US20150114394A1 - Method and apparatus to attain and maintain target arterial blood gas concentrations using ramp sequences - Google Patents

Method and apparatus to attain and maintain target arterial blood gas concentrations using ramp sequences Download PDF

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US20150114394A1
US20150114394A1 US14/398,034 US201314398034A US2015114394A1 US 20150114394 A1 US20150114394 A1 US 20150114394A1 US 201314398034 A US201314398034 A US 201314398034A US 2015114394 A1 US2015114394 A1 US 2015114394A1
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gas
petx
breath
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series
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Michael Klein
Joseph Fisher
James Duffin
Marat Slessarev
Cathie Kessler
Shoji Ito
Olivia Sobczyk
Anne Battisti-Charbonney
Daniel Michael Mandell
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Definitions

  • the present invention relates to an apparatus and method for controlling end tidal gas partial pressures in spontaneously breathing or ventilated subjects and to the use of such an apparatus and method for research, diagnostic and therapeutic purposes.
  • the end-tidal partial pressures of gases are determined by the gases inspired into the lungs, the mixed venous partial pressures of gases in the pulmonary circulation, and the exchange of gases between the alveolar space and the blood in transit through the pulmonary capillaries. Changes in the end-tidal partial pressures of gases are reflected in the pulmonary end-capillary partial pressures of gases, which in turn flow into the arterial circulation.
  • the gases in the mixed-venous blood are determined by the arterial inflow of gases to the tissues and the exchange of gases between the tissue stores and the blood, while the blood is in transit through the tissue capillary beds.
  • the mass balance equation is computed based on a tidal model of the lung as described hereafter.
  • a concentration of gas X for example in a first inspired gas (the first inspired gas also referred to, in one embodiment of the invention, as a controlled gas mixture) is computed to target or attain PetX[i] T in a respective breath [i].
  • F I X may be output from the mass balance equation by testing iterations of its value without directly solving for F I X.
  • the volume of gas delivered to the subject in a respective breath [i] comprises a first inspired gas of known volume and a second inspired neutral gas.
  • the mass balance equation is computed in terms of discrete respective breaths [i] including 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].
  • the invention is directed to a method of 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 the steps of:
  • a concentration of gas X (F I X) is computed to target or attain PetX[i] T in a respective breath [i].
  • the mass balance equation is solved for F I X.
  • the mass balance equation is computed based on a tidal model of the lung.
  • the mass balance equation is computed in terms of discrete respective breaths [i] including 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].
  • the method comprises the step of tuning one or more inputs required for computation of F I X, for example, with respect to any terms and/or by any methods described in this application.
  • the volume of inspired gas entering the subject's alveoli is controlled 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.
  • the gas inspired by the subject is inspired via a sequential gas delivery circuit (as defined below).
  • 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].
  • the gas inspired by the subject in each respective breath [i] comprises a first inspired gas and a second inspired optionally 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.
  • F I X 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 I X for the respective breath [i]
  • a “tidal model of the lung” means any model of the movement of gases into and out of the lung that acknowledges that inspiration of gas into, and the expiration of gas from the lung, occurs in distinct phases, each inspiration-expiration cycle comprising a discrete breath, and that gases are inspired in to, and expired from, the lungs via the same conduit.
  • a tidal model of lung is preferably understood to yield a value of F I X on a breath by breath basis from a mass balance equation.
  • the mass balance equation is computed in terms of discrete respective breaths [i] including 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].
  • the mass balance equation is solved for F I X.
  • the mass balance equation (optionally written in terms of one or more concentration of gas X in one or more discrete volumes of gas):
  • the individual respective tidal volume for a breath [i] may consist of a first inspired gas having a concentration of gas X corresponding to F I X and second inspired neutral gas.
  • the volume of the first inspired gas may be fixed, for example by controlling the rate of flow of first inspired gas into a sequential gas delivery circuit.
  • the mass balance equation comprises terms corresponding to all or an application-specific subset of the terms in equations 1 or 2 forth below as described hereafter.
  • An “application-specific subset” means a subset tailored to either a minimum, intermediate or logistically optimal standard of accuracy having regard to the medical or diagnostic application of the invention in question or the sequence of PetX[i] T values targeted.
  • Optional terms and mandatory inclusions in the subset may be considered application-specific as a function of the sequence of PetX[i] T values targeted in terms of the absolute size of the target value and/or the relative size of the target value going from one breath to the next as discussed below.
  • the O 2 or CO 2 re-inspired from the anatomical dead space (V D ) is small compared to the O 2 or CO 2 in the other volumes that contribute to the end-tidal partial pressures.
  • V D anatomical dead space
  • the O 2 or CO 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.
  • the demands of a diagnostic application may be ascertained empirically or from the literature. For example, a measure of short response times of brain blood vessels to hypercapnic stimulus can be determined to require a square wave change in the stimulus such as a change of 10 mmHg P ET CO 2 from one breath to the next. Another example is when measuring response of BOLD signal with MRI to changes in partial pressure of CO 2 in the blood, the changes needed may be determined to be abrupt as the BOLD signal has considerable random drift over time.
  • one or more inputs for computation of PetX[i] T are “tuned” as defined below to adjust, as necessary or desirable, estimated or measured values for FRC and/or total metabolic production/consumption of gas X so as to reduce the discrepancy between targeted and measured end tidal partial pressures of gas X i.e. an actual value, optionally measured at the mouth.
  • Tuning can be done when a measured baseline steady state value of PetX[i] is defined for a series of test breaths.
  • the present invention is directed to 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:
  • a concentration of gas X (F I X) is computed to target or attain PetX[i] T in a respective breath [i].
  • the mass balance equation is solved for F I X.
  • control system may implement one or more embodiments of the method described herein.
  • the gas delivery device is a sequential gas delivery device.
  • control system is implemented by a computer.
  • the computer provides output signals to one or more rapid flow controllers.
  • the apparatus is connected to a sequential gas delivery circuit.
  • 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 partial pressure of gas X (PetX[i] T ) for a series of respective breaths N.
  • 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, wherein a selected volume of the first inspired gas is delivered in the first part of a respective breath [i] followed by the second inspired neutral gas for the remainder of the respective breath [i], wherein volume of the first inspired gas is fixed or selected for one or more sequential breaths by way of user input so that intake of the second inspired neutral gas at least fill the entirety of the anatomic dead space.
  • the apparatus is connected to a sequential gas delivery circuit.
  • the gas delivery device is a gas blender.
  • control system implements program code stored in a computer readable memory or comprises a signal processor embodied in one or more programmable IC chips.
  • the present invention is directed to a computer program product for use in conjunction with a gas delivery device to control an amount of at least one gas X in a subject's lung to attain a target end tidal partial pressure of a gas X in the subject's lung, comprising program code for:
  • a concentration of gas X (F I X) is computed to target or attain PetX[i] T in a respective breath [i].
  • the mass balance equation is solved for F I X.
  • the computer program product may be used in conjunction with a gas delivery device, to at least partially implement a control system for carrying out one or more embodiments of the method described herein.
  • the present invention is directed to a method of 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 the steps of:
  • F I ⁇ X ⁇ [ i ] ( P ET ⁇ X ⁇ [ i ] T - P ET ⁇ X ⁇ [ i - 1 ] T ) ⁇ ( FRC + V T ) + P ET ⁇ X ⁇ [ i - 1 ] T ⁇ ( FG 1 ⁇ T B ) - PB ⁇ Q ⁇ ( 1 - s ) ⁇ T B ⁇ ( C MV ⁇ X ⁇ [ i ] - C p ⁇ X ⁇ [ i ] ) FG 1 ⁇ T B ⁇ PB eq .
  • a concentration of gas X (F I X) is computed to target or attain PetX[i] T in a respective breath [i].
  • the mass balance equation is solved for F I X.
  • the gas inspired by the subject in each respective breath [i] comprises a first inspired gas and a second inspired neutral gas (as define hereafter), wherein a selected volume of 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.
  • target used with reference to achieving a logistically attainable PetX[i] T value for a respective breath [i] means “attain” with the relative precision pragmatically demanded by the particular therapeutic or diagnostic application in question or the sequence of targets sought to be attained in both absolute and relative (between contiguous breaths) terms.
  • a logistically attainable end tidal partial pressure of gas X could be attained with relative precision in one breath.
  • a PetX[i] T can be considered to be “attained” as a function of the difference between the targeted value and a steady state value measured for an individual. For example, assuming a measurement error of +/ ⁇ 2 mm. of Hg, in the case of CO 2 , for a PetX[i] T between 30 and 50 mmHg, a measured PetCO 2 value that is within 1 to 3 mm.
  • Hg of PetX[i] T can be considered to be “attained”. Tuning to an extent that achieves a measured value within this range will serve as an indicator as to whether tuning has been successfully completed or should be continued. However in principle, tuning may be iterated until the difference between the measured and targeted PetX is minimized. However, for a PetCO 2 [i] T between 51 and 65 mmHg, a measured PetX value that is within (i.e +/ ⁇ ) 1 to 5 mm. of Hg of PetCO 2 [i] T can be considered to be “attained” and the success of a given tuning sequence can be judged accordingly.
  • a measured PetO 2 value that is within 5-10% of PetO 2 [i] T can be considered to be one which has “attained” PetO 2 [i] T .
  • the target PetO 2 value is between 75 mm of Hg and 150 mm of Hg a range of measured values that proportionately is within (i.e.
  • +/ ⁇ ) 4 mm and 8 mm of Hg (5 and 10% of 75 respectively) to +/ ⁇ 8 mm to 15 mm of Hg (5-10% of 150) can be considered to be attained (similarly for a target of 100 mm of Hg, +/ ⁇ 5-10 mm of Hg; and for a PetO2[i] T of 200 mm Hg, +/ ⁇ 10-20 mm of Hg).
  • a PetX[i] T can be considered to be “targeted” with a deliberately reduced precision (as opposed to “attained” as a goal) if parameters known to impinge on accuracy, that can be optimized (described herein e.g. tuning FRC and total metabolic consumption/production of gas X) are deliberately not optimized.
  • the invention as defined herein (not to the exclusion of variations apparent to those skilled in the art) is nevertheless exploited inasmuch as various aspects of the invention described herein provide for a prospective targeting system, a system that can be judiciously optimized (or not) to accommodate a variety of circumstances and sub-optimal uses thereof.
  • a PetX[i] T can be considered to have been “targeted” by exploiting the invention as defined, in one embodiment, after executing a sequence of tuning breaths, wherein the tuning sequence optionally establishes that the optimizations defined herein make the target “attainable”.
  • one or more inputs for computation of PetX[i] T are “tuned” as defined below to adjust, as necessary or desirable, estimated or measured values for FRC and/or total metabolic production/consumption of gas X so as to reduce the discrepancy between targeted and measured end tidal partial pressure of gas X i.e. an actual value, optionally measured at the mouth.
  • Tuning is preferably done when a measured baseline steady state value of PetX[i] is ascertained for a series of ensuing test breaths.
  • an estimated or measured value for the subject's functional residual capacity (FRC) is tuned.
  • FRC is tuned in a series of tuning breaths by:
  • FRC is tuned in a series of tuning breaths in which a sequence of end tidal partial pressures of gas X is targeted at least once by:
  • an estimated or measured value of the subject's total metabolic production or consumption of gas X is tuned.
  • the total metabolic production or consumption of gas X is tuned in a series of tuning breaths by comparing a targeted end tidal partial pressure of gas X (PetX[i+x] T ) for the at least one tuning breath [i+x] with a corresponding measured end tidal partial pressure of gas X for the corresponding breath [i+x] to quantify any discrepancy and adjusting the 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 I X.
  • a targeted end tidal partial pressure of gas X PetX[i+x] T
  • a corresponding measured end tidal partial pressure of gas X for the corresponding breath [i+x] to quantify any discrepancy
  • 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 I X.
  • the total metabolic consumption or production of gas X is tuned in a series of tuning breaths in which a sequence of end tidal partial pressures of gas X is targeted at least once by:
  • PetX[i] T differs from the baseline steady state value for PetX[i]; (c) comparing the targeted end tidal partial pressure of gas X (PetX[i+x] 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 . . .
  • the apparatus according to the invention is a “sequential gas delivery device” as defined hereafter.
  • the sequential gas delivery device optionally comprises a partial rebreathing circuit or a sequential gas delivery circuit as defined hereafter.
  • the rate of gas exchange between the subject's mixed venous blood and alveoli for a respective breath [i] may be controlled by providing a partial re-breathing circuit through which the subject inspires a first gas in which the concentration of gas X is F I X and a second gas having a partial pressure of gas X which is substantially equivalent to the partial pressure of gas X in the subject's end tidal expired gas prior to gas exchange in the current respective breath [i] (the subject's last expired gas which is made available for re-breathing) or a gas formulated in situ to match a concentration of gas X which would have been exhaled in a prior breath.
  • this may be accomplished by setting the rate of gas flow into the partial rebreathing circuit for a respective breath [i] to be less than the patient's minute ventilation or minute ventilation minus anatomic dead space ventilation (i.e. such that the last inspired second gas at least fills the anatomical dead space if not also part of the alveolar space) and using this rate or the volume of inspired gas it represents in a current breath to compute F I X for a respective breath [i].
  • the invention is also directed to a method of controlling an amount of at least one gas X in a subject's lung to attain, preliminary to or during the course of a diagnostic or therapeutic procedure, at least one target end tidal partial pressure of a gas X.
  • a input of a concentration of gas X in the mixed venous blood entering the subject's lung for gas exchange in the respective breath [i](C MV X[i]) can be obtained (e.g. predicted) by a compartmental modelling of gas dynamics.
  • “Compartmental modeling of gas dynamics” means a method in which body tissues are modeled as system of one or more compartments characterized in terms of parameters from which the mixed-venous return of gas X can be predicted. These parameters include the total number of compartments, the fraction of the total cardiac output received by the respective compartment, the respective compartment's storage capacity for gas X and the fraction of the overall production/consumption of gas X that can be assigned to the compartment.
  • the total number of compartments (ncomp) in the model must be known or selected, and then each compartment (k) is assigned a fraction of the total cardiac output (qk), a storage capacity for gas X (dXk), and a fraction of the overall production/consumption rate of gas X (vXk).
  • the storage capacity for any gas X in a compartment is known for an average subject of a particular weight, and then scaled proportional to the actual weight of the subject under test.
  • Modeling/predicting the mixed-venous return can be done for any gas X using the following information:
  • a formula for conversion of end-tidal partial pressures to blood content of gas X i.e. determining the content of the gas X in the pulmonary end-capillary blood based on data with respect to partial pressures).
  • gas X examples include isoflorane, carbon dioxide and oxygen.
  • Compartmental modeling of gas dynamics may be simplified using a single compartment model.
  • Means for controlling gas delivery typically include suitable gas flow controllers for controlling the rate of flow of one or more component gases.
  • the gas delivery may be controlled by a computer for example an integrated computer chip or an external computer running specialized computer readable instructions via which inputs, computations and other determinations of parameter and controls are made/handled.
  • the computer readable instructions may be embodied in non-transitory computer readable medium which be distributed as a computer program product.
  • logistically attainable target values for end tidal partial pressures of gas X may be set for respective breaths within a series breaths which are taken preliminary to or as part of a diagnostic or therapeutic procedure. Typically these values are defined in advance for the series or for at least part of the series of breaths. As described below, these individually logistically attainable values may be used to attain values in multiple breaths that are not logistically attainable in one breath.
  • the term “tuning” and related terms means that a value for an estimated or measured parameter that is required to compute F I X is adjusted, as necessary or desirable, to enable more precise computation of the F I X required to achieve a PetX[i] T , preferably based on observed differences between the target PetX[i] T set for one or more respective breaths and actual PetX[i] value(s) obtained for the respective breath(s), if any, such that post-adjustment observed value(s) more closely match the respective target value(s).
  • the tuned parameter(s) can be understood to fall into two categories: lung and non-lung related parameters.
  • the lung related parameter is FRC.
  • Non-lung related parameters are preferably tissue related parameters, preferably those required for computing a compartmental model of gas dynamics, preferably parameters governing total metabolic production or consumption of gas X in the body or the overall cardiac output, optionally parameters affecting assessment of the contribution of a respective compartment to the mixed venous content of gas X, preferably as a function of the production or consumption of gas X in the respective compartment, the assigned storage capacity for gas X in the respective compartment and the contribution of blood flow from the respective compartment to the total cardiac output, for example, by observing that a repeatedly targeted value does not drift when attained.
  • Drift can be defined in the negative or considered to have been corrected for, for example, if an adjusted value for a tissue related parameter results in a variation of no greater than 1 to 2 mm of Hg (ideally approximately 1 mm of Hg or less) between observed and targeted end tidal values of gas X for a series of 5 consecutive breaths (i.e. where the end tidal partial pressure of gas X is sought to be maintained for a series of breaths e.g. 30 breaths and observed drift is corrected).
  • Tuning FRC is important for transitioning accurately between end-tidal values.
  • Tuning non-lung related parameters e.g. VCO2 is important so that the steady state error between end-tidal values is small.
  • the tuning requirements depend on the goals of the targeting sequence. For example, in the case of inducing a step increase in the end-tidal partial pressure of CO2 from 40 mmHg to 50 mmHg, if attaining 50 mmHg in the first breath is important, FRC is preferably tuned. If achieving 50 mmHg in the first breath is not vital, but achieving this target in 20 breaths is all that may matter, a non-lung related parameter such as VCO2 should be tuned.
  • both FRC and a non-lung related parameter should be tuned. If you don't care if you get to 50 mmHg in the first breath, and then drift to 55 after 20 breaths, don't tune either.
  • Tuned FRC (good transition), untuned VCO2 (bad steady state error)—40, 50, 51, 52, 53, 54, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55 Untuned FRC (bad transition), tuned VCO2 (no steady state error)—40, 50, 56, 53, 52, 51, 50, 50, 50, 50, 50, 50, 50 Tuned FRC (good transition), tuned VCO2 (no steady state error)—40, 50, 50, 50, 50, 50, 50, 50 Untuned FRC (bad transition), untuned VCO2 (bad steady state error)—40, 62, 60, 58, 57, 56, 55, 55, 55, 55, 55.
  • a target would be set for each respective breath [i] and that target would be effectively attained with a degree of accuracy and immediacy necessary for the application in question. Accordingly, a tidal based model for targeting end tidal partial pressure of a gas X provides a tunable flexible system for attaining those targets in line with a wide variety of objectives of the user.
  • this tuning can be applied independently to each of the gases that are being targeted, as each gas can be targeted independently of the other gases.
  • An attainable target may be maintained in one or more subsequent breaths by setting the target end tidal value for the respective breath to be the same as PetX[i ⁇ 1].
  • a target that is not attainable in one breath may be obtained in a series of breaths [i] . . . [i+n].
  • a particular end tidal partial pressure is not logistically attainable in one breath. If logistically attainable at all, such a target may be logistically attained only after multiple breaths. In contrast to methods requiring negative feedback, such as dynamic end tidal forcing, in one aspect of the method of the present invention this number of breaths may be pre-defined prospectively. This number of breaths may also be minimized so that the ultimate end tidal target is attained as rapidly as logistically feasible, for example by simple computational trial and error with respect to an incremented series of target.
  • logistic constraints could be seen as limitations to inhaling the amount of the gas X that needs to be inhaled to reach a target concentration on the next breath; this could be because of limitations of available concentration X, or volume of inspired gas or both.
  • Mandatory constraints are at least those inherent in any method of controlling the end tidal partial pressure of a gas X by way of inhalation of concentrations of gas X in that F I X cannot be less 0% and greater than 100% for any given breath. Constraints may also be selected as a matter of operational necessity or efficiency so called “operational constraints” which may be self-imposed but not mandatory in all cases.
  • the model of gas dynamics that is used to predict C MV X[i] in the mixed venous blood entering the subject's lung for gas exchange in the respective breath [i] estimates a value of C MV X[i]) by: (a) dividing tissues to which the subject's arterial blood circulates into one or more compartments (k); and (b) determining the contribution of a respective compartment to the mixed venous content of gas X as a function of the production or consumption of gas X in the respective compartment, the assigned storage capacity for gas X in the respective compartment and the contribution of blood flow from the respective compartment to the total cardiac output or pulmonary blood flow.
  • gas X is carbon dioxide
  • the content of carbon dioxide in the mixed venous blood leaving a compartment C v CO2 k [i] is determined by assigning to a compartment a fraction of the overall metabolic carbon dioxide production (vco2 k ), a fraction of the total cardiac output (q k ) and a storage capacity for carbon dioxide (dCO2 k ).
  • the afore-described system is a prospective end-tidal targeting system.
  • the tissue model Prior to execution of an end-tidal targeting sequence, the tissue model is used to predict the time course of the mixed-venous blood gases that will result from ideal execution of the sequence.
  • the time course of predicted mixed-venous gases is used to compute the series of inspired gas mixtures required to realize the target end-tidal partial pressures of gases.
  • the end-tidal partial pressures of gases adhere to the targets allows prediction of the mixed-venous gases
  • prediction of the mixed-venous gases allows a priori calculation of the inspired gas mixtures required to accurately implement the end-tidal targets.
  • the system is tuned to obtain tuned values for certain parameters before execution of the sequence so that the end-tidal partial pressures of gases induced during sequence execution closely adhere to the target functions without the need for any feedback control.
  • the program code includes code for directing a suitable gas delivery device such as a rapid flow controller to deliver a gas X containing gas having an F I X output from a mass balance equation.
  • gas delivery means by contrast to gas delivery device refers to a discrete component of a gas delivery device that is used to control the volume of gas delivered at a particular increment in time such as a rapid flow controller.
  • each of the key method steps for carrying out the invention can be functionally apportioned to different physical components or different computer programs and combinations of both.
  • a device according to the invention will optionally comprise one or more physical components in the form of a gas analyzer, a pressure transducer, a display, a computer, a gas delivery device such as a rapid flow controller, a gas channeling means (gas conduits/tubes), standard electronic components making up a PCB, input devices for setting parameters etc.
  • the various means for carrying out these steps include without limitation one in the same physical means, or different physical means on different devices, the same device or the same device component. Depending on the number of added gases these components may multiplied or where possible shared.
  • the present invention is also directed to a device comprising an integrated circuit chip configured for carrying out the method, or a printed circuit board (comprising discrete or integrated electronic components).
  • the device optionally includes at least one gas delivery means such as a rapid flow controller.
  • the device optionally includes an input device for inputting various parameters described herein. The parameters can be input via a variety of means including, but not limited to, a keyboard, mouse, dial, knob, touch screen, button, or set of buttons.
  • any input, computation, output, etc. described herein can be accomplished by a variety of signal processing means including, but not limited to, a programmable processor, a programmable microcontroller, a dedicated integrated circuit, a programmable integrated circuit, discrete analog or digital circuitry, mechanical components, optical components, or electrical components.
  • signal processing steps needed for executing the inputs, computations and outputs can physically embodied in a field programmable gate array or an application specific integrated circuit.
  • blending may be used to describe the act of organizing delivery of one gas in conjunction with at least one other and hence the term blending optionally encompasses physical blending and coordinated release of individual gas components.
  • a signal processor or processing device in the form of a computer may use machine readable instructions or dedicated circuits to perform the functions contemplated herein including without limitation by way of digital and/or analog signal processing capabilities, for example a CPU, for example a dedicated microprocessor embodied in an IC chip which may be integrated with other components, for example in the form of a microcontroller.
  • Key inputs may include input signals from—a pressure transducer, a gas analyzer, any type of input device for inputting a target end tidal partial pressure of gas X (for example, a knob, dial, keyboard, keypad, mouse, touch screen etc.), input from a computer readable memory etc.
  • Key outputs include output of the flow and/or composition of gas required to a flow controller.
  • a compartmental model for mixed venous blood carbon dioxide dynamics may assign body tissues to k compartments e.g. 5 compartments and assign the contribution of a respective compartment to the mixed venous content of carbon dioxide as a function of the production of carbon dioxide in the respective compartment, the assigned storage capacity for carbon dioxide in the respective compartment and the contribution of blood flow from the respective compartment to the total cardiac output.
  • the present invention is directed to a non-transitory computer readable memory device having recorded thereon computer executable instructions for carrying out one or more embodiments of the above-identified method.
  • the invention is not limited by a particular physical memory format on which such instructions are recorded for access by a computer.
  • Non-volatile memory exists in a number of physical forms including non-erasable and erasable types. Hard drives, DVDs/CDs and various types of flash memory may be mentioned.
  • the invention in one broad aspect, is directed to a non-transitory computer readable medium comprising computer executable instructions for carrying out one or more embodiments of the above-identified method.
  • the instructions may take the form of program code for controlling operation of an electronic device, the program code including code for carrying out the various steps of a method or control of an apparatus as defined above.
  • a “gas delivery device” means any device that can make a gas of variable/selectable composition available for inspiration.
  • the gas delivery apparatus may be used in conjunction with a ventilator or any other device associated with a breathing circuit from which the subject is able to inspire a gas of variable/controllable composition without substantial resistance.
  • the composition of the gas and/or flow rate is under computer control.
  • such a device may be adapted to deliver at least one gas (pure or pre-blended) at a suitable pre-defined rate of flow.
  • the rate of flow may be selectable using a form of input device such a dial, lever, mouse, key board, touch pad or touch screen.
  • the device provides for one or more pure or blended gases to be combined i.e. “a gas blender”.
  • a “gas blender” means a device that combines one or more stored (optionally stored under pressure or delivered by a pump) gases in a pre-defined or selectable proportion for delivery a selectable rate of flow, preferably under computer control.
  • stored gases may be combined with pumped room air or a combination of pure or blended (each blended gas may have at least 10% oxygen for safety) gases respectively contain one of carbon dioxide, oxygen and nitrogen as the sole or predominant component.
  • the selectable proportion is controlled automatically using an input device, optionally by variably controlling the flow of each stored gas (pure or pre-blended) separately, preferably using rapid flow controllers, to enable various concentrations or partial pressures of a gas X to be selected at will within a pre-defined narrow or broad range.
  • a suitable blender may employ one or more gas reservoirs, or may be a high flow blender which blows gas past the mouth i.e. in which gas that is not inspired is vented to the room.
  • a “partial rebreathing circuit” is any breathing circuit in which a subject's gas requirements for a breath are made up in part by a first gas of a selectable composition, and a rebreathed gas to the extent that the first gas does not fully satisfy the subject's volume gas requirements for the breath.
  • the first gas must be selectable in at least one of composition or amount. Preferably the amount and composition of the first gas is selectable.
  • the rebreathed gas composition optionally consists of previously exhaled gas that has been stored or a gas formulated to have the same concentration of gas X as previously exhaled gas or a second gas has a gas X concentration that is selected to correspond (i.e. has the same concentration) as that of the targeted end tidal gas composition for a respective breath [i].
  • the circuit is designed or employable so that the subject receives the entirety of or a known amount of the first gas in every breath or in a consecutive series of breaths forming part of gas delivery regimen.
  • a re-breathed gas serves a key role in that it does not contribute significantly to the partial pressure gradient for gas flow between the lung and the pulmonary circulation when intake of the gas at least fills the entirety of the anatomic dead space. Therefore, in the case of a spontaneously breathing subject (whose tidal volume is not controlled e.g. via a ventilator) the subject's unpredictable tidal volume does not defeat prospective computation of the controlled gas composition required to attain or target PetX[i] for a respective breath [i].
  • the “rebreathed gas” may be constituted by or substituted by a prepared gas (in terms of its gas X content).
  • the second gas has a gas X concentration that is selected to correspond to that of the targeted end tidal gas composition for a respective breath [i].
  • the volume of the first inspired gas may also be adjusted (e.g. reduced) to target PetX[i] T for a respective breath [i] such that the subject receives an optimal amount of a gas having a gas X concentration that corresponds to PetX[i] T .
  • the gas X content of a prepared gas can be formulated to represent a gas of a “neutral” composition.
  • the total inspired gas for a respective breath [i] will comprise a first inspired gas having a controlled volume and gas X concentration (F I X) and a second gas which has a gas X content whose contribution to establishing a partial pressure gradient between the lung and pulmonary circulation is optionally minimized.
  • the second inspired gas content of gas X can be optimized to attain a targeted end tidal concentration (for a universal set of circumstances) and in a sub-optimal sense this concentration at least does not defeat the ability to prospectively compute an F I X for the purposes of attaining or targeting a PetX[i] for a respective breath [i] (i.e. not knowing the subject's tidal volume for a respective breath [i] will not preclude such computation).
  • “Prospectively” or a “prospective computation” means, with reference to a determination of an amount of gas X required to be inspired by the subject in an inspired gas to attain or target a PetX[i] T for a respective breath [i] (optionally computed in terms of F I X), using inputs required to compute a mass balance equation (preferably including C MV X[i]), without necessary recourse to feedback to attain rapidly and repeatably.
  • the system of the present invention is adapted to attain logistically achievable end tidal values rapidly and accurately (as defined herein) without recourse to feedback.
  • a negative feedback system suffers from an inherent trade-off between response time and stability. According to the present invention, recourse to feedback is designed to be unnecessary for the purpose of attaining logistically achievable PetX targets rapidly and predictably.
  • Gas composition analysis is performed by continuously drawing gas from proximal to the subject's airway into a gas analyzer through a sampling catheter.
  • the gas analyzer returns a time varying signal of gas composition which is, however, delayed from the actual ventilatory phase of the subject by the travel time through the sampling catheter and the response time of the gas analyzer. Therefore, at the start of any inspiration, the end-tidal partial pressures of gases from the immediately previous breath are not yet known.
  • the sampling catheters are long, such as in an MRI environment where the patient is in the MRI scanner and the gas analyzers must be placed in the control room, this delay can reach three or more breaths. As in any negative feedback system, this delay in measuring the controlled parameter will further destabilize and limit the response time of the system.
  • a “sequential gas delivery device” means, with respect to delivering a gas in successive respective breaths [i], a device for delivery of a controlled gas mixture in the first part of a respective breath [i] followed by a “neutral” gas in the second part of the respective breath [i].
  • a controlled gas mbcture is any gas that has a controllable composition with respect to one or more gases of interest used to compose it. Accordingly, where the gas of interest is a gas X, the controlled gas mixture has an amount of gas X, optionally defined in terms of a concentration of gas X denoted as F I X.
  • the controlled gas mixture may be referred to, for convenience, as a first inspired gas.
  • Gas inspired in any breath is “neutral”, inter alia, if it has the same composition as gas expired by the subject in a previous breath.
  • the term “neutral” gas is used because the gas in question is one which has the same partial pressure of one or more gases of interest as the blood, in the alveoli, or in the pulmonary capillaries, and hence, upon inspiration into the alveolar space, in the second part of a respective breath, this gas does not exchange any gas with the pulmonary circulation.
  • a gas of interest is generally one for which the end tidal partial pressure is sought to be controlled according to the invention.
  • a volume of gas that enters the alveolar space and exchanges gas with the pulmonary circulation for a breath [i] may be defined independently of a fixed tidal volume, for example by:
  • the rebreathing circuit is a sequential gas delivery circuit.
  • volume of gas that enters the alveolar space and exchanges gas with the pulmonary circulation is determined by utilizing a fixed tidal volume set for the respective breath (e.g. using a ventilator) and subtracting a volume corresponding to the subject's anatomic dead space volume.
  • the F I X may be set independently of the concentration of any other component of the inspiratorygas.
  • a gas X and a gas Y are components of the inspired gas and a target arterial concentration of gas X and a target arterial concentration of a gas Y are selected for a respective breath, independently of each other, and, if present, independently of the concentration of any other component Z of the inspiratory gas.
  • a mass balance equation that comprises terms “corresponding to” all or an application-specific subset of the terms in equations 1 or 2 above means that the same underlying parameters are accounted for.
  • the invention is directed to an apparatus for controlling an amount of at least one gas X in a subject's lung to attain a series of targeted end tidal partial pressures of at least one gas X (PetX T ), the series of targeted end tidal partial pressures of at least one gas X (PetX T ) adapted to stimulate a physiological response, the apparatus comprising:
  • control system for controlling the gas delivery device, wherein the control system is adapted to target a series of PetX T values for a respective series of intervals, the control system including means for:
  • the series of PetX T values preferably comprise at least one of a set of PetX T increments and a set of PetX T decrements.
  • interval is used broadly to mean a time interval of selected length, an interval defined by the duration of a respective inspiratory cycle and a previous or ensuing expiratory cycle, for example, a respective breath [i] defined by an inspiratory cycle and the expiratory cycle which follows it, and/or an interval defined by a pattern of a physiological response.
  • pattern of a physiological response means a pattern sufficient to define a dose-response (stimulus-response) relationship for a full range of the physiologic response or for at least a part thereof that reveals a pattern of interest, wherein the increments in dose or stimulus are selected to disclose the true shape of the dose response curve.
  • a portion of interest may of diagnostic or medical interest to define a normal pattern of the response for example to differentiate between variations in a normal response for different groups e.g. ages, and optionally a differential response e.g. particular range or prevalence of a response or a different or pathologic response, associated with a condition or disease.
  • a pattern may disclose a linear, exponential or sigmoidal dose response curve for an individual or group of common individuals selected from at least one of persons having a ‘normal’ physiological response and persons disclosing a different or pathological physiological response.
  • a pattern may disclose that a response is sigmoidal and not linear (e.g.
  • an interval of diagnostic interest may be a fraction of the amount of time required to observe the time course of the response wherein the fraction is sufficiently small to obtain a set of values defining the pattern of response.
  • the ramp sequence may also be selected to determine a time course of a full or partial range of a physiological response by tracking signals signifying that a particular condition, associated with a direct or indirect measure of the response, has been met, the condition preferably of the type satisfied by attainment or projected attainment of a threshold amount change in a measurable parameter correlated with a physiologic response to a stimulus comprising or consisting of an increment or decrement in a subject's end tidal partial pressure of gas X.
  • a fraction or proportionate amount of a time period required to observe a continuous time course of a physiological response or satisfy a set threshold amount of change in the response is then defined to be sufficient to demarcate the end of a previous interval and the beginning of a next ensuing interval.
  • the time course may be selected to grade individuals in terms of the overall appearance of the pattern (measurement of a continuous variable) or differentiate between populations with respect satisfying one or more individual criteria (e.g. a discontinuous variable eliciting a yes/no answer).
  • a gas delivery device can be controlled to attain a series of targeted end tidal partial pressures of at least one gas X (PetX T ) by the prospective model described herein; or by a combination of a prospective model and feedback control (known as dynamic end tidal forcing), for example, wherein the feedback loop (e.g. using a PID controller) adds a control signal to adjust a prospective determination of F I X; the control signal generated based on the difference between the target and measured end tidal values.
  • Computation of FIX can be accomplished using the tidal model equations herein by adapting the continuous flow equations published by Robbins and Swanson.
  • the invention is directed to a method of controlling an amount of at least one gas X in a subject's lung to attain at least one targeted end tidal partial pressure of the at least one gas X, comprising the steps of:
  • a Obtaining input of a logistically attainable end tidal partial pressure of gas X (PetX[i] T ) for a series of respective breaths [i]; b. 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] T for a respective breath [i] using inputs required to compute a mass balance equation, 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 optionally c.
  • the respective PetX[i] T for the series of breaths [i] increases every Nth breath in respective selected increments (“Z”) from the start of the series to the end of the series (from PetX[i 1 ] T to PetX[i n ] T ), wherein either N equals 1 and Z is greater than 0 in each breath in the series, or N is greater than 1 and Z may be zero in breaths which are not the Nth breath and Z is greater than 0 in every Nth breath.
  • the respective PetX[i] T for the series of breaths [i] decreases every Nth breath in respective selected decrements (“Z”) from the start of the series to the end of the series (from PetX[i 1 ] T to PetX[i n ] T ), wherein either N equals 1 and Z is greater than O, or N is greater than 1 and Z may be zero in breaths which are not the Nth breath and Z is greater than 0 in every Nth breath
  • PetX[i] T may change every Nth breath in respective selected increments or decrements (“Z”) from the start of the series to the end of the series (from PetX[i 1 ] T to PetX[i n ] T ), wherein N equals 1 and Z is greater than 0.
  • N is greater than 1 and Z may be zero in breaths which are not the Nth breath.
  • Embodiments in which PetX[i 1 ] T increases include the following.
  • Z is changing and for the series of fifty breaths as follows: Z equals, respectively 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8 0, 0, 0, 0, 0, 0, 8.
  • Z is selected to correspond to a selected rate of change in a physiological response to a stimulus (the stimulus being a correlate of PetX[i] T such as the arterial partial pressure of gas X (PaX)).
  • the selected rate of change corresponds to a rate wherein a targeted physiologic response is substantially realized for each increment/decrement before the next increment/decrement, such that successive measurements of the response are substantially matched to an increment/decrement in a change in stimulus. Accordingly, it is possible to plot the change in response with respect to the change in PetX[i] T with substantial accuracy.
  • the rate of change in PetX[i] T may be selected such that three time constants in the progress of the response (approximately 95% response) are achieved before the next increment/decrement in PetX[i] T stimulus is given.
  • a time interval for executing the range in stimulus “R” or the range (extent) of the expected response “r” may be selected and the target change per breath in stimulus readily mathematically determined. For example, with respect to ramping up PetCO 2 [i] T from 35 to 50 mm of Hg over a selected time period (e.g. approx. 5 minutes) increasing PetCO 2 [i] T approx. 0.25 mm Hg every breath may define a suitable ramp sequence.
  • this rate may be corroborated.
  • a greater than 95% CVR response to a change in PaCO 2 may be determined to be achieved in 16-18 seconds.
  • increments of 1 mm of Hg every 16 second would be suitable.
  • the time interval over which the response is measured and the range of change in stimulus range may be input to facilitate execution of a ramp sequence so that a series of PetCO 2 [i] T targets for the intervening breaths may be correspondingly obtained.
  • N is advantageously 1, 2 or 3 breaths, optionally 1 breath, and Z is the optionally the same for each increase, depending on the total time interval for executing the range in stimulus Z or desired response range optionally ranging from 0.2 to 2 mm Hg.
  • N is advantageously 1 to 5
  • Z is the optionally the same for each increase, Z ranging from 1 to 20 mm Hg.
  • a “ramp sequence” where the targets are increased or decreased at a rate selected for observing a substantial response to an increment or decrement in stimulus (termed a “ramp sequence”); e.g. with respect to an exponential response, optionally at least a response corresponding to two time constants, optionally at least a 90-95% response or a response corresponding to three time constants, optionally approximately linearly with respect to time, the response (e.g. CVR) to a change in the end tidal concentration of gas X e.g. carbon dioxide, is substantially achieved within a given time increment e.g.
  • gas X e.g. carbon dioxide
  • the invention is also directed to 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:
  • a gas delivery device (2) a control system for controlling the gas delivery device including means 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 MV X[i]); b. Obtaining input of a logistically attainable end tidal partial pressure of gas X (PetX[i] T ) for a respective breath [i]; c.
  • N may be fixed at 1 in which case Z will be greater than 0 or N is greater than 1 and Z may be zero in breaths which are not the Nth breath and Z is greater than 0 in every Nth breath.
  • FIG. 1 is a schematic overview of the movement of blood and the exchange of gases throughout the entire system.
  • FIG. 2 is a detailed schematic representation of the movement of blood and the exchange of gases at the tissues.
  • 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.
  • 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.
  • 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.
  • FIG. 6 is a graphic representation of a tuning sequence and observed errors that can be used to tune model parameters.
  • FIG. 7 is a Table of abbreviations (Table 1) used in the specification
  • FIGS. 8 a and 8 b are graphical representations of changes in target end tidal values of CO2 and response—mid-cerebral artery blood flow velocity, for a slow responder and a fast responder as revealed by a ramp sequence.
  • FIG. 9 is a graphical representation of blood flow responses to PCO 2 predicted for the model of a brain vascular territory with a partially-stenosed vessel branch and a healthy branch in parallel as revealed by a ramp sequence.
  • the invention is described hereafter in terms of one or more optional embodiments of a gas X, namely carbon dioxide and oxygen.
  • Mass balance equations of gases in the lung are conventionally derived from a continuous flow model of the pulmonary ventilation.
  • ventilation is represented as a continuous flow through the lungs, which enters and exits the lungs through separate conduits.
  • the anatomical dead space would not factor into the mass balance other than to reduce the overall ventilatory flow into the alveolar space.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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].
  • 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.
  • a second gas delivery device e.g. a gas blender
  • 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.
  • 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.
  • Gas expired in previous breaths, collected in a reservoir, is re-inspired in a subsequent breath.
  • 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.
  • 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.
  • 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.
  • 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.
  • a second gas source for example a second reservoir
  • 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.
  • 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.
  • 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.
  • the partial pressures of gases in the pulmonary blood equilibrate with the partial pressure of gases in the lungs (P 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 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.
  • the gas contents of the arterial blood 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 MV [i]).
  • the arterial blood flows through the tissue capillary beds, where gases are exchanged between the blood and the tissues.
  • tissue capillary beds 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 can be determined from these characteristics.
  • the gas contents of the mixed-venous blood leaving the tissues (C 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 R ).
  • FIG. 2 The Tissues
  • the total blood flow (Q) enters the tissue capillary beds from the arterial circulation, where the gas contents of the arterial blood (C a [i]) are modified by gas exchange between the blood and the tissues.
  • 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 can be determined from the arterial inflow of gases, and the assumed production or consumption, and storage of the gas in the compartment.
  • FIG. 3 the Lungs (No Sequential Rebreathing)
  • 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 MV [i]) entering the pulmonary circulation and the gas contents of the pulmonary end-capillary blood (C p [i]) leaving the pulmonary circulation.
  • the starting volume of the lungs in any breath is given by the functional residual capacity (FRC).
  • FRC functional residual capacity
  • 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 ET [i ⁇ 1] T ).
  • the first part of inspiration draws gas in the anatomical dead space (V 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.
  • VG 1 a volume of a controlled gas mixture with controllable partial pressures of gases (P 1 [i]) is inspired.
  • FIG. 4 the Lungs (Sequential Rebreathing)
  • 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 MV [i]) entering the pulmonary circulation and the gas contents of the pulmonary end-capillary blood (C p [i]) leaving the pulmonary circulation.
  • the starting volume of the lungs in any breath is given by the functional residual capacity (FRC).
  • FRC functional residual capacity
  • 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 ET [i ⁇ 1] T ).
  • the first part of inspiration draws gas in the anatomical dead space (V 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.
  • VG 1 a volume of a controlled gas mixture with controllable partial pressures of gases (P I [i]) is inspired.
  • the average volume of the controlled gas mixture inspired into the alveoli in each breath is given by the flow rate of the controlled gas mixture (FG 1 ) to the sequential gas delivery circuit (SGDC) delivered over one breath period (T B ).
  • the balance of the tidal volume (V T ) is composed of a volume of neutral gas (VG 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
  • the apparatus consists of a gas blender (GB), a Hi-OX 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 1 , SG 2 , SG 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.
  • FIG. 6 Tuning
  • parameters representing inputs for computation of F I X can be tuned so that the measured end-tidal partial pressures of O2 (P ET O2[i] M ) and the measured end-tidal partial pressures of CO2 (P ET O2[i] M ) during any sequence more closely reflect the target end-tidal partial pressures of O2 (P ET O2[i] T ) and the target end-tidal partial pressures of CO2 (P ET CO2[i] T ).
  • 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.
  • 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 (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.
  • the bicarbonate concentration ([HCO 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).
  • 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).
  • 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):
  • 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).
  • 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:
  • the breath period (T B ) can be measured using a pressure transducer (PT) or flow transducer (FT) proximal to the subject's airway.
  • PT pressure transducer
  • FT flow transducer
  • 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.
  • n R The number of breaths for recirculation to occur (n 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 B ) and an average recirculation time (0.3 min) (28) according to the relationship:
  • n R 0.3 /T B
  • the overall metabolic O2 consumption 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:
  • VCO2 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:
  • V CO2 0.8 ⁇ V O2
  • the functional residual capacity (FRC) can be measured using a variety of respiratory manoeuvres (31). If measurement is not available or possible, it can be estimated from the subject's height (H), age (A), and sex (G) according to the relationship:
  • V D 1.765 ⁇ W+ 32.16 for males
  • V D 1.913 ⁇ W+ 21.267 for females (36)
  • the rate at which the controlled gas mixture is made available for inspiration should be set so that the volume of the neutral gas inspired in each breath (VG 2 ) is greater than or equal to the anatomical dead space (V 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.
  • V T The tidal volume (V 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 1 ) is made available for inspiration (FG 1 ), the breath period (T B ), and the anatomical dead space (VD) according to the empirical relationship:
  • V T FG 1 ⁇ T B +V D
  • 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.
  • the operator enters a target sequence of n breaths consisting of a target end-tidal partial pressures of O2 (P ET O2[i] T ) and a target end-tidal partial pressure of CO2 (P ET CO2[i] T ) for every breath (i) of the sequence.
  • pH of the pulmonary end-capillary blood (pH[i]) can be calculated from the Henderson Hasselbalch equation using the blood bicarbonate concentration ([HCO 3 ]), the blood CO2 partial pressure (P p CO2[i]), and the solubility of CO2 in blood (0.03 mmol/L/mmHg) (9).
  • pH ⁇ [ i ] 6.1 + log ⁇ ( [ HCO 3 ] 0.03 ⁇ P p ⁇ CO ⁇ ⁇ 2 ⁇ [ i ] )
  • the O2 saturation of pulmonary end-capillary blood (S p O2[i]) can be calculated from experimental equations using the body temperature (T), the blood pH (pH[i]), the blood CO2 partial pressure (P p CO2[i]), and the blood O2 partial pressure (P p O2[i]) (42).
  • CO2 content of pulmonary end-capillary blood can be calculated from the blood haemoglobin concentration (Hb), the O2 saturation of the blood (S p O2[i]), the blood pH (pH[i]), and the blood CO2 partial pressure (P p CO2[i]) (45).
  • 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).
  • the content of O2 in the arterial blood (C a O2[i]) is a weighted average of the O2 content of the pulmonaryend-capillary blood (C p O2[i]) and the O2 content of the blood which is shunted directly from the mixed-venous circulation (C MV O2[i]).
  • the content of CO2 in the arterial blood (C a CO2[i]) is a weighted average of the CO2 content of the pulmonary end-capillary blood (C p CO2[i]) and the CO2 content of the blood which is shunted directly from the mixed-venous circulation (C MV CO2[i]).
  • each compartment (j) represents a single tissue or group of tissues.
  • Each compartment is assigned a storage capacity for O2 (dO2 j ).
  • Each compartment is also modelled as being responsible for a fraction (vo2 j ) of the overall metabolic O2 consumption (VO2), and receiving a fraction (q j ) of the total cardiac output (Q).
  • the content of O2 in the venous blood leaving a compartment (C V O2 j [i]) is equal to the content of O2 in the compartment.
  • C V ⁇ O ⁇ ⁇ 2 j ⁇ [ i ] C V ⁇ O ⁇ ⁇ 2 j ⁇ [ i - 1 ] + 100 ⁇ T B d ⁇ ⁇ O ⁇ ⁇ 2 j ⁇ ( q j ⁇ Q ⁇ ( C a ⁇ O ⁇ ⁇ 2 ⁇ [ i ] - C V ⁇ O ⁇ ⁇ 2 j ⁇ [ i - 1 ] ) - vo ⁇ ⁇ 2 j ⁇ VO ⁇ ⁇ 2 )
  • the model assumes a single compartment with a storage capacity for O2 (dO2 k ) proportional to the subjects weight (W) (49).
  • the mixed-venous O2 content leaving the tissues (C MV(T) O2[i]) is the sum of the O2 content leaving each compartment (C V O2 j [i]) weighted by the fraction of the cardiac output (q j ) received by the compartment.
  • the O2 content of the mixed-venous blood leaving the tissues (C MV(T) O2[i]) can be assumed to be equal to the arterial inflow of O2 to the tissues (Q ⁇ C a O2 j [i]) less the overall metabolic O2 consumption of the tissues (VO2) distributed over the cardiac output (Q).
  • the O2 content of the mixed-venous blood entering the pulmonary circulation (C MV O2[i]) is equal to the O2 content of the mixed-venous blood leaving the tissues delayed by the recirculation time (C MV(T) O2[i ⁇ n R ])
  • each compartment (k) represents a single tissue or group of tissues.
  • Each compartment is assigned a storage capacity for CO2 (dCO2 k ).
  • Each compartment is also modelled as being responsible for a fraction (vco2 k ) of the overall metabolic CO2 production (VCO2), and receiving a fraction (q k ) of the total cardiac output (Q).
  • the content of CO2 in the venous blood leaving a compartment (C V CO2 k [i]) is equal to the content of CO2 in the compartment.
  • 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 V CO2 j [i ⁇ 1]), the compartment parameters, and the period of the breath (T B ).
  • the model assumes a single compartment with a storage capacity for CO2 (dCO2 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.
  • the mixed-venous CO2 content leaving the tissues (C MV(T) CO2[i]) is the sum of the CO2 content leaving each compartment (C V CO2 k [i]) weighted by the fraction of the cardiac output (q k ) received by the compartment.
  • CO2 content of the mixed-venous blood entering the pulmonary circulation (C MV CO2[i]) is equal to the CO2 content of the mixed-venous blood leaving the tissues delayed by the recirculation time (C MV(T) CO2[i ⁇ n R ])
  • V T a tidal volume of gas is inspired into the alveoli.
  • gas is inspired in the following order: a) the gas in the anatomical dead space (V 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 ET O2[i ⁇ 1] T ) and a partial pressure of CO2 equal to the target end-tidal partial pressure of CO2 from the previous breath (P ET CO2[i ⁇ 1] T ); b) a volume of controlled gas mixture (VG 1 ) with controllable partial pressure of O2 (P I O2[i]) and controllable partial pressure of CO2 (P I CO2[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.
  • FRC functional residual capacity
  • a volume of O2 is transferred between the alveolar space and the pulmonary circulation (VB 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 MV O2[i]) and the pulmonary end-capillary O2 content (C p O2[i]) leaving the pulmonary circulation. This transfer occurs over the breath period (T B ).
  • a volume of CO2 is transferred between the alveolar space and the pulmonary circulation (VB 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 MV CO2[i]) and the pulmonary end-capillary CO2 content (C p CO2[i]) leaving the pulmonary circulation. This transfer occurs over the breath period (T B ).
  • the average volume of the controlled gas mixture inspired into the alveoli in each breath (VG 1 ) is given by the tidal volume (V T ) less the anatomical dead space (V D ).
  • the end-tidal partial pressure O2 (P ET O2[i] 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 ET CO2[i] T ) is simply the total volume of CO2 in the alveolar space, divided by the total volume of the alveolar space.
  • the partial pressure of O2 in the controlled gas mixture (P I O2[i]) and the partial pressure of CO2 in the controlled gas mixture (P I CO2[i]) can be set to induce target end-tidal partial pressures.
  • some of the terms (braced terms in the numerator of the above equations) contributing to the target end-tidal partial pressure of O2 (P ET O2[i]r) or the target end-tidal partial pressure of CO2 (P ET CO2[i] T ) may be neglected.
  • the O2 or CO2 re-inspired from the anatomical dead space (V D ) is small compared to the O2 or CO2 in the other volumes that contribute to the end-tidal partial pressures.
  • the O 2 or CO 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.
  • the partial pressure of O2 in the controlled gas mixture (P I O2[i]) and the partial pressure of CO2 in the controlled gas mixture (P I CO2[i]) required to induce a target end-tidal partial pressure of O2 (P ET O2[i] T ) or a target end-tidal partial pressure of CO2 (P ET CO2[i] T ) depends strongly on the tidal volume (V T ), anatomical dead space (V D ), and the functional residual capacity (FRC).
  • P I ⁇ O ⁇ ⁇ 2 ⁇ [ i ] P ET ⁇ O ⁇ ⁇ 2 ⁇ [ i ] T ⁇ ( V T - V D ) - PB ⁇ Q ⁇ ( 1 - s ) ⁇ T B ⁇ ( C MV ⁇ O ⁇ ⁇ 2 ⁇ [ i ] - C p ⁇ O ⁇ ⁇ 2 ⁇ [ i ] ) V T - V D
  • P I ⁇ CO ⁇ ⁇ 2 ⁇ [ i ] P ET ⁇ CO ⁇ ⁇ 2 ⁇ [ i ] T ⁇ ( V T - V D ) - PB ⁇ Q ⁇ ( 1 - s ) ⁇ T B ⁇ ( C MV ⁇ CO ⁇ ⁇ 2 ⁇ [ i ] - C p ⁇ CO ⁇ ⁇ 2 ⁇ [ i ] ) V T - V D
  • V T tidal volume
  • FRC functional residual capacity
  • T B breath period
  • V D anatomical dead space
  • This method is optional, especially where a simpler approach is preferred, and the subject's ventilation can be reasonably controlled or predicted.
  • the volumes and partial pressures required to calculate the partial pressure of O 2 in the controlled gas mixture (P I O2[i]) and the partial pressure of CO 2 in the controlled gas mixture (P I CO2[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.
  • partial pressures can be converted to fractional concentrations and vice-versa.
  • the partial pressure of O2 in the controlled gas mixture (P I O2[i]) and the partial pressure of CO2 in the controlled gas mixture P I CO2[i]) may be converted a fractional concentration of O2 in the controlled gas mixture (F I O2[i]) and a fractional concentration of CO2 in the controlled gas mixture (F I CO2[i]).
  • V T a tidal volume of gas is inspired into the alveoli.
  • gas is inspired in the following order: a) the gas in the anatomical dead space (V 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 ET O2[i ⁇ 1] T ) and a partial pressure of CO2 equal to the target end-tidal partial pressure of CO2 from the previous breath (P ET CO2[i ⁇ 1] T ); b) a volume of controlled gas mixture (VG 1 ) with controllable partial pressure of O 2 (P I O2[i]) and controllable partial pressure of CO2 (P I CO2[i]); c) a volume of neutral gas (VG 2 ) with a partial pressure of O2 and CO
  • a volume of O2 is transferred between the alveolar space and the pulmonary circulation VB 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 MV O2[i]) and the pulmonary end-capillary O2 content (C p O2[i]) leaving the pulmonary circulation. This transfer occurs over the breath period (T B ).
  • a volume of CO2 is transferred between the alveolar space and the pulmonary circulation (VB 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 MV CO2[i]) and the pulmonary end-capillary CO2 content (C p CO2[i]) leaving the pulmonary circulation. This transfer occurs over the breath period (T B ).
  • V D the average volume of the controlled gas mixture inspired into the alveoli in each breath (VG 1 ) is given by the rate at which the controlled gas mixture is made available for inspiration (FG 1 ) delivered over a single breath period (T B ):
  • V T tidal volume
  • V D volume of gas that remains in the anatomical dead space
  • the end-tidal partial pressure O2 (P ET O2[i] 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 ET CO2[i] T ) is simply the total volume of CO2 in the alveolar space, divided by the total volume of the alveolar space.
  • the partial pressure of O2 in the controlled gas mixture (P I O2[i]) and the partial pressure of CO2 in the controlled gas mixture (P I CO2[i]) can be set to induce target end-tidal partial pressures.
  • some of the terms (braced terms in the numerator of the above equations) contributing to the target end-tidal partial pressure of O2 (P ET O2[i] T ) or the target end-tidal partial pressure of CO2 (P ET CO2[i]) may be neglected.
  • the O 2 or CO 2 re-inspired from the anatomical dead space (V D ) is small compared to the O 2 or CO 2 in the other volumes that contribute to the 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.
  • the above equations can be used to calculate the partial pressure of O2 in the controlled gas mixture (P I O2[i]) and the partial pressure of CO2 in the controlled gas mixture (P I CO2[i]) required to induce a target end-tidal target partial pressure of O2 (P ET O2[i] T ) and a target end-tidal partial pressure of CO2 (P ET CO2[i] T ) where the target end-tidal partial pressure of O2 from the previous breath (P ET O2[i ⁇ 1] T ), the target end-tidal partial pressure of CO2 from the previous breath (P ET CO2[i ⁇ 1] T ), the functional residual capacity (FRC), tidal volume (V T ), rate at which the controlled gas mixture is made available for inspiration (FG 1 ), the breath period (T B ), cardiac output (Q), intrapulmonary shunt fraction (s), recirculation time (n R ), mixed-venous content of O2 entering the pulmonary circulation (C MV O2[
  • V T tidal volume
  • FRC functional residual capacity
  • T B breath period
  • V D anatomical dead space
  • partial pressures can be converted to fractional concentrations and vice-versa.
  • the partial pressure of O2 in the controlled gas mixture (P I O2[i]) and the partial pressure of CO2 in the controlled gas mixture (P I CO2[i]) may be converted a fractional concentration of O2 in the controlled gas mixture (F I O2[i]) and a fractional concentration of CO2 in the controlled gas mixture (F I CO2[i]).
  • the gas delivery device is capable of delivering a controlled mixture of the desired composition at the required flow rate
  • n SG source gases (SG 1 . . . SG n G ) are blended to deliver the required mixture to the Hi-Ox SR sequential gas delivery circuit (SGDC).
  • Each gas (m) contains a known fractional concentration of O2 (fo2 m ) and a known fractional concentration of CO2 (fco2 m ).
  • the flow rate of each gas (FSG m [i]) required to deliver the total desired flow rate of the controlled gas (FG 1 ) with the required partial pressure of O2 (P I O2[i]) and the required partial pressure of CO2 (P I CO2[i]) can be determined by solving the following set of equations:
  • the gas blender is capable of delivering a controlled mixture of the desired composition at the required flow rate
  • 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.
  • the targets may be modified and/or the rate at which the controlled gas mixture is made available to the circuit (FG 1 ) modified, or where applicable, the tidal volume (V T ) modified, until the composition is physically realizable.
  • 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 T ) modified, and/or different source gases used.
  • the target end-tidal partial pressure of O2 (P ET O2[i] T ) is not logistically feasible because the partial pressure of O2 in the controlled gas mixture (P I O2[i]) required to induce the target end-tidal partial pressure of O2 is not physically realizable.
  • the rate at which the controlled gas mixture is made available to the circuit (FG 1 ) may be modified.
  • the tidal volume (V T ) may be modified.
  • the target end-tidal partial pressure of O2 (P ET O2[i] T ) is not logistically feasible because the partial pressure of O2 in the controlled gas mixture (P I O2[i]) required to induce the target end-tidal partial pressure of O2 is not physically realizable.
  • P I O2[i] partial pressure of O2 in the controlled gas mixture
  • the target end-tidal partial pressure of O2 decreases.
  • the rate at which the controlled gas mixture is made available to the circuit (FG 1 ) may be modified.
  • the tidal volume (V T ) may be modified.
  • the rate at which the controlled gas mixture is made available to the circuit (FG 1 ) is modified to make a target end-tidal partial pressure of O2 (P ET O2[i] T ) or a target end-tidal partial pressure of CO2 (P ET CO2[i] T ) logistically feasible to induce.
  • 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.
  • 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.
  • the index [0] represent the value of a variable for all breaths before the start of the sequence (all values of i ⁇ 0).
  • the subject is allowed to breathe freely, without intervention, until the measured end-tidal partial pressure of O2 (P ET CO2 M ) and the measured end-tidal partial pressure of CO2 (P ET CO2 M ) are stable—these are taken as the baseline partial pressure of O2 (P ET O2 O M ) and the baseline partial pressure of CO2 (P ET CO2 0 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.
  • the correction factor ( ⁇ ) 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.
  • the correction factor ( ⁇ ) 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.
  • the estimate of the functional residual capacity 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 ET O2[i] M ) in steady state.
  • the estimate of the overall metabolic CO2 production (VCO2) influences the induced/measured end-tidal partial pressure of CO2 (P ET CO2[i] M ) in steady state.
  • 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.
  • 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.
  • the Tuning Sequence Described Above is Only an Example of One Sequence that can be Used to Tune the Estimates of the Physiological Parameters.
  • 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 ET O2[i] M ⁇ P ET O2[i ⁇ 1] M ) and the targeted change in the end-tidal partial pressure of O2 (P ET O2[i] T ⁇ P ET O2[i ⁇ 1] 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 ET O2[i] T ⁇ P ET O2[i ⁇ 1] T ), or a difference between the measured change in the end-tidal partial pressure of CO2 (P ET CO2[i] M ⁇ P ET CO2[i ⁇ 1] M ) and the targeted change in the end-tidal partial pressure of CO2 (P ET CO2[i] T ⁇ P ET CO2[i ⁇ 1] T ) in breaths where the target end-tidal partial
  • 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.
  • 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.
  • a ramp sequence reveals the sigmoidal nature of a pattern of a physiological response mid-cerebral artery blood flow velocity—showing its sigmoidal nature over different time courses depending on whether the subject is a fast or slow responder.
  • FIG. 9 blood flow responses to PCO 2 predicted for the model of a brain vascular territory with a partially-stenosed vessel branch and a healthy branch in parallel. Where there is some blood flow resistance upstream from the branches, it causes the partially-stenosed vessel to encroach on its vasodilatory reserve by an auto-regulatory mechanism.
  • a vasodilatory stimulus such as in increase in arterial CO 2 will stimulate all vessels to dilate, but those vessels that have already dilated in response to the increase in upstream resistance have a reduced range of response.
  • the solid red line in FIG. 9 depicts the sigmoidal response of a normal branch.
  • the dotted blue line depicts the response of the partially stenosed vessel branch when coupled in parallel with the normal vessel branch, showing steal in hypercapnia and reverse steal in hypocapnia.
  • the slopes of the straight lines show the predicted CVR values for PCO 2 stimulus ranges 40-45 and 40-50 mmHg.
  • the filled circle marks the resting blood flow at resting PCO 2 and the open circles show the measured responses for a healthy territory (solid circles and line) and a territory perfused via a stenosed vessel (dotted circles and line).
  • the model outlined in FIG. 9 was investigated a comprehensive manner by using it to predict the change in CBF region by region in response to graded changes in P ET CO2 in a patient with steno-occlusive disease.
  • FIG. 10 shows an example of the development of steal with hypercapnia, and reverse steal (Robin Hood effect) with hypocapnia [Lassen, 1968 #16325]. Both of these conditions were observed in the same patient, confirming that steal and reverse steal are a function of the changes taking place in the parallel branches of the vascular bed with intact cerebral autoregulation.
  • the CVR map in response to a hypercapnic change in P ET CO2 from 30 to 50 mmHg is shown in FIG. 10A and colour coded with the scale shown.
  • We interpret the blue colour of the right MCA territory as signifying a vascular bed with reduced vasodilatory reserve (presumably as a result of MCA stenosis).
  • the hypercapnic increase in P ET CO 2 from 30 to 40 mmHg produces a large increase in flow in the healthy left MCA region, but a lesser increase in the compromised right MCA region ( FIG. 10 , CVR B).
  • the right MCA territory demonstrates some vasodilatory reserve.
  • further hypercapnia to 50 mmHg results in a greater steal and the CVR values are negative, and the map is coloured blue ( FIG. 10 , CVR C).
  • our conceptual model predicts that withdrawal of the vasodilatory stimulus will abolish the steal and induce a reverse steal via the Robin Hood effect.

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