Method and apparatus for determining cardiac output

[0001] This application claims priority under 35 U.S.C. § 120 as a Continuation of U.S. patent application Ser. No. 10/172,271 filed Jun. 14, 2002 now U.S. Pat. No. 6,699,203, which claims priority under 35 U.S.C. § 120 as a Continuation of U.S. patent application Ser. No. 09/691,595 filed Oct. 18, 2000, now U.S. Pat. No. 6,413,226, which claims priority from provisional U.S. Patent Appln. No. 60/369,708 filed Apr. 3, 2002, the contents of which are incorporated herein by reference.

[0002] 1. Field of the Invention

[0003] The present invention pertains to a method and apparatus for determining the cardiac output of a patient, and, more particularly, to a method of determining cardiac output by analyzing the effect that an induced change in the patient's arterial oxygen concentration has on their oxygen uptake and fractional arterial oxygen concentration, and to an apparatus for use in implementing such a method.

[0004] 2. Description of the Related Art

[0005] There are several generally accepted techniques for measuring cardiac output (CO), which is the total volumetric flow of blood through the heart, and, thus, through the body at any given time. These techniques include: thermodilution, dye dilution, the direct Fick method, and partial CO₂ rebreathing. Thermodilution involves injecting cold saline directly into the right atrium of the heart and measuring the temperature change downstream in the pulmonary artery using a temperature sensor placed in this artery. Cardiac output is determined based on this temperature change versus time. Dye dilution is similar to thermodilution except that a dye, rather than cold saline, is injected into the pulmonary artery. The amount of dye collected downstream is measured to determine the patient's cardiac output.

[0006] According to the direct Fick method, either the content of oxygen (O₂) or the content of carbon dioxide (CO₂) in both the arterial blood and mixed venous blood are measured. The Fick equation, written for oxygen, is: CO=O₂ uptake/(the content of O₂ in arterial blood−the content of O₂ in mixed venous blood). The Fick equation, written for carbon dioxide, is: CO=CO₂ excreted/(the content of CO₂ in mixed venous blood−the content of CO₂ in arterial blood). As noted above, the direct Fick method requires obtaining a mixed venous blood sample, which is only available in the pulmonary artery. See FIG. 1.

[0007] It can thus be appreciated that thermodilution, dye dilution, and the direct Fick method for determining cardiac output all require insertion of a catheter into the patient at, near, or through the heart. More specifically, in implementing these cardiac output measurements, a catheter is usually floated through the chambers of the heart in order to insert the saline or dye or to obtain the necessary blood sample at the correct location. For this reason, either of the above cardiac output measurement techniques is very invasive. Indeed, it is known that an arrhythmia may result from the placement of the catheter in or through the heart. Therefore, these cardiac output measurement techniques are typically only performed in the most critical of situations, where the need to know the patient's cardiac output outweighs the risk to the patient in taking this measurement.

[0008] The partial CO₂ rebreathing technique for measuring cardiac output, on the other hand, is a noninvasive approach believed to have been developed by Novametrix Medical Systems, Inc. of Wallingford, Conn. (Novametrix). This method is implemented using a device referred to as a NICO™ sensor, which is distributed by Novametrix. The NICO sensor measures the flow of gas to and from the patient and the CO₂ content in the patient's exhaled gas.

[0009] The partial CO₂ rebreathing cardiac output measurement technique is based on the CO₂ Fick equation in conjunction with what is called partial CO₂ rebreathing. According to this partial CO₂ rebreathing technique, cardiac output is measured by comparing the patient's CO₂ excretion to the arterial CO₂ content during normal breathing and during rebreathing, in which the patient rebreathes expired gases for a period of time. Cardiac output is determined as: CO=the change in CO₂ excretion/the change in the arterial CO₂ content.

[0010] Arterial CO₂ is typically determined from a sample of arterial blood. However, in order to eliminate the need for a blood sample to measure the arterial CO₂ content, the partial CO₂ rebreathing technique substitutes end tidal CO₂ (ETCO₂) for the required arterial CO₂ measurement. Therefore, the cardiac output equation becomes: CO=the change in CO₂ excretion/the change in the ETCO₂.

[0011] This partial CO₂ rebreathing technique, however, has several disadvantages. Namely, the patient is preferably intubated or breathing through a trachea tube when taking the flow and CO₂ measurements to capture the total volume of CO₂. In addition, the patient must be heavily sedated or unconscious so that he or she is not breathing spontaneously. If the patient is breathing spontaneously, the increased CO₂ level in the blood during the rebreathing phase would automatically trigger the patient's respiratory system to speed up or deepen the breaths to remove the excess CO₂. It is well known that for most patient's the level of CO₂ is more important than the level of O₂ as a mechanism for triggering ventilation. Such a change in rate or depth of breathing prevents an accurate determination of cardiac output under this technique. It should also be noted that the use of end tidal CO₂, as opposed to the arterial CO₂ content, may introduce errors in determining cardiac output, because there are situations where the end tidal CO₂ may not correlate with the arterial CO₂ content. The partial CO₂ rebreathing cardiac output measurement technique is also disadvantageous because it does not adequately account for shunt blood flow, which is blood that is not oxygenated during the respiratory cycle. This flow cannot be directly measured, but must be estimated when using this conventional cardiac output measurement technique.

[0012] Accordingly, it is an object of the present invention to provide a method of measuring cardiac output that overcomes the shortcomings of conventional cardiac output measurement techniques. This object is achieved according to one embodiment of the present invention by providing a cardiac output measurement method that includes measuring a first parameter indicative of a patient's oxygen uptake and a second parameter indicative of the patient's fractional arterial oxygen concentration. The present method also includes inducing a change in the patient's arterial oxygen concentration and repeating these measurements to monitor the effects resulting from inducing the change in the patient's arterial oxygen concentration. The patient's cardiac output is determined based on the data collected.

[0013] It is yet another object of the present invention to provide an apparatus for non-invasively determining the cardiac output of a patient, including a spontaneously breathing patient, that does not suffer from the disadvantages associated with conventional cardiac measurement systems. This object is achieved by providing an apparatus that includes a system for measuring a first parameter indicative of a patient's oxygen uptake and means for measuring a second parameter indicative of the patient's fractional arterial oxygen concentration, such as a pulse oximeter. A processor determines the cardiac output based on the first parameter, and the second parameter. In addition, an output device outputs the result indicative of the patient's cardiac output.

[0014] These and other objects, features and characteristics of the present invention, as well as the methods of operation and functions of the related elements of structure and the combination of parts and economies of manufacture, will become more apparent upon consideration of the following description and the appended claims with reference to the accompanying drawings, all of which form a part of this specification, wherein like reference numerals designate corresponding parts in the various figures. It is to be expressly understood, however, that the drawings are for the purpose of illustration and description only and are not intended as a definition of the limits of the invention.

[0025] FIG. 1 schematically illustrates a patient's cardiopulmonary system, which is useful in understanding the cardiac output measurement system of the present invention. The cardiac output measurement technique of the present invention measures the output, i.e., rate of flow of blood, from the left side of the heart. As described in detail below, the cardiac output measurement method of the present invention uses the transfer of oxygen from the lungs to the arteries in order to determine cardiac output.

[0026] The presently preferred method of determining the cardiac output includes the following steps, each of which is discussed in detail below:

[0027] (1) quantitatively measuring (a) a parameter indicative of the oxygen uptake of the patient, and (b) a parameter indicative of the patient's fractional arterial oxygen concentration (XaO₂);

[0028] (2) inducing a change in the patient's arterial oxygen concentration while taking measurements (a) and (b) set forth in step (1) to monitor the effects of the change in the patient's arterial oxygen concentration; and

[0029] (3) from the data collected regarding the effect of the change in the patient's arterial oxygen concentration, determining the patient's cardiac output.

[0030] According to the present invention, the patient's cardiac output (CO) is determined based on the change in oxygen uptake versus the change in fractional arterial oxygen concentration resulting from the induced change in the arterial oxygen concentration. Stated another way:

[0031] $\begin{array}{cc}\mathrm{CO}=\frac{\mathrm{change}\mathrm{in}\mathrm{the}\mathrm{oxygen}\mathrm{uptake}}{\mathrm{change}\mathrm{in}\mathrm{the}\mathrm{arterial}\mathrm{oxygen}\mathrm{concentration}}.& \left(1\right)\end{array}$

[0032] It is important to note that the patient's arterial oxygen concentration, not their carbon dioxide concentration, is what is being manipulated in order to induce a change in the patient's oxygen uptake and fractional arterial oxygen concentration. As a result, this method can be performed on a spontaneously breathing patient, as well as on a patient who is not spontaneously breathing. Unlike changing the patient's CO₂ concentration, changing the patient's arterial O₂ concentration for a short time will not cause the patient to automatically attempt to alter their breathing pattern to move the O₂ concentration back to normal. Because this cardiac output measurement technique involves inducing a change in the patient's arterial oxygen concentration, it is referred to as an oxygen concentration modification cardiac output measurement method.

[0033] In one embodiment of the present invention, which is described in detail below, the patient's fractional arterial oxygen concentration is measured non-invasively using a conventional pulse oximeter. Thus, unlike conventional cardiac output measurement methods, the oxygen concentration modification cardiac output measurement method of the present invention can be performed non-invasively on a spontaneously breathing patient.

I. Measuring Airflow, Percent O₂ Inhaled/Exhaled, and the Fractional Arterial Oxygen Concentration

[0034] According to the present invention, the patient's quantitative airflow and a parameter indicative of the percent oxygen inhaled and exhaled by the patient are measured to determine the patient's oxygen uptake. Oxygen uptake, also referred to as oxygen consumed by the patient, is the amount of oxygen absorbed into the blood in the lungs. It is typically expressed in liters as a volume VO₂ or in liters per minute (lpm) as a volume flow rate {dot over (V)}O₂. Thus, equation (1) can be rewritten as follows:

[0035] $\begin{array}{cc}\mathrm{CO}\left(\mathrm{liters}\right)=\frac{\Delta {\mathrm{VO}}_2}{\Delta {\mathrm{XaO}}_2\left(T\right)},& \left(2\right)\end{array}$
where T is a period over which the arterial oxygen concentration changes in response to a change in oxygen absorbed into the blood, as discussed in greater detail below with reference to FIG. 4. Equation (1) can also be rewritten as:

[0036] $\begin{array}{cc}\mathrm{CO}\left(\mathrm{lpm}\right)=\frac{\Delta \stackrel{.}{V}{O}_2}{\Delta {\mathrm{XaO}}_2}.& \left(3\right)\end{array}$

[0037] Oxygen uptake, which is measured during a breathing cycle, is determined by measuring the volumetric airflow Q_patient to and from the patient, the % O₂ inhaled, and the % O₂ exhaled during that breathing cycle. Volumetric airflow is measured using a flow meter, such as a conventional pneumotach, that is capable of quantitatively measuring the flow of gas to and from the patient's airway. U.S. Pat. No. 6,017,315 to Starr et al., the contents of which are incorporated herein by reference, describes a suitable flow meter that quantitatively measures the flow of gas to and from a patient.

[0038] The % O₂ inhaled and % O₂ exhaled is measured using a conventional oxygen analyzer. An example of a combination flow sensing element and O₂ concentration analyzer window suitable for use in the present invention is taught in provisional U.S. Patent Application No. 60/170,918, the contents of which are incorporated herein by reference. More specifically, the present invention contemplates determining the % O₂ inhaled by measuring the patient's fraction of inspired oxygen (FIO₂) as a parameter indicative of the percent oxygen inhaled and exhaled, and multiplying this FIO₂ by 100, i.e., % O₂ inhaled=FIO₂ (inhaled)*100. A similar process is used to determine % O₂ exhaled.

[0039] Oxygen uptake, VO₂, for one breath, is determined as follows:

[0040] $\begin{array}{cc}{\mathrm{VO}}_2\mathrm{inhaled}={\int }_{t_1}^{t_2}\left(Q_{\mathrm{patient}}\left[\%O_2/100\right]\right)dt,& \left(4\right)\\ {\mathrm{VO}}_2\mathrm{ex}\mathrm{haled}={\int }_{t_2}^{t_3}\left(Q_{\mathrm{patient}}\left[\%O_2/100\right]\right)dt,\mathrm{and}& \left(5\right)\end{array}$
VO₂=VO₂inhaled−VO₂exhaled,  (6)

where t₁ is the start of inhalation, t₂ is the end of inhalation or start of exhalation, and t₃ is the end of exhalation. Oxygen uptake in liters per minute is then determined as:
{dot over (V)}O₂=VO₂*f_breath,  (7)
were f_breath is the frequency of breaths, i.e., breaths per minute.

[0041] There are a variety of parameters indicative of fractional arterial oxygen concentration, XaO₂, of a patient that can be measured and used in the cardiac output determination method. One embodiment of the present invention contemplates measuring at least one of the following blood gas constituents, SaO₂, PaO₂, and CaO₂ as the parameter indicative of the patient's fractional arterial oxygen concentration XaO₂. These parameters are measured from an arterial blood sample or using a continuously indwelling catheter. It is preferable for one or more of these constituents to be measured continuously, for example, using an indwelling catheter so that the effects of the induced change in arterial oxygen concentration on the oxygen uptake and fractional arterial oxygen concentration can be monitored on a substantially continuous basis. This is especially important because of the relatively short duration of the effects of the induced change in arterial oxygen concentration resulting from the oxygen concentration modification step.

[0042] The present invention also contemplates measuring the pulse oximetry oxygen saturation level (SpO₂) of the patient as the parameter indicative of the fractional arterial oxygen concentration XaO₂. This measurement is advantageous in that the SpO₂ can be measured non-invasively using a conventional pulse oximeter. It can also be taken on a generally continuous basis to closely monitor the effects of the induced oxygen concentration modification on the patient's actual fractional arterial oxygen concentration.

[0043] Although the SpO₂ level can be taken from almost any location on the patient, such as the finger or ear, in a preferred embodiment, the SpO₂ is measured across the nasal septum. This location is especially desirable because it represents a relatively direct flow from the carotid artery, as shown in FIG. 1.

[0044] Depending on which parameter, SpO₂, SaO₂, PaO₂, or CaO₂, indicative of fractional arterial oxygen concentration XaO₂ is measured, a conversion may be required in order to arrive at the patient's actual fractional arterial oxygen concentration XaO₂. The only parameter indicative of fractional arterial oxygen concentration XaO₂ that does not have to be converted in order to arrive at the patient's fractional arterial oxygen concentration XaO₂ is the arterial oxygen content measurement CaO₂, because CaO₂ is a direct measurement of the fractional arterial oxygen concentration. Thus, CaO₂=XaO₂, and no conversion is necessary.

[0045] Oxygen saturation, SaO₂, on the other hand, is not a direct measurement of the fractional arterial oxygen concentration XaO₂. If SaO₂ is the measured parameter, a conversion is needed, so that the measured SaO₂ can be used as the fractional arterial oxygen concentration XaO₂. For a normal adult, there is a linear relation between SaO₂ and CaO₂ and, hence, between SaO₂ and XaO₂. More specifically, the following relationship is known:
Vol % O₂=(Hb concentration)(O₂ saturation (SaO₂))(O₂ carrying capacity of Hb),  (8)
where, for a normal adult, the O₂ carrying capacity of hemoglobin (Hb) is approximately 1.34 mlO₂/gmHb, and the Hb concentration is approximately 15 gmHb/100 mlblood. Thus, for a normal adult:

[0046] $\begin{array}{cc}{\mathrm{XaO}}_2=\frac{\mathrm{Vol}\%O_2}{100}=\frac{15\mathrm{gmHb}}{100\mathrm{ml}\mathrm{blood}}*\frac{{\mathrm{SaO}}_2}{100}*\frac{1.34\mathrm{ml}{O}_2}{\mathrm{gmHb}}.& \left(9\right)\end{array}$
Equation (9) can be simplified as:
XaO₂=SaO₂*k,  (10)
where, for a normal adult:

[0047] $\begin{array}{cc}k=\frac{\left(15\right)\left(1.34\right)}{\left(100\right)\left(100\right)}·& \left(11\right)\end{array}$
Of course, the values for Hb concentration (15 gmHb) and O₂ carrying capacity of Hb (1.34 mlO₂) can differ depending on the individual. Therefore, if the Hb concentration and O₂ carrying capacity of Hb for an individual are known, a more exact relationship (k value) between SaO₂ and XaO₂ can be determined. The present invention contemplates that the values for Hb concentration and/or O₂ carrying capacity of Hb can be directly input by the user, automatically input from measurements taken by a co-oximeter or other equivalent device via a communication link with such a device, manually or automatically selected from a range of values based on information about the patient, or a default value can be used.

[0048] There is also a known relationship, albeit nonlinear, between PaO₂ and SaO₂. This nonlinear relationship is graphically depicted in FIG. 2, which is referred to as an oxygen-hemoglobin dissociation curve 10. If PaO₂ is the measured parameter, it must first be converted to an SaO₂ using the dissociation curve, which can be accomplished using any conventional technique. Thereafter, the conversion factor k for SaO₂ must be used to arrive at the patient's fractional arterial oxygen concentration XaO₂ as discussed above.

[0049] A patient's SaO₂, PaO₂, or CaO₂ can only be measured by sampling the patient's arterial blood or using a continuously indwelling catheter, either of which is a relatively invasive procedure. SpO₂, on the other hand, which is an estimation of SaO₂, is measured non-invasively. Therefore, measuring the patient's SpO₂ has the advantage of being fast, easy, and non-invasive. If SpO₂ is taken as the measured parameter, it is considered an approximation of SaO₂, i.e., SpO₂≈SaO₂. Thus, the conversion factor k is applied to the measured SpO₂ to arrive at the patient's fractional arterial oxygen concentration XaO₂, i.e., XaO₂≈SpO₂*k.

II. Inducing a Change in Arterial Oxygen Concentration

[0050] The present technique for determining a patient's cardiac output involves inducing a change the patient's arterial oxygen concentration. This can be done in a variety of ways, several of which are discussed below, so long as there is a measurable difference between the patient's baseline arterial oxygen concentration and the patient's arterial oxygen concentration following the induced change therein. Because the goal of this process is to force a change in the patient's arterial oxygen concentration, this step in the cardiac output measurement process of the present invention is referred to herein as the “oxygen concentration modification step.”

[0051] It should be noted that the arterial oxygen concentration can either be increased or decreased depending on the condition of the patient. For example, a generally healthy patient has an oxygen saturation level of approximately 98%. As a result, there is very little room to improve oxygenation, e.g., up to 99%. Therefore, the present invention contemplates reducing the patient's oxygen saturation as one technique for inducing a change in the patient's arterial oxygen concentration, especially in those patients with a relatively high baseline SaO₂.

[0052] Reducing the patient's oxygen saturation can be accomplished by reducing the fraction of inspired oxygen (FIO₂) in the patient's inhaled gas. This can be accomplished, for example, by increasing the concentration of other inhaled gas constituents, such as nitrogen, which has the effect of lowering the patient's arterial oxygen saturation. In one embodiment of the present invention, the patient breathes nitrogen for one or more breaths, thereby reducing their arterial oxygen concentration. This technique is particularly suited for patients with a relatively high baseline oxygen concentration. This technique is particularly suited for patients with a relatively high baseline oxygen concentration.

[0053] As noted above, changing the patient's arterial oxygen concentration can also be accomplished by increasing the fraction of inspired oxygen in the inhaled gas. This can be accomplished, for example, by adding supplemental oxygen to the patient's inhaled gas, and, therefore, is particularly suited for patients with a relatively low baseline oxygen concentration.

[0054] The present invention also contemplates changing the patient's arterial oxygen concentration by having the patient rebreathe expired gas. However, because this will raise the patient's CO₂ level, this technique is best used on non-spontaneously breathing patients, where increased levels of CO₂ will not cause unusual breathing patterns. For a non-spontaneously breathing patient, the present invention also contemplates changing the arterial oxygen concentration by momentarily pausing the ventilator used to provide the patient's breathing.

[0055] Rebreathing expired gas can be used to change the patient's arterial oxygen concentration in a spontaneously breathing patient if steps are taken to minimize the increase in the patient's CO₂ level. For example, the carbon dioxide CO₂ is preferably is removed from the rebreathed gas so that the patient does not dramatically alter their breathing pattern due to rebreathing of exhaled carbon dioxide.

[0056] An exemplary embodiment of the present invention contemplates using a conventional CO₂ “scrubbing” technique for removing the CO₂ from the gas rebreathed by the patient. This is accomplished, for example, by placing a CO₂ scrubber in the rebreathing circuit or by passing the patient's exhaled gas through a CO₂ scrubber before it is returned to the patient. In either case, the rebreathed gas will have a lower oxygen concentration, thereby accomplishing the goal of changing the patient's arterial oxygen concentration without having the patient breathing CO₂, which will likely trigger a relatively rapid increase in the patient's breath rate.

III. Determining Cardiac Output

[0057] The present invention contemplates several techniques for calculating cardiac output based on the changes in oxygen uptake and the change in fractional arterial oxygen concentration resulting from the induced change in arterial oxygen concentration. Each of these techniques is discussed in turn below.

[0058] A. Technique 1—Calculating Cardiac Output Based on the Area Under the Curves

[0059] It is well known that the flow of fluid in a stream or conduit can be measured by monitoring a known mass or bolus of an indicator fluid downstream of wherein it was introduced into that stream. For example, it is known that the flow of fluid can be expressed as follows:

[0060] $\begin{array}{cc}\mathrm{Flow}=\frac{m}{\stackrel{\_}{c}T}=\frac{\mathrm{mass}\mathrm{of}\mathrm{indicator}\mathrm{injected}}{\begin{array}{c}\mathrm{concentration}\mathrm{of}\mathrm{indicator}\times \\ \mathrm{time}\mathrm{period}\mathrm{of}\mathrm{change}\mathrm{in}\mathrm{concentration}\end{array}}& \left(12\right)\end{array}$
This relation is described, for example, by L. A. Geddes et al. in the textbook entitled, “Principles of Applied Biomedical Instrumentation”, 3rd Edition, 1989, pages 576-578, and is the same principle used to measure cardiac output using the dye dilution technique.

[0061] The present invention contemplates introducing a bolus of non-oxygen into a patient's circulatory system as the indicator fluid rather than introducing a conventional dye. In other words, the present invention contemplates perturbing the cardio-respiratory system by removing a known volume of oxygen, which is referred to herein as introducing a bolus of non-oxygen into the system. Introducing a bolus of non-oxygen is equivalent to inducing a change in the patient's arterial oxygen concentration as described above. If the indicator fluid is a bolus or mass of non-oxygenated blood, the relationship described in equation (12) can be written as follows:

[0062] $\begin{array}{cc}\mathrm{CO}=\frac{{\mathrm{VO}}_{2\left(\mathrm{bolus}\right)}}{\left({\stackrel{\_}{X}}_a{O}_2\right)\left(T\right)},& \left(13\right)\end{array}$
where CO is cardiac output, VO_2(bolus), is the volume of non-oxygen taken up or absorbed by the blood in the lungs, i.e., the oxygen uptake of the non-oxygen bolus. T is the period over which the arterial oxygen concentration changes, i.e., a decrease in the illustrated embodiment, in response to the change in oxygen taken up by the patient (See FIG. 4), which is also a decrease in the illustrated embodiment. Finally, X_aO₂ is the mean arterial oxygen concentration over period T.

[0063] FIGS. 3A and 3B are graphs that illustrate the change in a patient's volume flow rate of oxygen taken in by the blood {dot over (V)}O₂ (FIG. 3A) and the change in oxygen uptake VO₂ (FIG. 3B) that takes place during the oxygen concentration modification step, in which a change in the arterial oxygen concentration, XaO₂, is induced using any of the above-described techniques. More specifically, FIGS. 3A and 3B illustrate the change in oxygen uptake that takes place by having the patient take one breath, i.e., from time t₁ to t₃, that is relatively devoid of oxygen. It should be noted that the change in oxygen uptake volume is illustrated in a step fashion in FIG. 3B because oxygen uptake is measured and calculated on a breath-by-breath basis. As shown in FIGS. 3A and 3B, it takes several breaths for the patient's oxygen uptake to stabilize back to its baseline level. Area A in FIG. 3A represents the change in the oxygen uptake Δ{dot over (V)}O₂ of the patient that occurs as a result of the oxygen concentration modification step. Similarly, FIG. 3B represents a histogram of the oxygen uptake volumes 100, 102, 104, and 106 resulting from the oxygen modification step.

[0064] FIG. 4 illustrates the change in arterial oxygen concentration XaO₂ resulting from the induced change in arterial oxygen concentration, which, in this embodiment, involves having the patient take one breath that is devoid of oxygen. In other words, FIG. 4 graphically shows the decrease in arterial oxygen concentration that occurs over time period T resulting from the oxygen concentration modification step shown in FIGS. 3A and 3B, which, in the present embodiment, is a decrease in the oxygen uptake.

[0065] The volume of non-oxygen taken by the patient's blood, VO_2(bolus), which is shown as area A in FIG. 3A, can be calculated as follows:

[0066] $\begin{array}{cc}{\mathrm{VO}}_{2\left(\mathrm{bolus}\right)}={\int }_0^T\left[\stackrel{.}{V}{O}_{2\left(\mathrm{baseline}\right)}\left(0\right)-\stackrel{.}{V}{O}_{2\left(\mathrm{bolus}\right)}\left(1\right)\right]dt,& \left(14\right)\end{array}$
where {dot over (V)}O_2(bolus)(0) is the baseline steady-state volume flow rate of oxygen taken by the blood prior to the bolus injection, and {dot over (V)}O_2(bolus)(t) is the volume how rate oil oxygen taken up by the blood after the bolus injection. It should be noted that period T in equation (14) can be the same as period T in FIG. 4, or it can be a different period, so long as the function of calculating the volume of non-oxygen taken up by the blood is substantially met, i.e., area A is calculated to a close approximation.

[0067] The mean arterial oxygen concentration, X_aO₂, which is shown in FIG. 4, can be calculated as follows:

[0068] $\begin{array}{cc}{\stackrel{\_}{X}}_a{O}_2=\frac{1}{T}{\int }_0^T\left[X_a{O}_2\left(0\right)-X_a{O}_2\left(t\right)\right]dt,& \left(15\right)\end{array}$
where X_aO₂(0) is the baseline steady-state arterial oxygen concentration prior to the bolus injection, and X_aO₂(t) is the arterial oxygen concentration after the bolus injection.

[0069] Combining equations (14) and (15) into equation (13) yields:

[0070] $\begin{array}{cc}\mathrm{CO}=\frac{{\int }_0^T\left[\stackrel{.}{V}{O}_{2\left(\mathrm{baseline}\right)}\left(0\right)-\stackrel{.}{V}{O}_{2\left(\mathrm{bolus}\right)}\left(t\right)\right]dt}{{\int }_0^T\left[X_a{O}_2\left(0\right)-X_a{O}_2\left(t\right)\right]dt}.& \left(16\right)\end{array}$
Thus, a patient's cardiac output can be estimated by monitoring the patient's oxygen uptake using any conventional technique and by measuring a parameter indicative of the patient's fractional arterial oxygen concentration (XaO₂) before and after a bolus of non-oxygen is introduced into the patient's system, which has the effect of altering the patient's arterial oxygen concentration.

[0071] It can be appreciated that the expression {dot over (V)}O_2(baseline)(0)−{dot over (V)}O_2(bolus)(t) in the numerator in equation (16) represents the change in the volume flow rate of oxygen taken up by the blood relative to the baseline steady-state volume flow rate. In the example shown in FIGS. 3A and 3B, this change is shown as a lowering of the volume flow rate of consumed oxygen, i.e., dipping of the {dot over (V)}O_2(bolus)(t) curve below the baseline, because in this example, the patient was presented with a bolus of non-oxygen, e.g., by reducing the FIO₂.

[0072] However, the present invention also contemplates presenting the patient with a bolus of increased oxygen, e.g., by increasing the FIO₂. The result will be an increase in the volume flow rate of consumed oxygen, i.e., an increase of the {dot over (V)}O_2(bolus)(t) curve above the baseline. In which case, the change in the volume flow rate of oxygen taken by the blood relative to the baseline steady-state volume flow rate in equation (16) can be expressed as follows:

[0073] $\begin{array}{cc}{\mathrm{VO}}_{2\left(\mathrm{bolus}\right)}={\int }_0^T\left[\stackrel{.}{V}{O}_{2\left(\mathrm{bolus}\right)}\left(t\right)-\stackrel{.}{V}{O}_{2\left(\mathrm{baseline}\right)}\left(0\right)\right]dt.& \left(17\right)\end{array}$
This would similarly cause the change in arterial oxygen concentration to appear as in increase over the baseline value so that equation (16) can be expressed as:

[0074] $\begin{array}{cc}{\stackrel{\_}{X}}_a{O}_2=\frac{1}{T}{\int }_0^T\left[X_a{O}_2\left(t\right)-X_a{O}_2\left(0\right)\right]dt,& \left(18\right)\end{array}$
Thus, as before, we can substitute equations (17) and (18) into equation (13) to get:

[0075] $\begin{array}{cc}\mathrm{CO}=\frac{{\int }_0^T\left[\stackrel{.}{V}{O}_{2\left(\mathrm{bolus}\right)}\left(t\right)-\stackrel{.}{V}{O}_{2\left(\mathrm{baseline}\right)}\left(0\right)\right]dt}{{\int }_0^T\left[X_a{O}_2\left(t\right)-X_a{O}_2\left(0\right)\right]dt}.& \left(19\right)\end{array}$
Equation (19) represents situations where the patient receives an increased level of oxygen as a means to alter the arterial oxygen concentration. It should be noted, however, that equation (16) is suitable for either situation, because the signs in the numerator and denominator would cancel where there is an increase over the baseline value.

[0076] It can be further appreciated that the numerator in equation (13) represents by the sum of the volumes VO₂ in the histogram shown in FIG. 3B. That is, summing volumes indicated by levels 100, 102, 104, and 106 yields an indication of the total volume of non-oxygen taken in by the blood. Thus, equation (13) can be rewritten as:

[0077] $\begin{array}{cc}\mathrm{CO}=\frac{\sum _0^T\Delta {\mathrm{VO}}_2}{\stackrel{\_}{X}{\mathrm{aO}}_2*T},& \left(20\right)\end{array}$
where

[0078] $\sum _0^T\Delta {\mathrm{VO}}_2$
represents the sum of the bars of the histogram during period T (which is determined as discussed above with respect to FIG. 4). Substituting equation (15) into equation (20) allows equation (20) to be rewritten as:

[0079] $\begin{array}{cc}\mathrm{CO}=\frac{\sum _0^T\Delta {\mathrm{VO}}_2}{{\int }_0^T\left[X_a{O}_2\left(0\right)-X_a{O}_2\left(t\right)\right]dt}.& \left(21\right)\end{array}$
Either technique: 1) integrating curve {dot over (V)}O_2(bolus)(t) over period T (FIG. 3A, equations (16) and (19)), or 2) summing the changes in volume of oxygen taken in by the blood ΔVO₂ over period T (FIG. 3B, equations (20) and (21)) provides an estimation of cardiac output.

[0080] FIGS. 5A, 5B, and 6 are similar to FIGS. 3A, 3B, and 4, respectively, except that FIGS. 5A, 5B, and 6 take into consideration a scenario in which the bolus of oxygen or non-oxygen in the patient's blood begins to recirculate at time x during the oxygen concentration modification step. As shown in FIG. 5A, recirculation will cause the volume flow rate of oxygen taken by the blood {dot over (V)}O_2(bolus)(t), i.e., curve 103, to move toward the baseline level slower than if there was no recirculation, as indicated by portion 105 of curve 103. Similarly, as shown in FIG. 5B, the volume of oxygen taken in by the blood VO₂ will also move toward the baseline level more slowly. This can be appreciated by comparing FIG. 5A to 3A and FIG. 5B to FIG. 3B. As shown in FIG. 6, the arterial oxygen concentration XaO₂ curve 107 will also move toward the baseline, steady-state level more slowly than in the absence of recirculation.

[0081] The present invention contemplates dealing with the effects of recirculation by estimating time period T for use in the above cardiac output calculations. Estimating T involves extrapolating curve 107 using conventional extrapolation techniques, as shown by dashed line 109, to determine an extrapolated time t_a when the arterial oxygen concentration returns to the base line level. T is then determined from the start of the change in arterial oxygen concentration to time t_a, as shown in FIG. 6. This time period T based on extrapolation is then used, as shown in FIG. 5A to solve equation (15), or as shown in FIG. 5B to solve equation (19). For example, the consumed oxygen volumes corresponding to levels 110 112, and 114 would be used in solving equation (19), while levels 116, 118, and 120 would not.

B. Technique 2 for—Calculating Cardiac Output

[0082] In another formulation for cardiac output, we start with the simple relationship between the volume of oxygen contained in an arbitrary volume of flowing blood. The oxygen volume can be evaluated as:
ΔVO₂=(ΔX_aO₂)(ΔV),  (22)

[0083] If we solve for total blood volume, equation (22) becomes

[0084] $\begin{array}{cc}\Delta V=\frac{\Delta {\mathrm{VO}}_2}{\Delta X_a{O}_2},& \left(23\right)\end{array}$

[0085] We will assume that the volume of oxygen in the numerator of (23) is simply the oxygen taken up by the blood as measured at the airway. This is simply:
ΔVO₂=VO₂(t′_start)−VO₂(t′_end),  (24)
where t_start is the volume at an arbitrary starting point on the volume time curve of airway oxygen and t_end is the volume at some point in time after t_start.

[0086] The change in arterial oxygen concentration can then simply be written as:
ΔX_aO₂=X_aO₂(t′_start)−X_aO₂(t′_end),  (25)
where t′_start is the temporal location in the concentration curve that corresponds physically to t_start and t′_end is the temporal location in the concentration curve that corresponds physically to t_end.

[0087] Substituting equations (24) and (25) into (23), we have

[0088] $\begin{array}{cc}\Delta V=\frac{{\mathrm{VO}}_2\left(t_{\mathrm{start}}\right)-{\mathrm{VO}}_2\left(t_{\mathrm{end}}\right)}{X_a{O}_2\left(t_{\mathrm{start}}^{\prime }\right)-X_a{O}_2\left(t_{\mathrm{end}}^{\prime }\right)},& \left(26\right)\end{array}$

[0089] Because equation (26) represents the volume of blood, we can calculate the cardiac output as:

[0090] $\begin{array}{cc}\mathrm{CO}=\frac{\Delta V}{t_{\mathrm{end}}^{\prime }-t_{\mathrm{start}}^{\prime }}.& \left(27\right)\end{array}$

[0091] Note that because cardiac output is the flow of blood, we must use the time span associated with the flowing blood, t′_end−t′_start.

[0092] Finally, substituting equation (26) into equation (27) we have:

[0093] $\begin{array}{cc}\mathrm{CO}=\left[\frac{1}{t_{\mathrm{end}}^{\prime }-t_{\mathrm{start}}^{\prime }}\right]\left[\frac{{\mathrm{VO}}_2\left(t_{\mathrm{start}}\right)-{\mathrm{VO}}_2\left(t_{\mathrm{end}}\right)}{X_a{O}_2\left(t_{\mathrm{start}}^{\prime }\right)-X_a{O}_2\left(t_{\mathrm{end}}^{\prime }\right)}\right].& \left(28\right)\end{array}$

[0094] Referring now to FIGS. 7 and 8, for example, t_start corresponds to point t₁, t′_start corresponds to point t₄, t_end is arbitrarily selected for illustration purposes as t₃, t′_end therefore correspond to point t₅. Thus, cardiac output can be determined as:

[0095] $\begin{array}{cc}\mathrm{CO}=\left[\frac{1}{t_5-t_4}\right]\left[\frac{{\mathrm{VO}}_2\left(t_1\right)-{\mathrm{VO}}_2\left(t_3\right)}{X_a{O}_2\left(t_4\right)-X_a{O}_2\left(t_5\right)}\right].& \left(29\right)\end{array}$
C. Technique 3—Calculating Cardiac Output Based on the Magnitude of the Curves

[0096] Yet another technique for determining cardiac output involves comparing the magnitude of the change in oxygen uptake with the magnitude of the change in arterial oxygen concentration resulting from the oxygen concentration modification step. FIGS. 9 and 10 illustrate the changes in the patient's oxygen uptake and arterial oxygen saturation, respectively, resulting from the oxygen concentration modification step. From FIG. 9, it can be appreciated that there is a relatively large initial drop in oxygen uptake at the start of the oxygen concentration modification step, i.e., from time t₁ to t₃. The magnitude of this drop can be determined from the output of the flow sensor and the oxygen analyzer using any conventional technique. From FIG. 10, it can be appreciated that there is a corresponding drop in arterial oxygen saturation. Although, as noted above, this drop in arterial oxygen concentration is delayed in time from the initial drop in oxygen uptake. This drop begins at time t_c and reaches a maximum difference from the initial baseline level at time t_m. The value of the fractional arterial oxygen concentration at t_m, XaO₂(t_m), can be determined using any conventional technique.

[0097] As a side note, it is worth remembering that the oxygen concentration modification step also contemplates increasing the patient's arterial oxygen in some situations. In which case, the change in oxygen uptake will be in the positive direction, opposite that shown in FIGS. 3A, 3B, 5A, 5B, 7, and 9. Similarly, the change in the fractional arterial oxygen concentration will also be in the positive direction, opposite that shown in FIGS. 4, 6, 8, and 10. The techniques for determining cardiac output discussed herein are equally applicable where the oxygen concentration modification step is performed by increasing the patient's arterial oxygen.

[0098] Referring again to FIGS. 9 and 10, one embodiment of the present invention contemplates comparing the magnitude of the change in oxygen uptake from time t₁ to t₃ with the magnitude of the change in arterial oxygen concentration from time t_c to t_m, so that the patient's cardiac output is defined as:

[0099] $\begin{array}{cc}\mathrm{CO}=\frac{\frac{\Delta V{O}_2\left(\mathrm{Magnitude}{t}_1\mathrm{to}{t}_3\right)}{t_3-t_1}}{Xa{O}_2\left(\mathrm{Magnitude}{t}_c\mathrm{to}{t}_m\right)}=\frac{\Delta \stackrel{.}{V}{O}_2\left(\mathrm{Magnitude}{t}_1\mathrm{to}{t}_3\right)}{\Delta Xa{O}_2\left(\mathrm{Magnitude}{t}_c\mathrm{to}{t}_m\right)}.& \left(28\right)\end{array}$
It can be appreciated that equation (30) represents a direct calculation for cardiac output because the units represented by the numerator are, for example, liters/second or liters/minute, and the denominator is unitless.

[0100] Another embodiment of the present invention contemplates determining cardiac output based on the time period t_c to t_e, where t_c to t_e=t₁ to t₃, so that

[0101] $\begin{array}{cc}\mathrm{CO}=\frac{\frac{\Delta V{O}_2\left(\mathrm{Magnitude}{t}_1\mathrm{to}{t}_3\right)}{t_3-t_1}}{\Delta Xa{O}_2\left(\mathrm{Magnitude}{t}_c\mathrm{to}{t}_e\right)}=\frac{\Delta \stackrel{.}{V}{O}_2\left(\mathrm{Magnitide}{t}_1\mathrm{to}{t}_3\right)}{\Delta Xa{O}_2\left(\mathrm{Magnitide}{t}_c\mathrm{to}{t}_e\right)}.& \left(29\right)\end{array}$
As with equation (30), equation (31) also represents a direct calculation for cardiac output because the units represented by the numerator are, for example, liters/second or liters/minute, and the denominator is unitless. In these embodiments, the change in magnitude of the oxygen uptake and fractional arterial oxygen concentration are monitored during the oxygen modification step, which is why this technique is referred to in the preceding section heading as the “Magnitude of the Curve” technique.

[0102] The determination of cardiac output using equations (30) or (31) can also be understood by referring back to equation (16). That is, equation (16) can be readily derived to arrive at equation (30) or (31). For example, if equation (16) is adjusted by multiplying the denominator across the expression we have:

[0103] $\begin{array}{cc}\mathrm{CO}{\int }_0^T\left[X_a{O}_2\left(0\right)-X_a{O}_2\left(t\right)\right]dt={\int }_0^T\left[\stackrel{.}{V}{O}_{2\left(\mathrm{baseline}\right)}\left(0\right)-\stackrel{.}{V}{O}_{2\left(\mathrm{bolus}\right)}\left(t\right)\right]dt.& \left(32\right)\end{array}$
Differentiating both sides of equation (32) with respect to time yields the following expression:
CO[X_aO₂(0)−X_aO₂(t)]=[{dot over (V)}O_2(baseline)(0)−{dot over (V)}O_2(bolus)(t)]  (33)
which can be rewritten as:

[0104] $\begin{array}{cc}\mathrm{CO}=\frac{\left[\stackrel{.}{V}{O}_{2\left(\mathrm{baseline}\right)}\left(0\right)-\stackrel{.}{V}{O}_{2\left(\mathrm{bolus}\right)}\left(t\right)\right]}{\left[X_a{O}_2\left(0\right)-X_a{O}_2\left(t\right)\right]}.& \left(34\right)\end{array}$
It can be appreciated that equation (34) corresponds to equations (30) and (31), where Δ{dot over (V)}O₂ in equation (30) or (31) is equal to the expression {dot over (V)}O_2(baseline)(0)−{dot over (V)}O_2(bolus)(t) in equation (34), and where ΔX_aO₂ in equations (30) and (31) is equal to the expression X_aO₂(0)−X_aO₂(t) in equation (34), except that specific times t_m or t_c are used in equations (30) and (31) in place of {dot over (V)}O_2(bolus)(t) in equation (34).

[0105] One embodiment of the present invention contemplates determining the baseline oxygen uptake and baseline arterial oxygen concentration before performing the oxygen concentration modification step so that the changes in oxygen uptake and baseline arterial oxygen concentration resulting from the oxygen concentration modification step can be compared to this baseline. It is to be understood, however, that in an alternative embodiment of the present invention, the baseline oxygen uptake and baseline arterial oxygen concentration are established after the effects of the oxygen concentration modification step; namely, after the patient's cardio-pulmonary system has returned to a steady state following the oxygen concentration modification step.

[0106] FIGS. 11 and 12 schematically illustrate an exemplary embodiment of a cardiac output measurement device 30 used to implement the above-described cardiac output measurement method. Cardiac output measurement device 30 includes a patient flow measurement system 32 for quantitatively measuring the flow of gas to and from the patient and an oxygen analyzer 34 that measures the patient's fraction of inspired oxygen (FIO₂). Patient flow measurement system 32 includes a flow sensor 33, also referred to as a flow element, that creates a pressure differential for measuring the flow of gas passing through the flow element Oxygen analyzer 34 includes an oxygen analyzing element 35, which is essentially an airway adapter optical window and an O₂ transducer having phototransmitter and photodector, that is used to measure the amount of oxygen passing in front of the optical window. Flow sensor 33 and oxygen analyzing element 35 are preferably located proximate to the patient's airway. The outputs of the patient flow and oxygen analyzing systems are provided to a microprocessor 36 for calculating the patient's oxygen uptake.

[0107] Cardiac output measurement device 30 includes means 38 for detecting a parameter indicative of the fractional arterial oxygen concentration, XaO₂, of a patient. As noted above, this parameter is any one of either SpO₂, SaO₂, PaO₂, or CaO₂. An example of a sensor that measures SpO₂ is a conventional pulse oximeter, and a sensor that measures SaO₂, PaO₂, or CaO₂ is a continuous indwelling catheter. Depending on the parameter measured, a conversion to XaO₂ may be necessary. This can be done, for example, by microprocessor 36. In the embodiment illustrated in FIG. 12, the pulse oximeter includes a pulse oximeter sensor 39 in contact with the patient to measure the oxygen saturation SpO₂ of patient 37.

[0108] The present invention contemplates that cardiac output measurement device 30 includes an input/output interface 40 for communicating with the user. For example, a display or other indicator may be provided that notifies the user when to induce that change in arterial oxygen concentration, as well as outputs the cardiac measurement result. A communication link 42 can also be provided for downloading or receiving information and commands to or from a remote location.

[0109] One embodiment of the present invention contemplates that one or more of the patient flow measurement system, the oxygen analyzing system, and the fractional arterial oxygen concentration measuring system can be implemented in a separate, stand-alone, module with the output of each being provided to processor 36. This enables different types of patient flow, oxygen analyzing, and arterial oxygen concentration measuring systems to be used with a common cardiac output determination module. One benefit being that existing patient flow sensors, oxygen analyzers, and arterial oxygen concentration measuring systems, such as a conventional pulse oximeter, can be used to provide the required inputs to the cardiac output module.

[0110] However, the present invention also contemplates that the patient flow measuring system, the oxygen analyzing system, and arterial oxygen concentration measuring system, or any combination thereof, can be integrated into a single housing 43, as shown, for example, in FIG. 12. In this embodiment, the measuring elements of each system, such as the flow element 33, the airway adapter and O₂ transducer 35, and the pulse oximeter sensor 39, provide inputs, e.g., electronic, optical, pneumatic, or otherwise, to one or more processing systems in housing 43.

[0111] Also necessary for purposes of the present invention, as shown in FIG. 12, is a device or technique, generally indicated at 50, for inducing a change in the patient's arterial oxygen concentration. In the illustrated exemplary embodiment, device 50 is a rebreathing system that captures the patient's expired gas in a collection reservoir 52. A valve 54 controls the flow of gas, so that when the cardiac output system is not actuated, the patient's airway communicates with ambient atmosphere or a conventional ventilator or pressure support system (not shown). In this embodiment, when the cardiac output is to be measured, valve 54 is controlled manually or via processor 36, to cause the patient's exhaled gas to be delivered to reservoir 52 where it is collected. Because the gas collected in reservoir 52 has been exhaled by the patient, its oxygen concentration is significantly reduced.

[0112] In a further embodiment of the present invention, a device 56 for removing CO₂ is included in rebreathing system 50, so that the spontaneously breathing patient does not rebreathe significant amounts of CO₂. In a preferred embodiment of the present invention, device 56 is a CO₂ scrubber that removes CO₂ from the gas passing therethrough. As noted above, for a non-spontaneously breathing patient, CO₂ removal device 56 is optional, because their breathing pattern is controlled by the ventilator regardless of the CO₂ levels inhaled by the patient.

[0113] Although the invention has been described in detail for the purpose of illustration based on what is currently considered to be the most practical and preferred embodiments, it is to be understood that such detail is solely for that purpose and that the invention is not limited to the disclosed embodiments, but, on the contrary, is intended to cover modifications and equivalent arrangements that are within the spirit and scope of the appended claims.