. circulation .Math. .Math. ({VB}_{O .Math. .Math. 2})}{}}{PB .Math. Q .Math. (1 - s) .Math. T_{B} .Math. (C_{MV} .Math. CO .Math. .Math. 2 [i] - C_{p} .Math. CO .Math. .Math. 2 [i])} \end{matrix} \end{matrix})}{\underset{\underset{Total .Math. .Math. volume .Math. .Math. of .Math. .Math. the .Math. .Math. alveolar .Math. .Math. space}{}}{V_{T} + FRC}}$

[0256] 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.IO2[i]) and the partial pressure of CO2 in the controlled gas mixture (P.sub.ICO2[i]) can be set to induce target end-tidal partial pressures.

[0257] 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.

[0258] 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:

[00014] $P_{I} .Math. O .Math. .Math. 2 [i] = \frac{\begin{matrix} P_{ET} .Math. O .Math. .Math. {2 [i]}^{T} .Math. (FRC + V_{T}) - P_{ET} .Math. O .Math. .Math. {2 [i - 1]}^{T} .Math. (FRC + V_{D}) - \\ PB .Math. Q .Math. (1 - s) .Math. T_{B} .Math. (C_{MV} .Math. O .Math. .Math. 2 [i] - C_{p} .Math. O .Math. .Math. 2 [i]) \end{matrix}}{(V_{T} - V_{D})} .Math. .Math. P_{I} .Math. CO .Math. .Math. 2 [i] = \frac{\begin{matrix} P_{ET} .Math. CO .Math. .Math. {2 [i]}^{T} .Math. (FRC + V_{T}) - P_{ET} .Math. CO .Math. .Math. {2 [i - 1]}^{T} .Math. (FRC + V_{D}) - \\ PB .Math. Q .Math. (1 - s) .Math. T_{B} .Math. (C_{MV} .Math. CO .Math. .Math. 2 [i] - C_{p} .Math. CO .Math. .Math. 2 [i]) \end{matrix}}{(V_{T} - V_{D})}$

[0259] These equations can be used to calculate the partial pressure of O2 in the controlled gas mixture (P.sub.IO2[i]) and the partial pressure of CO2 in the controlled gas mixture (P.sub.ICO2[i]) required to induce a target end-tidal partial pressure of O2 (P.sub.ETO2[i].sup.T) and 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.ETO.sub.2[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.MV, O2[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.

[0260] Notice that the partial pressure of O2 in the controlled gas mixture (P.sub.IO2[i]) and the partial pressure of CO2 in the controlled gas mixture (P.sub.ICO2[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).

[0261] 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.TOR

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

[0262] Herein, the above general equations for calculating the composition of the controlled gas mixture reduce to the following:

[00015] $P_{I} .Math. O .Math. .Math. 2 [i] = \frac{\begin{matrix} P_{ET} .Math. O .Math. .Math. {2 [i]}^{T} .Math. (V_{T} - V_{D}) - PB .Math. Q .Math. (1 - s) .Math. \\ T_{B} .Math. (C_{MV} .Math. O .Math. .Math. 2 [i] - C_{p} .Math. O .Math. .Math. 2 [i]) \end{matrix}}{V_{T} - V_{D}}$ $P_{I} .Math. CO .Math. .Math. 2 [i] = \frac{\begin{matrix} P_{ET} .Math. CO .Math. .Math. {2 [i]}^{T} .Math. (V_{T} - V_{D}) - PB .Math. Q .Math. (1 - s) .Math. \\ T_{B} .Math. (C_{MV} .Math. CO .Math. .Math. 2 [i] - C_{p} .Math. CO .Math. .Math. 2 [i]) \end{matrix}}{V_{T} - V_{D}}$

[0263] 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.IO2[i]) and the partial pressure of CO2 in the controlled gas mixture (P.sub.ICO2[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.

[0264] This method, therefore, is optional, especially where a simpler approach is preferred, and the subject's ventilation can be reasonably controlled or predicted.

[0265] 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.IO2[i]) and the partial pressure of CO.sub.2 in the controlled gas mixture (P.sub.ICO2[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.

[0266] 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.IO2[i]) and the partial pressure of CO2 in the controlled gas mixture (P.sub.ICO2[i]) may be converted a fractional concentration of O2 in the controlled gas mixture (F.sub.IO2[i]) and a fractional concentration of CO2 in the controlled gas mixture (F.sub.ICO2[i]).

[00016] $F_{I} .Math. O .Math. .Math. 2 [i] = \frac{P_{I} .Math. O .Math. .Math. 2 [i]}{PB}$ $F_{I} .Math. CO .Math. .Math. 2 [i] = \frac{P_{I} .Math. CO .Math. .Math. 2 [i]}{PB}$

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

[0267] 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−1].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.IO2[i]) and controllable partial pressure of CO2 (P.sub.ICO2[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.

[0268] A volume of O2 is transferred between the alveolar space and the pulmonary circulation (VB.sub.O2[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.Math.s).Math.T.sub.B.Math.(C.sub.MVO2[i]−C.sub.pO2[i])

[0269] 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.Math.s).Math.T.sub.B.Math.(C.sub.MVCO2[i]−C.sub.pCO2[i])

[0270] Assuming a neutral gas at least fills the subject's 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

[0271] 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.I) 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

[0272] 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.

[00017] $P_{ET} .Math. O .Math. .Math. {2 [i]}^{T} = \frac{(\begin{matrix} \overset{\overset{O .Math. .Math. 2 .Math. .Math. in .Math. .Math. FRC}{}}{P_{ET} .Math. O .Math. .Math. {2 [i - 1]}^{T} .Math. FRC} + \overset{\overset{\begin{matrix} O .Math. .Math. 2 .Math. .Math. re .Math. - .Math. inspired \\ from .Math. .Math. V_{D} \end{matrix}}{}}{P_{ET} .Math. O .Math. .Math. {2 [i - 1]}^{T} .Math. V_{D}} + \\ \overset{\overset{\begin{matrix} O .Math. .Math. 2 .Math. .Math. in .Math. .Math. controlled \\ gas .Math. .Math. mixture \end{matrix}}{}}{P_{I} .Math. O .Math. .Math. 2 [i] .Math. ({FG}_{1} .Math. T_{B})} + \overset{\overset{O .Math. .Math. 2 .Math. .Math. in .Math. .Math. neutral .Math. .Math. gas}{}}{P_{ET} .Math. O .Math. .Math. {2 [i - 1]}^{T} .Math. (V_{T} - V_{D} - {FG}_{1} .Math. T_{B})} + \\ \overset{\overset{\begin{matrix} O .Math. .Math. 2 .Math. .Math. transfered .Math. .Math. into .Math. .Math. lung \\ from .Math. .Math. the .Math. .Math. circulation .Math. .Math. ({VB}_{O .Math. .Math. 2}) \end{matrix}}{}}{PB .Math. Q .Math. (1 - s) .Math. T_{B} .Math. (C_{MV} .Math. O .Math. .Math. 2 [i] - C_{p} .Math. O .Math. .Math. 2 [i])} \end{matrix})}{\underset{\underset{Total .Math. .Math. volume .Math. .Math. of .Math. .Math. the .Math. .Math. alveolarspace}{}}{V_{T} + FRC}}$ $P_{ET} .Math. CO .Math. .Math. {2 [i]}^{T} = \frac{(\begin{matrix} \overset{\overset{CO .Math. .Math. 2 .Math. .Math. in .Math. .Math. FRC}{}}{P_{ET} .Math. CO .Math. .Math. {2 [i - 1]}^{T} .Math. FRC} + \overset{\overset{\begin{matrix} CO .Math. .Math. 2 .Math. .Math. re .Math. - .Math. inspired \\ from .Math. .Math. V_{D} \end{matrix}}{}}{P_{ET} .Math. CO .Math. .Math. {2 [i - 1]}^{T} .Math. V_{D}} + \\ \overset{\overset{\begin{matrix} CO .Math. .Math. 2 .Math. .Math. in .Math. .Math. controlled \\ gas .Math. .Math. mixture \end{matrix}}{}}{P_{I} .Math. CO .Math. .Math. 2 [i] .Math. ({FG}_{1} .Math. T_{B})} + \overset{\overset{CO .Math. .Math. 2 .Math. .Math. in .Math. .Math. neutral .Math. .Math. gas}{}}{P_{ET} .Math. CO .Math. .Math. {2 [i - 1]}^{T} .Math. (V_{T} - V_{D} - {FG}_{1} .Math. T_{B})} + \\ \overset{\overset{\begin{matrix} CO .Math. .Math. 2 .Math. .Math. transfered .Math. .Math. into .Math. .Math. lung \\ from .Math. .Math. the .Math. .Math. circulation .Math. .Math. ({VB}_{CO .Math. .Math. 2}) \end{matrix}}{}}{PB .Math. Q .Math. (1 - s) .Math. T_{B} .Math. (C_{MV} .Math. CO .Math. .Math. 2 [i] - C_{p} .Math. CO .Math. .Math. 2 [i])} \end{matrix})}{\underset{\underset{Total .Math. .Math. volume .Math. .Math. of .Math. .Math. the .Math. .Math. alveolarspace}{}}{V_{T} + FRC}}$

[0273] 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.IO2[i]) and the partial pressure of CO2 in the controlled gas mixture (P.sub.ICO2[i]) can be set to induce target end-tidal partial pressures.

[0274] 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.

[0275] 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:

[00018] $P_{I} .Math. O .Math. .Math. 2 [i] = \frac{\begin{matrix} (P_{ET} .Math. O .Math. .Math. {2 [i]}^{T} - P_{ET} .Math. O .Math. .Math. {2 [i - 1]}^{T}) .Math. (FRC + V_{T}) + P_{ET} .Math. O .Math. .Math. {2 [i - 1]}^{T} .Math. \\ ({FG}_{1} .Math. T_{B}) - PB .Math. Q .Math. (1 - s) .Math. T_{B} .Math. (C_{MV} .Math. O .Math. .Math. 2 [i] - C_{p} .Math. O .Math. .Math. 2 [i]) \end{matrix}}{{FG}_{1} .Math. T_{B}}$ $P_{I} .Math. CO .Math. .Math. 2 [i] = \frac{\begin{matrix} (P_{ET} .Math. CO .Math. .Math. {2 [i]}^{T} - P_{ET} .Math. CO .Math. .Math. {2 [i - 1]}^{T}) .Math. (FRC + V_{T}) + P_{ET} .Math. CO .Math. .Math. {2 [i - 1]}^{T} .Math. \\ ({FG}_{1} .Math. T_{B}) - PB .Math. Q .Math. (1 - s) .Math. T_{B} .Math. (C_{MV} .Math. CO .Math. .Math. 2 [i] - C_{p} .Math. CO .Math. .Math. 2 [i]) \end{matrix}}{{FG}_{1} .Math. T_{B}}$

[0276] The above equations can be used to calculate the partial pressure of O2 in the controlled gas mixture (P.sub.IO2[i]) and the partial pressure of CO2 in the controlled gas mixture (P.sub.ICO2[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].sup.T), the target end-tidal partial pressure of CO2 from the previous breath (P.sub.ETCO2[i].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.MV O2[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.

[0277] Notice that where this form sequential rebreathing is employed, the anatomical dead space (V.sub.D) 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.

[0278] 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.TOR

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

[0279] Herein, the above general equations for calculating the composition of the controlled gas mixture reduce to the following:

[00019] $P_{I} .Math. O .Math. .Math. 2 [i] = \frac{P_{ET} .Math. O .Math. .Math. {2 [i]}^{T} .Math. {FG}_{1} - PB .Math. Q .Math. (1 - s) .Math. (C_{MV} .Math. O .Math. .Math. 2 [i] - C_{p} .Math. O .Math. .Math. 2 [i])}{{FG}_{1}}$ $P_{I} .Math. CO .Math. .Math. 2 [i] = \frac{P_{ET} .Math. CO .Math. .Math. {2 [i]}^{T} .Math. {FG}_{1} - PB .Math. Q .Math. (1 - s) .Math. (C_{MV} .Math. CO .Math. .Math. 2 [i] - C_{p} .Math. CO .Math. .Math. 2 [i])}{{FG}_{1}}$

[0280] 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).

[0281] 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.

[0282] 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.IO2[i]) and the partial pressure of CO2 in the controlled gas mixture (P.sub.ICO2[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.

[0283] 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.IO2[i]) and the partial pressure of CO2 in the controlled gas mixture (P.sub.ICO2[i]) may be converted a fractional concentration of O2 in the controlled gas mixture (F.sub.IO2[i]) and a fractional concentration of CO2 in the controlled gas mixture (F.sub.ICO2[i]).

[00020] $F_{I} .Math. O .Math. .Math. 2 [i] = \frac{P_{I} .Math. O .Math. .Math. 2 [i]}{PB}$ $F_{I} .Math. CO .Math. .Math. 2 [i] = \frac{P_{I} .Math. CO .Math. .Math. 2 [i]}{PB}$

Determine if Targets are Logistically Feasible

[0284] 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[i].sup.T) if:

1) The required partial pressures of gases in the controlled gas mixture are physically realizable:

0≦P.sub.IO2[i]≦PB a)

0≦P.sub.ICO2[i]≦PB b)

P.sub.IO2[i]+P.sub.ICO2[i]≦PB c)

2) The gas delivery device is capable of delivering a controlled mixture of the desired composition at the required flow rate
Where Sequential Rebreathing is Carried Out with a Hi-Ox.sub.SR Sequential Gas Delivery Circuit and a Gas Blender:

[0285] Assuming n.sub.SG 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.IO2[i]) and the required partial pressure of CO2 (P.sub.ICO2[i]) can be determined by solving the following set of equations:

[00021] ${.Math.}_{m = 1}^{^{n} .Math. SG} .Math. {FSG}_{m} [i] = {FG}_{1}$ ${.Math.}_{m = 1}^{^{n} .Math. SG} .Math. fo .Math. .Math. 2_{m} .Math. {FSG}_{m} [i] = \frac{P_{I} .Math. O .Math. .Math. 2 [i]}{PB} .Math. {FG}_{1}$ ${.Math.}_{m = 1}^{^{n} .Math. SG} .Math. fco .Math. .Math. 2_{m} .Math. {FSG}_{m} [i] = \frac{P_{I} .Math. CO .Math. .Math. 2 [i]}{PB} .Math. {FG}_{1}$

[0286] 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:

1)0≦P.sub.IO2[i]≦PB

2)0≦P.sub.ICO2[i]≦PB

3)P.sub.IO2[i]≦+P.sub.ICO2[i]≦PB

4) There exists a solution to the above system of equations, and

5)FSG.sub.m[i]≧0∀m

6) The gas blender is capable of delivering a controlled mixture of the desired composition at the required flow rate

[0287] It is therefore required that n.sub.SG≧3. It is computationally optimal to have n.sub.SG=3.

[0288] One possible set of gases is:

SG.sub.1: fco2.sub.1=0, fo2.sub.1=1
SG.sub.2: fco2.sub.2=1, fo2.sub.2=0
SG.sub.3: fco2.sub.3=0, fo2.sub.3=0

[0289] 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:

SG.sub.1: fco2.sub.1=0, fo2.sub.1=0.1
SG.sub.2: fco2.sub.2=0.4, fo2.sub.2=0.1
SG.sub.3: fco2.sub.3=0, fo2.sub.3=1

[0290] 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.

Adjusting Parameters to Make Logistically Infeasible Targets Logistically Feasible:

[0291] 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.IO2[i]) or the partial pressure of CO2 in the controlled gas mixture (P.sub.ICO2[i]) 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 the 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.

[0292] If P.sub.IO2[i]<0—The target end-tidal partial pressure of O2 (P.sub.ETO2[i]T is not logistically feasible because the partial pressure of O2 in the controlled gas mixture (P.sub.IO2[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.

[0293] If P.sub.IO2[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.IO2[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.

[0294] If P.sub.ICO2[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.ICO2[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.

[0295] If P.sub.ICO2[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.ICO2[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.

[0296] If P.sub.IO2[i]+P.sub.ICO2[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.IO2[i]) and the partial pressure of CO2 in the controlled gas mixture (P.sub.ICO2[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.

[0297] 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.n.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.IO2[i]) and the partial pressure of CO2 in the controlled gas mixture (P.sub.ICO2[i]) required to induce the targets are realizable with the current source gases.

[0298] 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

[0299] 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 measured 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.sup.M). 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.

Assume that End-Tidal Partial Pressures are Equal to the Baseline Measurements:

P.sub.ETO2[0].sup.T=P.sub.ETO2.sub.0.sup.M

P.sub.ETCO2[0].sup.T=P.sub.ETCO2.sub.0.sup.M

Assume Pulmonary End-Capillary Partial Pressures are Equal to End-Tidal Partial Pressures:

[0300]
P.sub.pO2[0]=P.sub.ETO2[0].sup.T

P.sub.pCO2[0]=P.sub.ETCO2[0].sup.T

Calculate O2 Blood Contents Assuming Steady State:

Pulmonary End-Capillary O2 Saturation:

[0301] [00022] $.Math. pH [0] = 6.1 + \log (\frac{[{HCO}_{3}]}{0.03 .Math. P_{p} .Math. CO .Math. .Math. 2 [0]})$ $S_{p} .Math. O .Math. .Math. 2 [0] = 100 .Math. \frac{- 8532.2289 .Math. z + 2121.401 .Math. z^{2} - 67.073989 .Math. z^{3} + z^{4}}{935960.87 - 31346.258 .Math. z + 2396.1674 .Math. z^{2} - 67.104406 .Math. z^{3} + z^{4}}$ $.Math. where$ $.Math. z = P_{p} .Math. O .Math. .Math. 2 [0] .Math. 10^{0.024 .Math. (37 - T) + 0.4 .Math. (p .Math. .Math. H [0] - 7.4) + 0.06 .Math. (\log .Math. .Math. 40 - \log .Math. .Math. P_{p} .Math. CO .Math. .Math. 2 [0])}$

Pulmonary End-Capillary O2 Content:

[0302] [00023] $C_{p} .Math. O .Math. .Math. 2 [0] = 1.36 .Math. Hb .Math. \frac{S_{p} .Math. O .Math. .Math. 2 [0]}{100} + 0.003 .Math. P_{p} .Math. O .Math. .Math. 2 [0]$

Mixed-Venous O2 Content:

[0303] [00024] $C_{MV (T)} .Math. O .Math. .Math. 2 [0] = C_{p} .Math. O .Math. .Math. 2 [0] - \frac{V .Math. O .Math. .Math. 2}{(1 - s) .Math. Q}$ $C_{MV} .Math. O .Math. .Math. 2 [0] = C_{MV (T)} .Math. O .Math. .Math. 2 [0]$

Arterial O2 Content:

[0304]
C.sub.aO2[0]=(1−s).Math.C.sub.pO2[0]+s.Math.C.sub.MVO2[0]

O2 Content of Each Compartment in the Model:

[0305] [00025] $For .Math. .Math. j = 1 .Math. .Math. .Math. .Math. .Math. n_{O .Math. .Math. 2}$ $C_{V} .Math. O .Math. .Math. 2_{j} [0] = C_{a} .Math. O .Math. .Math. 2 [0] - \frac{vo .Math. .Math. 2_{j} .Math. V .Math. .Math. O .Math. .Math. 2}{q_{j} .Math. Q}$

Calculate CO2 Blood Contents Assuming Steady State:

Pulmonary End-Capillary CO2 Content:

[0306] [00026] $C_{p} .Math. CO .Math. .Math. 2 [0] = (1.0 - \frac{0.02924 .Math. Hb}{(2.244 - 0.422 .Math. (\frac{Sp .Math. .Math. O .Math. .Math. 2 [0]}{100})) .Math. (8.740 - pH [0])}) .Math. C_{pl}$ $.Math. C_{pl} = 0.0301 .Math. P_{p} .Math. CO .Math. .Math. 2 [0] .Math. (1 + 10^{p .Math. .Math. H [0] - 6.10}) .Math. 2.226$

Mixed-Venous CO2 Content:

[0307] [00027] $C_{MV (T)} .Math. CO .Math. .Math. 2 [0] = C_{p} .Math. CO .Math. .Math. 2 [0] + \frac{V .Math. .Math. CO .Math. .Math. 2}{(1 - s) .Math. Q}$ $C_{MV} .Math. CO .Math. .Math. 2 [0] = C_{MV (T)} .Math. CO .Math. .Math. 2 [0]$

Arterial CO2 Content:

[0308]
C.sub.aCO2[0]=(1−s).Math.C.sub.pCO2[0]+s.Math.C.sub.MVCO2[0]

CO2 Content of Each Compartment in the Model:

[0309] [00028] $For .Math. .Math. k = 1 .Math. .Math. .Math. .Math. .Math. n_{CO .Math. .Math. 2}$ $C_{V} .Math. CO .Math. .Math. 2_{k} [0] = C_{a} .Math. CO .Math. .Math. 2 [0] + \frac{vco .Math. .Math. 2_{k} .Math. V .Math. .Math. CO .Math. .Math. 2}{q_{k} .Math. Q}$

Tuning the System

[0310] The parameters of the system can be tuned so that the measured end-tidal partial pressures of O2 (P.sub.ETO.sub.2[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.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.

Example Tuning Sequence:

[0311] The tuning sequence sets the target end-tidal partial pressure of O2 (P.sub.ETO2[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.

P.sub.ETO2[i].sup.T=P.sub.ETO2.sub.0.sup.M+5 i=1 . . . 60

P.sub.ETCO2[i].sup.T=P.sub.ETCO2.sub.0.sup.M+5 i=1 . . . 29

P.sub.ETCO2[i].sup.T=P.sub.ETCO2.sub.0.sup.M+10 i=30 . . . 60

[0312] 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].sup.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.ETCO2[30].sup.T−P.sub.ETCO2[29].sup.T)) [0313] α=200 ml/mmHg

[0314] In general, the correction factor (α) 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.

[0315] 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).

VO2=VO2.sub.0−β(P.sub.ETO2[60].sup.M−P.sub.ETO2[60].sup.T) β=10 ml/min/mmHg

[0316] 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.

[0317] 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).

VCO2=VCO2.sub.0+γ(P.sub.ETCO2[29].sup.M−P.sub.ETCO2[29].sup.T) γ=10 ml/min/mmHg

[0318] 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

[0319] In general, the correction factor (γ) 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.

General Requirements of a Tuning Sequence:

[0320] 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.

[0321] 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−1].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), reflect errors in the estimate of the functional residual capacity (FRC).

[0322] 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.ETO.sub.2[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. 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.

[0323] 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.

[0324] The tuning sequence described above is only an example of one sequence that can be used to tune the estimates of the physiological parameters.

[0325] 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−1].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.M−P.sub.ETCO2[i−1].sup.M) 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.

[0326] 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−1].sup.T). 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 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 O2. Therefore, 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.

[0327] 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 for a sufficiently long duration may be used to tune the estimate of the overall metabolic production of CO2.

[0328] 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.

[0329] Embodiments of mass balance equations:

[00029] $.Math. No .Math. .Math. SGD .Math. :$ $.Math. F_{I} .Math. X [i] = \frac{\begin{matrix} P_{ET} .Math. {X [i]}^{T} .Math. (FRC + V_{T}) - P_{ET} .Math. {X [i - 1]}^{T} .Math. (FRC + V_{D}) - \\ PB .Math. Q .Math. (1 - s) .Math. T_{B} .Math. (C_{MV} .Math. X [i] - C_{p} .Math. X [i]) \end{matrix}}{(V_{T} - V_{D}) .Math. PB}$ $.Math. SGD .Math. :$ $F_{I} .Math. X [i] = \frac{\begin{matrix} (P_{ET} .Math. {X [i]}^{T} - P_{ET} .Math. {X [i - 1]}^{T}) .Math. (FRC + V_{T}) + P_{ET} .Math. {X [i - 1]}^{T} .Math. \\ ({FG}_{1} .Math. T_{B}) - PB .Math. Q .Math. (1 - s) .Math. T_{B} .Math. (C_{MV} .Math. X [i] - C_{p} .Math. X [i]) \end{matrix}}{{FG}_{1} .Math. T_{B} .Math. PB}$

Example 1

[0330] 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=50 mm Hg, SD=1 mm; PetO.sub.2=100 mm Hg, SD=2 mm), normocapnia (100 seconds), hypercapnia (180 seconds), and normocapnia (110 seconds). FIG. 8, comprises a partial raw data set for 6 subjects.

[0331] The content of all of the patent and scientific references herein is hereby incorporated by reference.

REFERENCES

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APPARATUS TO ATTAIN AND MAINTAIN TARGET END TIDAL PARTIAL PRESSURE OF A GAS

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