Abstract:
Methods for noninvasively measuring, or estimating, functional residual capacity or effective lung volume include obtaining carbon dioxide and flow measurements at or near the mouth of a subject. Such measurements are obtained during baseline breathing and during and shortly after inducement of a change in the subject&#39;s effective ventilation. The obtained measurements are evaluated to determine the amount of time required for exhaled carbon dioxide levels to return to normal—effectively an evaluation of carbon dioxide “washout” from the subject&#39;s lungs. Conversely, carbon dioxide and flow measurements may be evaluated to determine the amount of time it takes carbon dioxide to “wash in,” or reach peak levels within, the lungs of the subject following the change in the subject&#39;s effective ventilation. Apparatus for effective such methods are also disclosed.

Description:
CROSS-REFERENCE TO RELATED APPLICATION  
       [0001]     This application is a continuation-in-part of application Ser. No. 10/121,219, filed on Apr. 11, 2002, pending. 
     
    
     BACKGROUND OF THE INVENTION  
       [0002]     1. Field of the Invention  
         [0003]     The present invention relates generally to techniques for determining functional residual capacity (FRC), the volume of gases that remain within a subject&#39;s lungs following exhalation, or, more broadly, the effective lung volume (ELV) of the subject, which includes gases that have diffused into the lung tissues. In particular, the present invention relates to techniques for noninvasively determining FRC or ELV.  
         [0004]     2. Background of Related Art  
         [0005]     Functional residual capacity (FRC) is the volume of gases, including carbon dioxide (CO 2 ), that remains within the lungs of a subject at the end of exhalation, or expiration. In healthy individuals, FRC usually comprises about 40% of total lung capacity, and typically amounts to about 1.8 liters to about 3.4 liters. FRC buffers against large breath-to-breath changes in the amount of carbon dioxide in the alveoli of the subject&#39;s lungs, which may be measured in terms of partial pressure of CO 2  (p ACO2 ) or as a fraction of gases that comprise CO 2  (f ACO2 ). With normal tidal volumes, p ACO2  and f ACO2  typically fluctuate by only about 2 mmHg or about 0.25%, respectively.  
         [0006]     A number of authors contend that CO 2  is stored in the lungs in three different compartments: (1) the gas volume (V A  or FRC); (2) the lung tissue; and (3) the pulmonary blood present at any given time in the lung. The lung tissue and pulmonary blood compartments are often represented in terms of their equivalent gas volumes (i.e., scaled by their effective storage capacity) and denoted V tiS  and V blood . While FRC only accounts for the volume of gases (including CO 2 ) in the alveoli, effective lung volume (ELV) includes FRC, as well as gases that remain diffused within the tissues of the lungs of the subject at the end of exhalation and, therefore, accounts for gases in all three compartments.  
         [0007]     While ELV is typically a slightly larger volume than FRC, these terms may be used interchangeably in the ensuing description for purposes of simplicity.  
         [0008]     Each compartment equilibrates with changes in CO 2  at a different rate. Gedeon, A., et al., “Pulmonary blood flow (cardiac output) and the effective lung volume determined from a short breath hold using the differential Fick method,” J. C LIN . M ONIT.  17:313-321 (2002) (hereinafter “Gedeon 2002”) teaches that V A  equilibrates instantly with changes in end tidal CO 2  (p ETCO2  when measured in terms of partial pressure and f etCO2  when measured in terms of the fraction of gases that comprise CO 2 ) and slowly (e.g., in about ten to about twenty seconds) with changes in p AC02  and content of CO 2  in arterial blood (c aCO2 ), while it takes less time for V tis  and V blood  to equilibrate when p AC02  and c aCO2  change.  
         [0009]     The relationship between a subject&#39;s chest wall and lungs and the elastic recoil of the lungs defines FRC and, thus, ELV. Lung diseases that change the elastic recoil of the lungs, including emphysema, asthma, and other restrictive diseases, affect FRC. Thus, FRC determinations may be useful in accurately diagnosing such conditions. FRC determinations are also useful in diagnosing and treating respiratory failure and hypoxemia.  
         [0010]     In lungs with an FRC below the lung&#39;s closing capacity, the airways start to close before the end of a subject&#39;s exhalation, which results in a decrease of p AO2  and a mismatch between ventilation, or the movement of gases into and out of the lungs through the mouth, and perfusion, or the movement of gases across the gas/blood barrier between the alveoli of the lungs and the pulmonary capillaries that surround the alveoli. This is known in the art as V/Q mismatch or V T /V Q  mismatch.  
         [0011]     The currently available techniques for measuring FRC include full body plethysmography, nitrogen washout, and helium dilution. All of these methods require cumbersome equipment and, therefore, may not be suitable for use in an intensive care setting that is already crowded with equipment.  
         [0012]     Gedeon 2002 proposed a noninvasive technique for determining ELV. Specifically, that technique includes measuring the {dot over (V)} M CO 2  and f etCO2  of a subject, having the subject hold his or her breath for three seconds, the re-measuring {dot over (V)} M CO 2  and f etCO2 . For the first breath following the breath-hold, f etCO2  increases and {dot over (V)} M CO 2 , which is calculated over the duration of the breath hold and the subsequent breath, decreases. Assuming, due to buffering by the CO 2  stores of the ELV, that {dot over (V)} B CO 2  (i.e., CO 2  passing from the pulmonary capillary blood into the alveoli of the lung) does not change during breath-holding, Gedeon contends that the decrease in {dot over (V)} M CO 2  must have resulted from the CO 2  going into the lung stores of CO 2 : 
 
[ f   etCO2 POST   −f   etCO2 PRE   ]×{circumflex over (V)}   A   *   =[{dot over (V)}   M   CO   2PRE   −{dot over (V)}   M CO 2POST   ]×[T   breath   +T   breathhold ]
 
 where [{dot over (V)} M CO 2PRE  and {dot over (V)} M CO 2POST  refer to measurements obtained respectively before and after the breath-holding maneuver. 
 
         [0013]     In addition to this relationship, Gedeon developed equations that relate pulmonary capillary blood flow (PCBF or, for the sake of simplicity in the ensuing equations, {dot over (Q)}) of the subject to the subject&#39;s ELV. Two of these equations compare the pre-breathhold conditions to the post-breathhold conditions and the pre-breathhold conditions to the recovery conditions. The ELV of an ELV and PCBF data pair that satisfies both of these equations is considered to be the subject&#39;s actual ELV.  
         [0014]     The technique of Gedeon 2002 is believed to provide inaccurate data, as it is based on the assumption that “CO 2  inflow [may] not [be] significantly affected” by breath-holding, while breath-holding will cause a change in p ACO2 . This assumption is inconsistent with the Fick equation, in which {dot over (V)} B CO 2  changes linearly with p ACO2  while PCBF and the amount of CO 2  in the venous blood (c vCO2  or, as Gedeon2002 refers to it, Pven) remain constant.  
         [0015]     In view of the foregoing, it is apparent that there is a need for a technique for accurately, noninvasively measuring FRC or ELV in virtually any healthcare setting.  
       SUMMARY OF THE INVENTION  
       [0016]     The present invention includes methods for noninvasively measuring, or estimating, FRC or ELV, as well as apparatus and systems for obtaining FRC and ELV measurements with minimal invasiveness.  
         [0017]     As an example of a method for noninvasively measuring, or estimating, FRC or ELV in accordance with teachings of the present invention, carbon dioxide and flow measurements may be obtained at or near the mouth of a subject. Such measurements are obtained during baseline, or “normal,” breathing, as well as during and shortly after inducement of a change in the subject&#39;s effective ventilation. For example, measurements may be obtained during or shortly following a rebreathing maneuver, in which a subject inhales gases including an above-normal amount of CO 2 . Continuing with the rebreathing example, the obtained measurements are evaluated to determine the amount of time required for exhaled CO 2  levels to return to normal-effectively an evaluation of CO 2  “washout” from the subject&#39;s lungs. Conversely, CO 2  and flow measurements may be evaluated to determine the amount of time it takes CO 2  to “wash in,” or reach peak levels within, the lungs of the subject following rebreathing. Of course, when other techniques are used to generate a perturbation, or change, in the effective ventilation (i.e., the total ventilation less the wasted ventilation due to deadspace associated with the apparatus, the individual, or a combination thereof) of a subject, amounts of CO 2  or another appropriate gas may be measured. By evaluating such measurements, the ELV of the subject may be substantially noninvasively determined, or estimated.  
         [0018]     A noninvasive ELV estimation apparatus that incorporates teachings of the present invention is configured (e.g., programmed) to evaluate CO 2  and flow data from a subject and process the same in such a way as to calculate ELV. A system of the present invention includes such an apparatus, as well as CO 2  and flow sensors, which obtain CO 2  and flow measurements in as noninvasive a manner as possible (with the possible exception of an endotracheal tube) and communicate data representative of the measured CO 2  and flow levels to the noninvasive ELV estimation apparatus.  
         [0019]     Other features and advantages of the present invention will become apparent to those of ordinary skill in the art through consideration of the ensuing description, the accompanying figures, and the appended claims. 
     
    
     BRIEF DESCRIPTION OF THE FIGURES  
       [0020]     In the figures, which illustrate various exemplary aspects of the present invention:  
         [0021]      FIG. 1  is a schematic representation of an alveolus of an individual, illustrating the locations at which various respiratory and blood gas parameters may be determined;  
         [0022]      FIG. 2  is a graph that illustrates the volume of gases in the carbon dioxide stores of a respiratory tract of an individual (V A ) during a series of respiratory cycles, or breaths;  
         [0023]      FIG. 3  is a plot of the transformed {circumflex over ({dot over (V)})} M CO 2  data points against c ACO2  data points, in which the plotted points are substantially in-line with one another;  
         [0024]      FIG. 4  is a schematic representation of an example of a monitoring system incorporating teachings of the present invention; and  
         [0025]      FIG. 5  is a line graph showing the correlation between two sets of ELV calculations that have been made in accordance with teachings of the present invention. 
     
    
     DETAILED DESCRIPTION  
       [0026]     The present invention includes methods for determining the FRC or ELV of a subject substantially noninvasively. In the inventive methods, FRC or ELV may be determined by evaluating a respiratory gas, such as carbon dioxide, and respiratory flow. Respiratory gas and flow signals may be used to determine a variety of parameters and, along with a mathematical model of the subject&#39;s lung, used to determine FRC or ELV. The ensuing description includes a discussion of the manner in which one or more exemplary algorithms are derived, as well as reasoning to support such derivation, to facilitate substantially a noninvasive determination of the subject&#39;s FRC or ELV.  
         [0027]     In accordance with teachings of the present invention, FRC and ELV may be determined while the respiratory and cardiovascular, or hemodynamic, performance of a subject are being determined in a substantially noninvasive manner. Exemplary measures of the cardiovascular performance of a subject include, but are not limited to, pulmonary capillary blood flow and cardiac output.  
         [0028]     The carbon dioxide Fick equation has long been used to determine both pulmonary capillary blood flow and cardiac output. One form of the carbon dioxide Fick equation follows: 
 
 PCBF=VCO   2 /( c   vCO2   −c   ACO2 ),  (1) 
 
 where PCBF represents pulmonary capillary blood flow, VCO 2  is carbon dioxide elimination, c vC02  is carbon dioxide content of the venous blood of the monitored individual, and c AC02  is the carbon dioxide content of the alveolar (i.e., pulmonary capillary) blood of the monitored individual. 
 
         [0029]     The most accurate way to measure VCO 2  would be to directly measure the flow of CO 2  from the blood within the pulmonary capillaries that surround the alveoli of the lungs to the alveoli, or carbon dioxide excretion ({dot over (V)} B CO 2 ). If VCO 2  could be measured in this manner, equation (1) becomes:  
             PCBF   =           V   .     B     ⁢     CO   2           c   vCO2     -     c   ACO2                 (   2   )             
 
 If the content of CO 2  in blood at the alveolus (c ACO2 ) is substantially the same as the content of CO 2  in arterial blood (c aCO2 ), then cardiac output ({dot over (Q)}) may be substituted for PCBF in equation (2). 
 
         [0030]     Rearranging equation (2) for a calculation of {dot over (V)} B CO 2  results in the following: 
 
 {dot over (V)}   B   CO   2   =−PCBF c   ACO2   +PCBF c   vCO2 .  (3) 
 
         [0031]     Notably, equation (3) takes the form of the standard equation for a line in a two-dimensional (x, y) coordinate system: y=m×+b. When {dot over (V)} B CO 2  signals (y-axis) are plotted in a two-dimensional coordinate system against c ACO2  signals α-axis) taken at various points during and before or after a change in the effective ventilation of an individual, it can be seen the slope (m) of a line extending through the plotted points will be −PCBF, while PCBF c vCO2  is the intercept (b).  
         [0032]     Equations (2) and (3) are based on the rate at which carbon dioxide leaves, or is eliminated from, the blood at the alveoli ({dot over (V)} B CO 2 ). If the flow of CO 2  from the blood into the alveoli, or carbon dioxide excretion ({dot over (V)} B CO 2 ), could be measured and plotted against c ACO2  during rebreathing or another change in the effective ventilation of the subject, data from every breath, including transitional data points, would fall on the line defined by equation (3).  
         [0033]     Unfortunately, {dot over (V)} CO 2  is not measured directly at the alveoli. It is measured in a less direct manner—at or near the subject&#39;s mouth. Carbon dioxide signals that originate at or near the mouth of a subject are typically obtained and processed, along with respiratory flow signals, to facilitate such measurements. Notably, U.S. Patent Publication U.S. 2002/0183643 A1 of Kück et al. (hereinafter “Kück”), the disclosure of which is hereby incorporated herein, in its entirety, by this reference, teaches that measurements of CO 2  that are taken at the mouth of a subject as the subject exhales do not necessarily correlate well with the amount of CO 2  that is given off by the blood as it passes by the alveoli of the subject&#39;s lungs. More specifically, CO 2  that is exhaled, or eliminated, from the subject&#39;s respiratory system, as measured at or near the subject&#39;s mouth ({dot over (V)} M CO 2 ) ultimately results from but does not correlate well with the amount of CO 2  that is excreted from the blood to the lungs of the subject ({circumflex over ({dot over (V)})} B CO 2 , when considered in terms of flow) during the same breath. Kück explains that such miscorrelation is caused by the CO 2  stores of a subject&#39;s lungs, specifically by the buffering capacity of the CO 2  stores.  
         [0034]     More specifically, {dot over (V)} M CO 2  includes both {dot over (V)} B CO 2  and CO 2  that has flowed into or out of the ELV of the subject&#39;s lungs, which include CO 2  stores ({dot over (V)} STORES CO 2 ). Thus, 
 
 {dot over (V)}   B   CO   2   ={dot over (V)}   M   CO   2   −{dot over (V)}   STORES   CO   2 .  (4) 
 
         [0035]     The CO 2  stores of a subject&#39;s lungs act as a buffer, absorbing some of the increased CO 2  and causing {dot over (V)} M CO 2  to change more gradually than {dot over (V)} B CO 2  changes.  
         [0036]     The CO 2  stores of an individual&#39;s lungs may be evaluated by use of a model of the lung, such as the simple model of the lung depicted in  FIG. 1 , in which a single alveolus  100  and a corresponding pulmonary capillary  102  represent the lung. The direction in which blood flows through pulmonary capillary  102  is represented by arrows  103 . The mouth of an individual is represented at reference  106 . In the model of  FIG. 1 , the carbon dioxide stores of the lung are depicted, for the purpose of simplicity, as comprising the physical gas volume  104  of the alveolus (V A ). As is known in the art, V A is related to tidal volume (V T ), as well as to the functional residual capacity (V FRC ) of the lung. In addition to the illustrated contributors to the CO 2  stores of the lung (i.e., FRC), CO 2  may be distributed within other stores, such as the alveolar tissues and other tissues of the lung (collectively the ELV). The lung model shown in  FIG. 1  also omits V T /V Q  mismatch and shunting of blood (i.e., the portion of cardiac output that does not flow through the pulmonary arteries and capillaries, or that is not PCBF). For modeling purposes, the mixing of air within the alveolus (including inspired gases, CO 2  escaping from the blood, flow of CO 2  into and out of the CO 2  stores, and gases within the alveolus) is assumed to occur instantaneously. The effective volume of the CO 2  stores of an individual&#39;s lungs are denoted herein as “V A   * .” 
         [0037]     The effects of the CO 2  stores may be evaluated to obtain an accurate {dot over (V)} B CO 2  based on direct {dot over (V)} M CO 2  measurements. For example, a model of the lung, such as that depicted in  FIG. 1 , may be evaluated on a breath-by-breath basis. By way of example only, a breath (n) may be delineated as the period from the end of one inspiration to the end of the next inspiration, as illustrated in  FIG. 2 . In addition,  FIG. 2  depicts an example of the effective volume of CO 2  stores in the subject&#39;s respiratory tract (e.g., lungs) during the course of respiration.  
         [0038]     If the effective volume of CO 2  stores (V A   * ) does not change from breath to breath, the amount of CO 2  that flows into and out of the CO 2  stores from one breath to the next may be expressed as a change in alveolar CO 2  fraction (f A CO 2 ) (i.e., the fraction of gases in the alveolus that comprise CO 2 ), or the difference between f A CO 2  for a particular breath (f A CO 2 (n)) and f A CO 2 for the previous breath f A CO 2 (n−1). Thus, the volume of the CO 2  stores ({dot over (V)} STORES CO 2 ) for a particular breath (n) may be determined by multiplying the effective volume in which the CO 2  stores are located (V A *) by the change in f A CO 2 from the previous breath (n−1) to the current breath (n) and by the subject&#39;s respiratory rate (RR).  
         [0000]     Equation (4) then becomes: 
 
 {dot over (V)}   B   CO   2 ( n )= {dot over (V)}   M   CO   2 ( n )+ V   A   * ( n )[ f   A   CO   2 ( n )− f   A   CO   2 ( n− 1)] RR.   (5) 
 
 Equation (5) is particularly useful for estimating {dot over (V)} B CO 2 from {dot over (V)} M CO 2  measurements that are obtained during the transition from “normal” breathing (e.g., nonrebreathing) to a change in the effective ventilation of the subject (e.g., rebreathing or another change in the effective ventilation). An estimate of {dot over (V)} B CO 2 is denoted herein as {circumflex over ({dot over (V)})} B CO 2  and may be substituted for {dot over (V)} B CO 2 in equation (5). 
 
         [0039]     While {dot over (V)} M CO 2  and RR may be measured directly, the alveolar CO 2  fraction (f ACO2 ) and V A * cannot. It is known, however, that f ACO2  is proportional to p ACO2 , which is proportional to p etCO2 , which may be measured directly (e.g., by use of a capnometer). The p etCO2  measurement may then be used, as known in the art, to obtain an f ACO2  value for each breath.  
         [0040]     V A   *  may be adaptively estimated, such as by using the linear correlation between +E,circ {dot over (V)} B CO 2 from equation (5), substituting {circumflex over (V)} A   * , the estimated effective alveolus volume, for V A   * , the actual effective alveolus volume, and using c ACO2  as a guide (see equation (3)). The more accurately {circumflex over (V)} A   *  reflects V A   * , the closer the data points of a plot of +E,circ {dot over (V)} B CO 2 against c ACO2  (which is also proportional to and may be determined from p etCO2 measurements in a manner known in the art) over the course of a change in the effective ventilation of an individual will be to a line representative of the actual pulmonary capillary blood flow or cardiac output of the individual. The ideal value for {circumflex over (V)} A   *  may, therefore, be determined as the value that results in the best linear fit between the plotted data (C ACO2  against +E,circ {dot over (V)} B CO 2 ) and, thus, a maximized correlation coefficient, or r 2  value. By way of example only, an adaptive, iterative, or search algorithm of a type known in the art may be used to determine {circumflex over (V)} A   *  for which the correlation coefficient, or r 2 , is maximized. The graph of  FIG. 3  shows an example of a {circumflex over (V)} A   *  value at which r 2  is maximized.  
         [0041]     Once an accurate {circumflex over (V)} A   *  estimate has been made, the effective volume of the FRC (V FRC ) or ELV (V ELV ) of the subject&#39;s lungs may also be estimated or determined. In this regard, equation (5) may be rewritten, as follows, to reflect the use of {circumflex over (V)} A   *  as an estimate for V A   * : 
 
 {circumflex over ({dot over (V)})}   B   CO   2 ( n )= {dot over (V)}   M   CO   2 ( n )+{circumflex over (V)} A   * ( n )[ f   ACO2 ( n )− f   ACO2 ( n− 1)] RR.   (6) 
 
         [0042]     The foregoing approach (particularly, the use of equation (6)) works well when a subject is mechanically ventilated (i.e., on a respirator), in which case the respiratory rate and tidal volume (V T ) of the individual&#39;s respiration are typically substantially stable, which provides for a “clean” f ACO2  signal.  
         [0043]     During spontaneous or mixed (i.e., mechanical and spontaneous) ventilation, it may be desirable to eliminate any noise that may occur in the f ACO2  signal when equation (6) is used, as such noise may result in an inaccurate estimation of {dot over (V)} B CO 2 (i.e., {circumflex over ({dot over (V)})} B CO 2 ). An algorithm that is less sensitive to noise than equation (6) may, therefore, also be useful for estimating {circumflex over ({dot over (V)})} B CO 2 , as described hereinafter.  
         [0044]     Assuming that pulmonary capillary blood flow and cardiac output do not change from one breath to the next, the carbon dioxide Fick equation (equation (2)) may be rewritten for two successive breaths:  
             PCBF   =             V   .     B     ⁢       CO   2     ⁡     (     n   -   1     )               c   vCO2     ⁡     (     n   -   1     )       -       c   ACO2     ⁡     (     n   -   1     )           =           V   .     B     ⁢       CO   2     ⁡     (   n   )               c   vCO2     ⁡     (   n   )       -       c   ACO2     ⁡     (   n   )                     (   7   )             
 
 Further, assuming that c vCO2  does not change from one breath to the next, equation (7) may be simplified to:  
             PCBF   =             V   .     B     ⁢       CO   2     ⁡     (     n   -   1     )         -         V   .     B     ⁢       CO   2     ⁡     (   n   )                 c   ACO2     ⁡     (   n   )       -       c   ACO2     ⁡     (     n   -   1     )                   (   8   )             
 
         [0045]     Measurements of the CO 2  fraction of gases in a subject&#39;s alveoli (f ACO2 ) may be used in place of the c ACO2  measurements of equation (8) when the slope of the CO 2  dissociation curve (s CO2 ), a standard curve which illustrates the rate at which CO 2  molecules dissociate from the hemoglobin molecules of red blood cells, and barometric pressure (p baro ) are also taken into consideration, as known in the art. Accordingly, equation (8) may be rewritten as follows:  
             PCBF   =             V   .     B     ⁢       CO   2     ⁡     (     n   -   1     )         -         V   .     B     ⁢       CO   2     ⁡     (   n   )                 s   CO2     ⁢           ⁢     p   baro     ⁢           ⁢       f   ACO2     ⁡     (   n   )         -       f   ACO2     ⁡     (     n   -   1     )                   (   9   )             
 
 Solving this expression for the difference in CO 2  fractions (f ACO2 (n)−f ACO2 (n−1)) yields:  
                   f   ACO2     ⁡     (   n   )       -       f   ACO2     ⁡     (     n   -   1     )         =             V   .     B     ⁢       CO   2     ⁡     (     n   -   1     )         -         V   .     B     ⁢       CO   2     ⁡     (   n   )               s   CO2     ⁢           ⁢     p   baro     ⁢           ⁢   PCBF               (   10   )             
 
 Substitution of equation (10) into equation (6) results in:  
                         V     .   ^       B     ⁢       CO   2     ⁡     (   n   )         =       ⁢           V   .     M     ⁢       CO   2     ⁡     (   n   )         +                     ⁢         RR   ⁢           ⁢       V   ^     A     *     (   n   )           s   CO2     ⁢           ⁢     p   baro     ⁢           ⁢   PCBF       [           V     .   ^       B     ⁢       CO   2     ⁡     (     n   -   1     )         -         V     .   ^       B     ⁢       CO   2     ⁡     (   n   )           ]                   (   11   )             
 
 This expression can now be solved for {circumflex over ({dot over (V)})} B CO 2 (n) to provide an accurate estimate of {dot over (V)} B CO 2 :  
                         V     .   ^       B     ⁢       CO   2     ⁡     (   n   )         =       ⁢         1       1   +     RR   ⁢           ⁢       V   ^     A     *     (   n   )             s   CO2     ⁢           ⁢     p   baro     ⁢           ⁢   PCBF         ⁢           ⁢       V   .     M     ⁢       CO   2     ⁡     (   n   )         +                     ⁢           RR   ⁢           ⁢       V   ^     A     *     (   n   )           s   CO2     ⁢           ⁢     p   baro     ⁢           ⁢   PCBF         1   +       RR   ⁢           ⁢     V   A     *     (   n   )           s   CO2     ⁢           ⁢     p   baro     ⁢           ⁢   PCBF           ⁢           ⁢       V     .   ^       B     ⁢       CO   2     ⁡     (     n   -   1     )                       (   12   )             
 
 Structurally, this result represents a first order, single-pole low pass filter of the form 
 
 {circumflex over ({dot over (V)})}   B   CO   2 ( n )=(1−α) {dot over (V)}   M   CO   2 ( n )+α {circumflex over ({dot over (V)})}   B   CO   2 ( n− 1),  (13) 
 
 where α, the transformation coefficient, may be represented as  
                   RR   ⁢           ⁢       V   ^     A     *     (   n   )           s   CO2     ⁢           ⁢     p   baro     ⁢           ⁢   PCBF         1   +       RR   ⁢           ⁢     V   A     *     (   n   )           s   CO2     ⁢           ⁢     p   baro     ⁢           ⁢   PCBF           .           (   14   )             
 
         [0046]     The RR in equation (14), which is the respiratory rate of the subject, is measured in breaths per minute. {circumflex over (V)} A   *  (n) is estimate of the CO 2  stores of the subject&#39;s lungs during breath (n) and is approximately equivalent to the volume of the FRC or ELV of the subject&#39;s lungs (V FRC * and V ELV *, respectively). SCO 2  is the slope of the standard carbon dioxide dissociation curve. p baro  is barometric pressure. PCBF, the pulmonary capillary blood flow the subject, does not need to be known to determine either α or {circumflex over (V)} A   *  (n).  
         [0047]     It is not necessary to know PCBF to calculate a because a determination of a merely requires that the linearity, or straightness, of a line through {dot over (V)} B CO 2  values that have been plotted against p etCO2  or c CO2  values be evaluated, not that the slope of the line, which is equal to PCBF, be evaluated. In that regard, the transformation coefficient (α) in equations (13) and (14) may be determined iteratively, by using an initial a value, then progressively increasing and/or decreasing the α value to determine the α value that provides for a plot of {dot over (V)} B CO 2  values against p etCO2  or c CO2  values with the greatest linearity (as opposed to an open loop) or, stated another way, that provides an optimal correlation coefficient (r2) between the {dot over (V)} B CO 2  values and the p etCO2  or c CO2  values. Other methods for determining an optimal α value include, without limitation, rote searching, global searching, gradient searching (e.g., use of a gradient descent search algorithm), use of a least mean squares algorithm, use of other predetermined equations or sets of predetermined equations, use of a truly adaptive filtering technique, and use of other techniques to determine the optimal a value, as known in the art.  
         [0048]     Use of an optimal transformation coefficient (α) (equation (14)) in equation (13) provides a relatively accurate, simple mathematical model of the lung of a subject. The algorithm of equation (13) may be used to calculate the amount of CO 2  that flows into and out of the carbon dioxide stores of the lungs on a “breath-to-breath” basis.  
         [0049]     The {circumflex over (V)} A * (n) of equation (14) is equivalent to ELV and flow may be converted to volume, which results in elimination of RR, allowing a to be expressed more simply as:  
               α   =           V   ^     A     *           s   CO2     ⁢           ⁢     p   baro     ⁢           ⁢     PCBF   /   RR       +         V   ^     A     *           ,           (   15   )             
 
 where Q is measured in terms of volume, rather than flow. If equation (15) were multiplied through with Δf ACO2  (i.e., f ACO2 (n)−f ACO2 (n−1), the expression could be viewed as calculating the relative amount of CO 2  stored in ELV over the total change in the amount of CO 2  from a change in the effective ventilation of a subject (e.g., rebreathing or another change in effective ventilation). 
 
         [0050]     If PCBF/RR is calculated from data obtained before and during a change in the effective ventilation of the subject (e.g., rebreathing or another change in effective ventilation), equation (15) may be rewritten as follows:  
             α   =           V   ^     A     *           Δ   ⁢           ⁢   V   ⁢           ⁢     CO   2         Δ   ⁢           ⁢     f   CO2         +         V   ^     A     *                 (   16   )             
 
 Equation (16) may be rearranged as follows:  
                 V   ^     A   *     =       α     1   -   α       ⁢     (     PCBF   /   RR     )     ⁢     s   CO2     ⁢     p   Baro               (   17   )             
 
 to solve for ELV ({circumflex over (V)} A *) 
 
         [0051]     Equation (17) may be used to substantially noninvasively determine ELV when virtually any change in the effective ventilation of the subject (e.g., rebreathing, change in respiratory rate, change in respiratory volume, etc.) has occurred, whether or not the subject continues to breathe as data is collected, with data obtained during “normal” breathing being compared with data obtained once the change in effective ventilation has occurred.  
         [0052]     Other techniques for determining an optimal α value are also within the scope of the present invention.  
         [0053]     Equation (6) does not take into account the possibility, or even likelihood, that the amount of CO 2  stored within the lungs ({dot over (V)} STORES CO 2 ) may vary from breath to breath. A more complex version of equation (6) accounts for this possibility: 
 
 {circumflex over ({dot over (V)})}   B   CO   2 ( n )= {dot over (V)}   M   CO   2 ( n )+( {circumflex over (V)}   A   * ( n )+ V   T ( n ))×( f   ACO2 ( n ) −f   ACO2 ( n− 1))+( V   T ( n )− V   T ( n− 1))× f   ACO2 ( n ),  (18) 
 
         [0054]     Accordingly, in another aspect, the present invention includes use of an algorithm that corrects ELV for possible changes in V CO2STORES  and combines the ELV correction with the CO 2  form of the differential Fick equation:  
                 Q   .     =               V   _     M     ⁢     CO   2       -     (           V   .     M     ⁢       CO   2     ⁡     (   n   )         +         V   ^     A   *     ·     [         f   ACO2     ⁡     (   n   )       -       f   ACO2     ⁡     (     n   -   1     )         ]                 s   CO2     ·     (         p   ACO2     ⁡     (   n   )       -       p   _     ACO2       )         ×   RR       ,           (   19   )             
 
 where {overscore (V)} M CO 2  is the average breath-to-breath volume, not flow, of carbon dioxide eliminated from the subject&#39;s lungs, as measured at the mouth, during breaths that precede and effective change in the ventilation of the subject (e.g., rebreathing or another change in effective ventilation). The ELV value of equation (19) includes tidal volume (V T ). For a closer estimate of FRC, the inspiratory tidal volume should be subtracted from ELV, as estimated for use in equation (19). Notably, accurate results may be obtained when {dot over (V)} M CO 2  (n) for each breath is calculated from expiration to inspiration (i.e., as {dot over (V)} M CO 2  (n)={dot over (V)} M CO 2expired (n−1)−{dot over (V)} M CO 2inspired (n)). 
 
         [0055]     Tidal volumes typically do not change drastically from breath-to-breath. Therefore, the expression V T (n)−V T (n−1) from equation (18) has been omitted from equation (19) without substantially affecting the accuracy of a subsequent ELV determination. Optionally however, a variation of equation (19) may consider the change in tidal volume from one breath to the next, as doing so could improve the accuracy of the {dot over (Q)} calculation and, thus, of the subsequent ELV estimation.  
         [0056]     If {dot over (V)} M CO 2  and p etCO2  reach good plateaus within a cycle, it might be possible to use them to calculate PCBF in equation (19). This is possible because ELV does not affect PCBF estimations from plateau values (algebraically, the f ACO2 (n)−f ACO2  (n−1) term vanishes at plateaus).  
         [0057]     Equation (19) can be solved for ELV ({circumflex over (V)} A *):  
                 V   ^     A   *     =       1         f   ACO2     ⁡     (   n   )       -       f   ACO2     ⁡     (     n   -   1     )           ·     [         V   M     ⁢     CO     2   ⁢   PRE         -       V   M     ⁢       CO   2     ⁡     (   n   )         -     PCBF   ·     s   CO2     ·     (         p   ACO2     ⁡     (   n   )       -     p     ACO2   ⁢           ⁢   PRE         )     ·     1   RR         ]               (   20   )             
 
         [0058]     Furthermore, if it is assumed that one CO 2  dissociation curve slope s CO2  (e.g., the average across the cycle&#39;s p etCO2  values) can be used, then it cancels and the equation simplifies to:  
                 V   ^     A   *     =       1         f   ACO2     ⁡     (   n   )       -       f   ACO2     ⁡     (     n   -   1     )           ·     [         V   M     ⁢     CO     2   ⁢   PRE         -       V   M     ⁢       CO   2     ⁡     (   n   )         -             V   M     ⁢     CO     2   ⁢   PRE         -       V   M     ⁢     CO     2   ⁢   DUR               p     ACO2   ⁢           ⁢   DUR       -     p     ACO2   ⁢           ⁢   PRE           ·     (         p   ACO2     ⁡     (   n   )       -     p     ACO2   ⁢           ⁢   PRE         )         ]               (   21   )             
 
 where the pre and during values represent the respective plateaus. Alternatively, PCBF can be determined through some other method, be it invasive (e.g., thermodilution), or noninvasive (e.g., electrical bioimpedance). 
 
         [0059]     Parts of equation (21) may be used in at least two embodiments of the present invention, one of which includes use of the first part of equation (21) to determine ELV. More specifically, if one could assume that {dot over (V)} B CO 2  is constant even though the p ACO2  is changing due to a change in the effective ventilation of the subject (e.g., rebreathing or another change in effective ventilation), ELV may be determined as follows:  
                 V   ^     A   *     =       1         f   ACO2     ⁡     (   n   )       -       f   ACO2     ⁡     (     n   -   1     )           ·     [         V   M     ⁢     CO     2   ⁢   PRE         -       V   M     ⁢       CO   2     ⁡     (   n   )           ]               (   22   )             
 
         [0060]     Equation (22) may be used to evaluate ELV when a change in the effective ventilation of the subject (e.g., rebreathing, change in respiratory rate, change in respiratory volume, etc.) has been effected, and while the subject continues to breathe (i.e., not during maneuvers which require breath-holding or which otherwise temporarily terminate breathing). In using equation (22) to determine ELV, data obtained during “normal” breathing may be compared with data obtained once the change in effective ventilation has occurred. For example, and not by way of limitation, breath (n−1) may represent a normal breath, while (n) may represent the first breath in which the change in effective ventilation has occurred.  
         [0061]     The second of these embodiments employs both the first part of equation (21) (i.e., equation (22), as well as the second part of equation (21):  
                 -           V   ⁢   CO       2   ⁢   PRE       -       V   ⁢   CO       2   ⁢   DUR             p     ACO2   ⁢           ⁢   DUR       -     p     ACO2   ⁢           ⁢   PRE             ·     (         p   ACO2     ⁡     (   n   )       -     p     ACO2   ⁢           ⁢   PRE         )       ]           (   23   )             
 
 or a broader variation thereof:  
             PCBF   ·     s   CO2     ·     1   RR     ·     (         p   ACO2     ⁡     (   n   )       -     p     ACO2   ⁢           ⁢   PRE         )             (   24   )             
 
 In this manner, the ELV calculation of equation (22) may be modified to compensate for changes in p AC02  during a breath, or continuously changing p ACO2 . Specifically, the ratio of the change in VCO 2  to the change in p AC02  in equation (23) and of {dot over (Q)} in equation (24) represents the slope of the line that describes the amount of CO 2  that exits the CO 2  stores through the mouth as CO 2  exiting the blood is added to the CO 2  stores, or the “sensitivity” with which changes in p etCO2  represent changes in p AC02  as CO 2  from the blood flows into the CO 2  stores, which in turn provides an indication of buffering capacity of the CO 2  stores. (p ACO2 (n)−{overscore (p)} AC02 ) provides an indication of the magnitude of the p ACO2  change to be scaled when p etCO2  is measured at or near the mouth. 
 
         [0062]     The  
       1   RR       
 
 in equation (24) may be substituted with a different value that represents the time interval between the start of a change in effective ventilation (e.g., rebreathing) and the time when the measured p AC02  left the alveoli. Generally, such a value will be less than  
         1   RR     .       
 
         [0063]     The combination of equations (23) and (24) may be used to substantially noninvasively determine ELV when virtually any change in the effective ventilation of the subject has occurred, whether or not the subject continues to breathe as data is collected. More specifically, data obtained during “normal” breathing may be compared with data obtained once the change in effective ventilation has occurred.  
         [0064]     Turning now to  FIG. 4 , an exemplary diagnostic system  1  that incorporates teachings of the present invention is schematically illustrated. Diagnostic system  1  includes, among other things, an airway  52  in communication with the airway A of an individual I, as well as a flow meter  72  and a carbon dioxide sensor  74  positioned along airway  52 . Flow meter  72  and carbon dioxide sensor  74  communicate signals to corresponding monitors  73  and  75 , which communicate electronically with a processor  82  of a respiratory monitor  80  (e.g., the processor and respiratory monitor of a NICO® monitor available from Novametrix Medical Systems (Wallingford, Conn.) division of Respironics, Inc). Processor  82  is programmed to determine at least VCO 2  and p etCO2  based on signals communicated thereto from flow meter  72  and carbon dioxide sensor  74 . In addition, processor  82  may be programmed to use signals from one or both of flow meter  72  and carbon dioxide sensor  74  or calculated parameters (e.g., VCO 2  and p etCO2 ) in the above-described algorithms (i.e., one or more of equations (1)-(24)) to facilitate the substantially noninvasive and accurate determination of individual I&#39;s ELV. Alternatively, such calculations may be made manually.  
         [0065]     In a method that incorporates teachings of the present invention, VCO 2  and p etCO2  values are obtained during both a baseline, or first, ventilatory state, and when a change in the effective ventilation of individual I has been effected, or a second ventilatory state. Alternatively, such values may obtained during a transition between first and second states, then compared with values obtained during the first or second state.  
         [0066]     The first ventilatory state may be effected under substantially “normal” breathing conditions. Alternatively, the baseline ventilatory state may be defined under a first set of other, selected breathing conditions. The second ventilatory state occurs when one or more respiratory control parameters are manipulated to achieve breathing conditions differ from those present during the first ventilatory state to a degree that effect a measurable change in minute ventilation.  
         [0067]     The second ventilatory state may be induced, for example, by altering the value of a limit variable, e.g., inspiratory pressure, tidal volume, flow rate or time, from a value of the limit variable during the first ventilatory state. In another exemplary method, a change in effective ventilation may be induced by altering the threshold value of a cycle variable from the threshold level of the cycle variable during the first ventilatory state. In a further exemplary method, a change in effective ventilation may be induced by altering the threshold triggering value of a triggering variable, such as inspiratory pressure or flow rate. In a still further method, a change in effective ventilation may be induced by delivering to the individual a series of at least three “sigh breaths,” which are deeper than normal breaths. Changes in effective ventilation may also comprise periods of unsteady, or “noisy,” breathing.  
         [0068]     The VCO 2  and p etCO2  values that are obtained are then processed in accordance with one or more of equations (1)-(24)) to substantially noninvasively and accurately determine individual I&#39;s ELV.  
       EXAMPLE  
       [0069]     Different effective FRC values were achieved by incrementally advancing an especially long endotracheal tube from an initial, normal position to a small distance within the bronchial tree of an anesthetized pig (at time=15:26) and, twenty-one minutes later (at time=15:47) to a position further within the bronchial tree. By ventilating only parts of the lung, the effective FRC was reduced with each advancement of the endotracheal tube.  
         [0070]     ELV was calculated for various breaths using equation (18). ELV values that were calculated when a sufficient f ACO2 (n)−f ACO2 (n−1) threshold was present and during certain breaths (e.g., the second breath into rebreathing, the first breath of recovery, etc.) were considered valid and are included as data points in the graph of  FIG. 5 . Notably, the plotted data points represent ELV minus inspiratory tidal volume. ELV values that were calculated from data obtained during transition from normal breathing into rebreathing are shown as diamond-shaped points. ELV values that were calculated from data obtained during the transition from rebreathing to recovery are shown as squares. The closeness of the lines that extend through the two sets of data indicates that the ELV values and, thus, the algorithm (equations (22 and 23)) from which they were calculated provides reasonable ELV values. Notably, the trends of the two sets of ELV calculations decrease, as expected, at times when the endotracheal tube was advanced further into the lungs of the pig. These trends, as well as their magnitude, are confirmed by the underlying VCO 2  signals  50  and p etCO2  signals  51 . Moreover, the ELV estimations remained relatively stable even when severe changes in p etCO2  were noted (see the p etCO2  trend after 15:50).  
         [0071]     Although the foregoing description contains many specifics, these should not be construed as limiting the scope of the present invention, but merely as providing illustrations of some of the presently preferred embodiments. Similarly, other embodiments of the invention may be devised which do not depart from the spirit or scope of the present invention. Features from different embodiments may be employed in combination. The scope of the invention is, therefore, indicated and limited only by the appended claims and their legal equivalents, rather than by the foregoing description. All additions, deletions and modifications to the invention as disclosed herein which fall within the meaning and scope of the claims are to be embraced thereby.