METHOD AND APPARATUS FOR ESTIMATING SHUNT

Field of the Invention

The present invention relates to a method, an apparatus and a computer program for estimating shunt, and in particular to a method, apparatus and computer program for minimally invasive estimation of shunt based on carbon dioxide measurements.

Description of the Prior Art

Human cells need oxygen (O₂) to live because they obtain energy by consuming O₂and glucose throughout aerobic metabolism. The lungs take O₂molecules from air during breathing, which diffuse into capillary blood through the alveolar-capillary membrane—a passive process called gas exchange. O₂molecules then bind to hemoglobin and are transported by the blood assuring an optimal O₂delivery to all body cells.

Gas exchange at the lung level is the key process and it depends on the close matching of ventilation delivering O₂to the gas exchange surface, the alveolar-capillary membrane, and blood perfusion taking up oxygen and offloading carbon dioxide. Ventilation-perfusion (V/Q) mismatch is the underlying cause of most gas exchange abnormalities and is often a result of pulmonary and cardiovascular diseases.

In this context, shunt is an important physiological parameter. There are numerous of different and often inconsistent definitions of shunt in the medical literature. In this application, shunt is the sum of anatomic shunt and pulmonary shunt. Anatomic shunt is the fraction of blood bypassing the alveoli of the lungs through anatomic channels. The anatomic shunt is often referred to as normal shunt or physiological shunt and is related to the anatomical fact that the blood of the bronchial veins and the Thebesian veins drain in the left heart without undergoing gas change in the pulmonary capillaries. The anatomic shunt accounts for approximately 2% to 4% of the normal cardiac output. Pulmonary shunt is the fraction of pulmonary blood flow perfusing the alveoli of the lungs but not participating in gas exchange due to insufficient ventilation, i.e. the fraction of total shunt caused by zero or low V/Q ratio. Thus, in this application, pulmonary shunt corresponds to what is often referred to as venous admixture, which includes blood passing through both zero V/Q areas and low (non-zero) V/Q areas of the lung. Pure pulmonary shunt (or simply pure shunt) is the part of cardiac output passing through zero V/Q areas of the lung, i.e. areas where V/Q=0. Here it should be noted that in some medical literature the term shunt only encompasses pure shunt (i.e. zero V/Q) and not blood from V/Q heterogeneity areas (i.e. low V/Q areas). V/Q mismatch is caused either by pulmonary shunt (low or zero V/Q) or dead space (high or infinite V/Q).

The result of pulmonary shunt is an impaired blood oxygenation known as hypoxemia (i.e. a decrease in O₂content in arterial blood), caused by the shunted venous blood (with low O₂content) that reaches the systemic arterial side without contacting the ventilated alveoli rich in O₂. This poorly oxygenated blood decreases the amount of O₂delivered to body cells and can affect the normal aerobic metabolism.

Taking into account the above explanations, the measurement of shunt is considered the gold standard for assessing blood oxygenation in critical care medicine. It integrates information regarding lung ventilation and perfusion and allows the assessment of the lung's efficiency in oxygenating blood. This index is a useful parameter that helps clinicians understand the primary cause of gas exchange abnormalities, to make differential diagnosis and to guide treatment in their patients. Therefore, the calculation of shunt is essential to assess pulmonary function in critically ill patients undergoing mechanical ventilation and has been related to their outcome.

The reference method to measure shunt in clinical practice is based on the measurement of arterial and mixed venous oxygen contents by means of the pulmonary artery catheter (PAC). Taking simultaneous arterial and mixed-venous blood samples shunt can be calculated by Berggren's equation¹, sometimes referred to as the pulmonary shunt equation, as:

shunt(%)=CcO2-CaO2CcO2-Cv_O2(Eq.1)

where CcO₂, CaO₂and CvO₂are the contents of O₂in pulmonary capillaries, arterial and mixed venous blood, respectively.

However, the above described method and equation for shunt determination has a number of shortcomings:

1) It is an invasive monitoring that is rarely justified even in most critically ill patients. This is because PAC is associated with potential severe complications like sepsis, pulmonary infarction, bleeding and arrhythmias among others. Besides, the use of PAC has significantly declined because its use has repeatedly failed to improve the outcome of critically ill patients.

2) The oxygen content method cannot measure CcO₂directly. This value is calculated based on the assumption that capillary blood is fully saturated. However, this assumption might not be true even if 100% inspired oxygen fraction (FiO₂) were used.

3) When using a FiO₂<1, this method becomes only a rough estimate of venous admixture.

There are also other methods for measuring shunt, such as the Multiple Inert Gas Elimination Technique and methods which create ventilation-perfusion maps by imaging and nuclear medicine methodologies. However, these methods are cumbersome, costly, time-consuming and impossible to apply at the bedside and, therefore, they cannot be considered clinical monitoring methods.

Due to said shortcomings, the above mentioned methods fail to easily and reliably provide an indication of shunt in mechanically ventilated patients in operating theatres or in intensive care units. Therefore, several indexes that are more easily obtainable at the bedside, like the PaO₂-FiO₂ratio, the alveolar to arterial gradient of PO₂(AaPO₂) and the respiratory index, have been introduced in daily practice as a surrogate of shunt at the bedside. Despite being widely used, most physicians agree that these indexes are not real substitutes of shunt in critically ill patients undergoing complex clinical processes.

Also other basic and less reliable approximations in the estimation of shunt have been discussed, e.g. in publications 2 to 6 in the list of references appended hereinafter. The estimations discussed in these publications are gross calculations based on simplistic and, many times unrealistic assumptions and, therefore, their clinical use is questionable.

There are numerous studies relating to estimation of physiological parameters playing an important role in pulmonary gas exchange, several of which are relevant to the present invention. For example, Suarez-Sipmann et al.⁷shows that the so called Bohr dead space (sometimes referred to as “true dead space”) can be reliably estimated using Bohr's formula when PACO₂is determined through volumetric capnography, and that Enghoff's modification of Bohr's formula (the Bohr-Enghoff's formula) using the concept of ideal PACO₂(PACO₂=PaCO₂) tends to overestimate dead space due to inclusion of the shunt effect.

There is also patent literature related to the estimation of physiological parameters that are relevant to the present invention. For example, WO 2012/069051 discloses a device for determining two or more respiratory parameters relating to an individual, e.g. an individual suffering from pulmonary gas exchange problems. The device has detection means for oxygen and carbon dioxide contents in inspired and expired gas and blood. The device is controlled by a computer with functionality for entering oxygenation, carbon dioxide and acid-base values from one or more blood samples from arterial, venous, central venous or mixed venous blood samples, and with the parameter estimation based on equations of gas exchange of both oxygen and carbon dioxide and equations describing the acid-base chemistry of blood potentially including the competitive binding of oxygen and carbon dioxide to hemoglobin.

Furthermore, minimally invasive oxygen based approaches for calculating shunt have been described in e.g. U.S. Pat. No. 6,042,550, and Peyton et al⁸. However, calculating shunt from O₂-related parameters has been proved difficult and uncertain since this requires several assumptions to be made regarding unknown physiological parameters, as will be discussed in more detail in the specification following hereinafter.

It is an object of the present invention to provide means for a reliable estimation of the shunt of a subject, and in particular the pulmonary shunt of the subject.

It is another object of the invention to provide such means that eliminates or at least mitigates one or more of the shortcomings associated with prior art described above.

It is yet another object of the invention to provide means for enabling reliable monitoring of shunt in clinical practice, e.g. for enabling monitoring of shunt of patients undergoing ventilatory treatments.

It is a particular object of the invention to provide means for a reliable estimation of the shunt of a subject, through which means it is possible to estimate the shunt of the subject in a way that is minimally invasive.

These and other objects are achieved by means of a method for estimating shunt of a subject, such as a human subject undergoing ventilatory treatment. The method involves determination of shunt at least partly based on a measured carbon dioxide (CO₂) in the expiration gas exhaled by said subject. The method comprises the steps of:

• • obtaining, from CO₂measurements on expiration gas exhaled by said subject, a first value related to alveolar CO₂of said subject;
  • obtaining a second value related to arterial CO₂of said subject;
  • obtaining a third value related to cardiac output (Q_T) or effective pulmonary perfusion (EPP) of said subject;
  • obtaining a fourth value related to CO₂elimination (VCO₂) of said subject, and
  • calculating the shunt of the subject based on said first, second, third and fourth values.

The objects are also achieved by an apparatus devised and configured to carry out the method, and a computer program for causing the apparatus to carry out the method when executed by a processing unit of the apparatus.

The invention makes use of the fact that a value related to Q_Tor EPP, the latter sometimes also referred to as effective pulmonary blood flow (EPBF) or pulmonary capillary blood flow (Q_pcbf), may be introduced and used in the calculation of shunt to eliminate the need for invasive venous blood samples, required in most methods for determination of shunt according to prior art.

The calculation of shunt is preferably based on a combination of the Fick principle for calculation of cardiac output or effective pulmonary perfusion and a modification of Berggren's equation for calculation of shunt where in the formula O₂is replaced by CO₂and the equation is rearranged accordingly. The Fick principle for cardiac output (Eq. 2A), the Fick principle for effective pulmonary perfusion (Eq. 2B) and the modified Berggren equation for CO₂based calculation of shunt (Eq. 3) are shown below.

Q_T(CvCO₂—CaCO₂)═VCO₂  (Eq. 2A)

EPP(CvCO₂—CcCO₂)═VCO₂  (Eq. 2B)

where Q_Tis the cardiac output, EPP is the effective pulmonary perfusion, CvCO₂is the venous CO₂content, CcCO₂is the capillary CO₂content and VCO₂is the CO₂elimination.

shunt(%)=CaCO2-CcCO2CvCO2-CcCO2(Eq.3)

where CaCO₂is the arterial CO₂content, CcCO₂is the capillary CO₂content and CvO₂is the venous CO₂content.

By combining equations 2A or 2B with equation 3, the denominator (CvCO₂—CcCO₂) in equation 3 can be eliminated, allowing shunt to be estimated without invasive procedures for obtaining values of CvCO₂, thereby enabling shunt to be calculated and monitored in a minimally invasive way.

Another important aspect of the invention is the conversion of measurable alveolar partial pressure, concentration or volume of CO₂into capillary CO₂content of the subject. Preferably, the first value related to alveolar CO₂is a value of alveolar CO₂partial pressure, concentration or volume substantially corresponding to a capillary CO₂partial pressure, concentration or volume of the subject. Such a value may be directly obtained from the CO₂measurements on the expiration gas exhaled by the subject, e.g. by means of volumetric capnography allowing a value of alveolar partial pressure of CO₂(PACO₂) which corresponds to a capillary partial pressure of CO₂(PcCO₂) to be determined from a volumetric capnogram derivable from the volumetric capnography. The alveolar CO₂partial pressure, concentration or volume substantially corresponding to a capillary CO₂partial pressure, concentration or volume of the subject may then be used to estimate capillary CO₂content using a known value of CO₂solubility in blood. In this way, the CcCO₂value in the numerator of the CO₂-based Berggren equation (Eq. 3) can be replaced by said first value related to alveolar CO₂and known parameters relating CO₂content to CO₂partial pressure. More exactly, as will be described in the detailed description following hereinafter, the inventive concept involves the introduction of the term S(PaCO₂—PACO₂), where S is the solubility of CO₂in blood, PaCO₂the arterial partial pressure of CO₂and PACO₂the alveolar partial pressure of CO₂, as representative for the arterial to capillary content difference used in the numerator of the CO₂-based Berggren equation (Eq. 3), which allows shunt to be determined without determination of the subject's capillary CO₂content.

An advantage of the proposed method for shunt estimation is that the calculation of shunt can be frequently repeated and carried out at the bedside, allowing reliable monitoring of shunt in clinical practice, e.g. in monitoring shunt of mechanically ventilated patients in operating theatres or in intensive care units.

Another advantage is that the shunt value can be calculated without having to use shunt-related surrogates or rough approximations of physiological parameters that play an important role in the pulmonary gas exchange. Thereby, the shunt value calculated in accordance with the principles of the present invention is believed to better represent the true shunt of the subject than shunt or shunt related parameters clinically available today.

Yet another advantage is that the shunt value can be calculated according to the principles of the present invention without the need for (total or partial) rebreathing. This allows shunt to be calculated independently of the type of therapy currently provided to the patient or the type of breathing circuit or ventilator currently used to provide breathing support to the patient.

Another advantage is that the calculated shunt value is a reliable measure of venous admixture, including shunt caused by both zero V/Q and low V/Q, i.e. including both pure shunt and V/Q heterogeneity. This provides more robustness in its interpretation both for diagnostic (i.e. classification) and therapeutic purposes. This means that, together with dead space measurements according to known principles, the shunt value calculated according to the principle of the invention provides information on the full spectrum of V/Q abnormalities (i.e. relative contributions of low or high V/Q to a given condition or response to therapeutic intervention).

As arterial CO₂content is used in the calculation, the calculated shunt value is affected by small contributions of the anatomical pathways by which un-oxygenated venous blood containing relatively high amounts of CO₂reaches the arterial (left heart) side. However, since this anatomic shunt constitutes only a very small fraction of total shunt, the calculated shunt value is thus a good measure of the pulmonary shunt fraction of total shunt. If desirable, the calculated shunt value may of course be adjusted by compensating for the contribution of the anatomic shunt. However, since the anatomic shunt typically remains rather constant, continuous monitoring of the shunt value calculated in accordance with the principles of the invention still provides reliable indications of changes in the pulmonary shunt of the subject.

Yet another advantage of the proposed principle for calculating shunt is that it is less sensitive to variations in FiO₂than methods employing Berggren's original O₂-based equation (Eq. 1). This is due to the fact that the oxygen content of blood flowing through low V/Q areas is very sensitive to the level of FiO₂used because higher FiO₂increases the O₂diffusion gradient across the alveoli thereby underestimating the true venous admixture. Thus, using a higher FiO₂in low V/Q alveoli can, to a certain extent, compensate for the reduced ventilation and result in similar values for CcO₂and CaO₂so that Berggren's O₂based equation (Eq. 1) cannot “see” these low V/Q areas. By using a FiO₂of 1.0 this compensatory effect is maximized and Berggren's equation almost only measures the zero V/Q or very low V/Q portions of the lung. Furthermore, when using 100% oxygen the poorly ventilated alveoli tend to collapse (as the only gas is oxygen that is rapidly consumed, the so called “reabsorption atelectasis”) and these units then become zero V/Q units, further reducing the contribution of low V/Q zones. CO₂always has a high gradient in the opposite direction (as CO₂in the inhaled air is always very low) and is also twenty-two times more soluble than oxygen so it diffuses much better. Therefore, even though the level of oxygenation affects CO₂release from the blood (in fact, the higher the oxygen the more likely the CO₂will abandon the blood would only depend on the level of oxygenation in the blood and not in the alveoli, and is therefore unlikely to have much influence on the shunt value calculated in accordance with the proposed principles.

The proposed method is a completely CO₂based method for estimating shunt, meaning that the value of shunt is calculated only through analysis of CO₂transport between the lungs and the blood of the subject. The method does not involve analysis of O₂transport. Using a different wording, the shunt value is calculated using nothing but CO₂related parameters, i.e. without using O₂related parameters such as the arterial O₂content (CaO₂), the capillary O₂content (CcO₂), the alveolar O₂content (CAO₂), the oxygen uptake (VO₂), the capillary oxygen saturation (ScO₂) and the fraction of inspired O₂(FiO₂).

Using a CO₂-based approach for shunt calculation is advantageous compared to an O₂based approach for several reasons. First, determination of VCO₂(i.e. CO₂elimination), which requires sufficient temporal resolution and synchronization between flow or volume and concentration or partial pressure determination, is less cumbersome than the determination of VO₂(i.e. O₂uptake). It is possible to estimate VO₂from VCO₂but this introduces uncertainties in the shunt calculation since it requires the patient's respiratory quotient (RQ) to be assumed, which quotient typically varies between 0.7-1.0. Secondly, the CO₂based approach does not need to assume certain (typically 100%) O₂saturation in capillary blood (ScO₂), an assumption that may be erroneous when using low FiO₂levels or if there are diffusion abnormalities in the lungs of the patient. Thirdly, the CO₂based approach does not require a measurement or any assumption of hemoglobin concentration and hemoglobin capacity values, nor does it require chemical analysis of blood in order to determine such values. Furthermore, the CO₂-based approach does not require calculation of alveolar O₂content, which alveolar O₂content, using an O₂-based approach, has to be calculated based on e.g. FiO₂and the above mentioned RQ and hemoglobin values. Instead, using the proposed CO₂based approach for calculating shunt, a value related to alveolar CO₂of the subject that can be used to estimate the capillary CO₂content is derivable directly from the CO₂measurements on the expiration gas.

Preferably, the proposed method involves capnography, and even more preferably second arterial CO₂related value, the third Q_Tor EPP related value and the fourth VCO₂related value is determined based on data obtained through capnography, and preferably volumetric capnography. Volumetric capnography typically involves measurements of the flow or volume of the expiration gas and the partial pressure, concentration or volume of CO₂in the expiration gas, and calculation of a volumetric capnogram from said measurements.

Preferably, said first value related to alveolar CO₂is a value of CO₂partial pressure (PACO₂), concentration or volume, and most preferably a PACO₂value. This value may be determined based on the CO₂measurements on the expiration gas, preferably by means of said volumetric capnography. In a preferred embodiment, said first value is set to a CO₂value found at or near the midpoint of the alveolar slope (phase III) of the volumetric capnogram, which value corresponds to a PACO₂value reflecting the capillary partial pressure of CO₂(PcCO₂). As mentioned above, this value related to alveolar CO₂may then be used to eliminate the term CcCO₂from the CO₂-based Berggren equation (Eq. 3) in order to calculate shunt without having to determine the capillary CO₂content of the subject.

Preferably, also the fourth value indicative of CO₂elimination is determined based on CO₂measurements on the expiration gas, advantageously through said volumetric capnography. For example, a value of VCO₂may be calculated from a capnogram, preferably a volumetric capnogram, and a value indicative of the respiratory rate (RR) of the patient. In a preferred embodiment, the CO₂elimination is determined as the area under the curve of the capnogram multiplied by the respiratory rate of the subject.

The third value indicative of Q_Tor EPP may be obtained by means of any known method for estimating cardiac output or effective pulmonary perfusion. Preferably, the value of Q_Tor EPP is non-invasively determined based on the measured CO₂content in the expiration gas. This may be achieved using known capnodynamic methods for Q_Tor EPP determination. It is also possible to use an independent method for determining a Q_Tor EPP related value, i.e. a method that does not use the measurements of CO₂content in the expiration gas exhaled by the subject in the Q_Tor EPP determination, whereby the independently determined value of Q_Tor EPP may be input to the apparatus of the present invention by an operator, and used by the apparatus in the calculation of shunt.

Preferably, said second value related to arterial CO₂is a value of arterial CO₂partial pressure (PaCO₂), concentration or volume, and most preferably a PaCO₂value. As of today, there are available methods for non-invasively estimating arterial partial pressure of CO₂, such as transcutaneous CO₂measurements. However, these methods may not reliably determine PaCO₂under all clinical circumstances. Therefore, this value is preferably obtained through an arterial blood sample, whereby the PaCO₂value derived from the blood sample may be input by an operator to the apparatus carrying out the method in order for the apparatus to use the PaCO₂value in the calculation of shunt. However, in order to make the proposed method completely non-invasive, it is contemplated that known non-invasively obtained surrogates of PaCO₂, such as partial pressure of end-tidal CO₂(PetCO₂), may be used instead of PaCO₂in the shunt calculation. A value of PetCO₂is directly available from a capnogram, preferably a volumetric capnogram, which makes it suitable for use when the proposed method is implemented as a capnography-based method, and preferably a volumetric capnography-based method, for calculation of shunt. Thus, in some embodiments, the proposed method for shunt calculation may be completely non-invasively performed based only on non-invasive measurements of CO₂content in the expiration gas exhaled by the subject. However, it may be desirable to obtain a PaCO₂value from an arterial blood sample in order to improve the accuracy of the method or for calibration purposes.

In one embodiment, shunt is calculated as:

shunt(%)=S(PaCO2-PACO2)S(PaCO2-PACO2)+VCO2QT(Eq.

where S is the CO₂solubility, PaCO₂is the partial pressure of arterial CO₂, PACO₂is the partial pressure of alveolar CO₂, VCO₂is the minute elimination of CO₂and Q_Tis the cardiac output.

In another embodiment, the value of cardiac output is replaced by a value of EPP, which makes it possible to calculate shunt as:

shunt(%)=S*EPP(PaCO2-PACO2)VCO2(Eq.5)

where S is the CO₂solubility, EPP is the effective pulmonary perfusion, PaCO₂is the partial pressure of arterial CO₂, PACO₂is the partial pressure of alveolar CO₂and VCO₂is the minute elimination of CO₂.

The parameters PaCO₂, PACO₂, VCO₂, Q_Tand EPP may be obtained in any of the above described ways. The CO₂solubility, S, is known and substantially constant within the relevant physiological range, typically but not necessarily 35 to 50 mmHg of CO₂.

The method described above is typically computer implemented, meaning that the method is performed by an apparatus through execution of a computer program.

Thus, according to one aspect of the invention, there is provided a computer program for estimating shunt of a subject, such as a human subject undergoing ventilatory treatment. The computer program comprises computer readable programming code which, when executed by a processing unit of an apparatus arranged to obtain CO₂measurements on expiration gas exhaled by said subject, causes the apparatus to:

• • obtain, from said CO₂measurements, a first value related to alveolar CO₂of said subject;
  • obtain a second value related to arterial CO₂of said subject;
  • obtain a third value related to cardiac output (Q_T) or effective pulmonary perfusion (EPP) of said subject;
  • obtain a fourth value related to CO₂elimination (VCO₂) of said subject, and
  • calculate the shunt of the subject based on said first, second, third and fourth values.

The computer program may further be configured to cause the apparatus to carry out any of the above described steps and calculations.

According to another aspect of the invention there is provided an apparatus for estimating shunt of a subject, such as a human subject undergoing ventilatory treatment. The apparatus is configured to obtain CO₂measurements on expiration gas exhaled by said subject, typically obtained from a sensor arrangement comprised in or connectable to the apparatus. The apparatus comprises a processing unit configured to:

• • obtain, from said CO₂measurements on expiration gas exhaled by said subject, a first value related to alveolar CO₂of said subject;
  • obtain a second value related to arterial CO₂of said subject;
  • obtain a third value related to cardiac output (Q_T) or effective pulmonary perfusion (EPP) of said subject;
  • obtain a fourth value related to CO₂elimination (VCO₂) of said subject, and
  • calculate the shunt of the subject based on said first, second, third and fourth values.

Preferably, the sensor arrangement comprises a CO₂sensor for measuring the partial pressure, concentration or volume of CO₂in the expiration gas, and a flow or volume sensor for measuring the flow or volume of expiration gas. The sensor arrangement may form part of a capnograph, and preferably a capnograph configured for volumetric capnography.

The apparatus may comprise a user interface configured to allow an operator to input the value related to arterial CO₂of the subject, such as a PaCO₂value, to the apparatus via said user interface, whereby the processing unit may be configured to use the input value in the calculation of shunt. Thereby, the apparatus can be configured to use a PaCO₂value obtained through an arterial blood sample in the shunt calculation.

The apparatus may be configured to receive also other values via the user interface, and to use the values in the shunt calculation. For example, the apparatus may, in some embodiments, be configured to receive a Q_Tor EPP related value determined through an independent method and input by an operator via the user interface, and to use said Q_Tor EPP related value in the shunt calculation.

Advantageously the apparatus comprises a display configured to display information related to the calculated value of shunt, e.g. a current value of shunt of the subject and/or a graph showing changes in shunt over time.

Preferably, the shunt value is calculated repeatedly, e.g. on a breath-by-breath basis, and the displayed information related to shunt may be updated accordingly.

In one embodiment, the apparatus is a ventilator that includes or is connectable to the sensor arrangement and configured to calculate the shunt of a subject connected to the ventilator based at least partly on the measurements obtained by the sensor arrangement.

In another embodiment the apparatus is a stand-alone device that includes or is connectable to the sensor arrangement, configured to calculate shunt of a subject that may or may not be connected to a ventilator. The device may be a conventional computer that calculates the shunt of the subject according to the principles of the present invention, and displays information relating to the calculated shunt value on a display of the computer.

According to an advantageous aspect of the invention there is provided an apparatus for estimating the shunt of a subject based on capnography, preferably volumetric capnography. To this end the apparatus comprises or is connectable to a capnograph that measures the flow or volume of expiration gas exhaled by a subject and the partial pressure, concentration or volume of CO₂in the expiration gas. The apparatus may be configured to:

• • Determine a first value related to alveolar CO₂of the subject. This value is a value of alveolar CO₂partial pressure, concentration or volume substantially corresponding to a capillary CO₂partial pressure, concentration or volume of the subject. Preferably, the value is determined by the apparatus based on capnographic data obtained by the capnograph, and preferably determined as a PACO₂value corresponding to the CO₂value found at or near the midpoint of the alveolar slope (phase III) of a volumetric capnogram derivable from said capnographic data.
  • Determine a second value related to arterial CO₂of the subject, typically determined by the apparatus to correspond to a PaCO₂value obtained through an arterial blood sample and received by the apparatus via a user interface of the apparatus, input via said user interface by an operator of the apparatus, or determined non-invasively by the apparatus based on the CO₂and flow or volume measurements obtained by the capnograph or another sensor arrangement comprised in or connected to the apparatus.
  • Determine a third value related to Q_Tor EPP of the subject, typically determined by the apparatus non-invasively using a capnodynamic equation or a set of capnodynamic equations and the CO₂and flow or volume measurements obtained by the capnograph
  • Determine a fourth value related to CO₂elimination (VCO₂) of the subject, typically non-invasively determined by the apparatus based on the CO₂and flow or volume measurements obtained by the capnograph or another sensor arrangement comprised in or connected to the apparatus.
  • Calculate an actual value of shunt of the subject using the first, second, third and fourth value, and typically also a known value of CO₂solubility in blood.

Further advantageous aspects of the present invention will be described in the detailed description following hereinafter.

FIG. 1A illustrates an apparatus 1A according to an exemplary embodiment of the invention. In this embodiment the apparatus is a ventilator for providing ventilatory treatment to a patient 3 connected to the ventilator. The ventilator is connected to the patient 3 via an inspiratory line 5 for supplying breathing gas to the patient 3, and an expiratory line 7 for conveying expiration gas away from the patient 3. The inspiratory line 5 and the expiratory line 7 are connected to a common line 9, via a so called Y-piece 11, which common line is connected to the patient 3 via a patient connector, such as an endotracheal tube.

A capnograph 13 configured for volumetric capnography measurements is arranged in the proximity of the airways opening of the patient 3. In this exemplary embodiment, the capnograph 13 is arranged in the common line 9 and exposed to all gas expired and inspired by the patient 3. The capnograph 13 comprises a flow or volume sensor 15 for measuring at least the flow or volume of expiration gas exhaled by the patient 3, and a CO₂sensor 17 for measuring the CO₂content in at least the said expiration gas. Typically but not necessarily the capnograph 13 also measures the flow or volume of inspiration gas inhaled by the patient 3, and the CO₂content in the inspiration gas.

The capnograph 13 is connected to the ventilator via a wired or wireless connection 19, and configured to transmit the flow and CO₂measurements to the ventilator for further processing by a processing unit 21 of the ventilator. The ventilator is preferably configured to generate a volumetric capnogram 23, hereinafter referred to as VCap, from the flow and CO₂measurements received from the capnograph 13, and to display the VCap 23 on a display 25 of the ventilator.

The processing unit 21 is typically part of a control unit 27 of the ventilator, which control unit 27 further comprises a non-volatile memory or data carrier 29 storing a computer program that causes the processing unit 21 to calculate the shunt of the patient 3 in accordance with the principles of the present invention, at least partly based on the flow or volume and CO₂measurements received from the capnograph 13, as will be described in more detail below. The ventilator is further configured to display information related to the calculated shunt value on the display 25. Preferably, the ventilator is configured to repetitively calculate the shunt value, e.g. on a breath-by-breath basis, and to display information on the display 25 enabling a ventilator operator to monitor changes in the shunt of the patient 3.

FIG. 1B illustrates an apparatus 1B according to another exemplary embodiment of the invention. In this embodiment, the apparatus is a conventional computer, connected to the capnograph 13 via the wired or wireless connection 19. Just like the control unit 27 of the ventilator in FIG. 1A, the computer comprises a processing unit 21 and a non-volatile memory or data carrier 29 storing a computer program that causes the processing unit 21 to calculate the shunt of the patient 3 in accordance with the principles of the present invention. In this embodiment, the patient 3 may or may not be connected to a ventilator. The computer also comprises a display 25 for display of VCap and information related to calculated shunt values.

Each of the ventilator 1A and the computer 1B further comprises a user interface 31 through which an operator can enter values of physiological parameters that may be used by the apparatus in the calculation of shunt. For example, a value indicative of arterial CO₂content of the patient 3, such as a PaCO₂value determined from an arterial blood sample, may be input to the apparatus via the user interface 31 and used in the calculation of shunt. Furthermore, in the same way a value indicative of QT or EPP of the patient 3, may be input by the user to the apparatus 1A, 1B via the user interface 31 and used in the calculation of shunt.

Reference will now be made to FIG. 2 and FIGS. 3A-3C, depicting the rationale of the proposed calculation of shunt using volumetric capnography.

FIG. 2 illustrates schematically a model of pulmonary gas exchange taking place in the alveoli A of the lungs of a subject. Venous blood coming from the systemic venous circulation carrying CO₂from the body into the right heart having CO₂content CvCO₂is transported towards the alveoli A in an arterial part of the pulmonary circulatory system. In a capillary part of the pulmonary circulatory system, CO₂moves from the pulmonary capillaries into the alveoli, resulting in CO₂offloading of capillary blood having high CO₂content CcCO₂. For most conditions it is reasonable to assume full equilibration between the alveolar partial pressure of CO₂(PACO₂) and the capillary partial pressure of CO₂(PcCO₂).

Some of the cardiac output (Q_T) of the subject does not participate in the gas exchange. The fraction of cardiac output participating in the gas exchange is the effective pulmonary perfusion (EPP), sometimes referred to as the effective pulmonary blood flow (EPBF) or pulmonary capillary blood flow (Q_pcbf). The fraction of cardiac output that does not participate in the gas exchange is the shunt. The CO₂rich shunt flow (Q_S) is mixed with the capillary blood flow from which CO₂was removed to form arterial blood having CO₂content CaCO₂, which arterial blood is then transported to a venous part of the pulmonary circulatory system to the left heart and pumped into the systemic arterial circulation and into the organs of the subject.

FIG. 3A shows the simplified Riley's three-compartment model of the lungs⁹, which represents the lungs as three distinct functional units: A) a shunt unit with perfusion but without ventilation, i.e. with zero V/Q, B) a normal unit which is normally ventilated and perfused, and C) a dead space high V/Q unit with ventilation but without perfusion, i.e. where V/Q approaches infinity.

FIG. 3B illustrates the representation of the three functional units A, B and C in the volumetric capnogram. The area under the curve of the volumetric capnogram is originated by the normally ventilated and perfused areas of the lungs (unit B) because this part of the lung is the one that receives CO₂from pulmonary capillaries and efficiently eliminates the CO₂by ventilation. VCap also gives information related to the functional units A and C.

VCap calculates dead space (unit C) non-invasively using Bohr's formula¹⁰(Eq. 6):

VDBohrVT=PACO2-PE_CO2PACO2(Eq.6)

where the alveolar partial pressure of CO₂(PACO₂) may be determined as the CO₂value found at the midpoint of the alveolar slope (Phase III) of the capnogram within the alveolar tidal volume^{7, 11}. The mixed partial pressure of CO₂of an entire breath (PĒCO₂) may also be non-invasively calculated from VCap using the following equation¹⁸:

PE_CO2=VTCO2,brVT*(BP-PH2O)(Eq.7)

where VTCO_2,bris the area under the curve of the VCap, BP is the barometric pressure, PH₂O is the water vapour pressure and VT is the tidal volume.

Enghoff's formula (Eq. 8) was originally described to calculate a “surrogate of dead space” replacing PACO₂by the arterial PCO₂(PaCO₂), in Bohr's original formula¹²as:

VDB-EVT=PaCO2-PE_CO2PaCO2(Eq.8)

This formula was used in the past because PACO₂was not available at the bedside. However, Enghoff's formula overestimates dead space because it replaces the alveolar PCO₂by the arterial PCO₂and thus includes all types of V/Q abnormalities beyond dead space in the calculation^{18, 19}.

VCap is related to shunt (unit A) because it is known that the difference between Bohr's formula (Eq. 6) and Enghoff's formula (Eq. 8) is caused by a fictitious “alveolar dead space” caused by shunt. This shunt dead space effect has been well described in respiratory physiology^{13, 14}.

FIG. 3C illustrates the VCap and its relation to dead space and the shunt effect, as described above. The gradient between mean alveolar (PACO₂) to mixed expired (PECO₂) partial pressure of CO₂represents the true dead space or Bohr's dead space (VD_Bohr/VT), calculated using Bohr's formula (Eq. 6). The gradient between arterial partial pressure of CO₂(PaCO₂) and PECO₂represents a global index of the inefficiencies of gas exchange (VD_B-ENT) that includes all types of V/Q abnormalities, calculated using the Bohr-Enghoff formula (Eq. 8). The differences between these formulas represent the shunt effect on dead space (hatched area). VTCO_2,bris the area under the curve of VCap.

Considering the VCap and its relationship to dead space and the shunt effect described above, the present invention presents a novel approach in respiratory medicine wherein shunt is calculated using the kinetics of CO₂instead of the one of O₂. Previous publications^15-18analyzed the correction of the shunt effect on dead space but did not investigate the possibility to measure shunt using CO₂.

According to the inventive concept, one of two novel formulas may be used to calculate the shunt of a subject using parameters minimally-invasively derived from CO₂measurements on expiration gas exhaled by said subject, preferably by means of volumetric capnography, together with values indicative of arterial CO₂and cardiac output or EPP of the subject. The new formulas add two important components of the CO₂kinetics that are related to shunt, namely the CO₂transport by blood and its elimination by ventilation. The formulas are algebraically derived from equation 2A (Fick's equation for Q_T), equation 2B (Fick's equation for EPP), and equation 3 (Berggren's equation replacing O₂by CO₂) as will be described in the following.

An important aspect of the present invention is the introduction of cardiac output (Q_T) or effective pulmonary perfusion (EPP) in the CO₂-based Berggren equation (Eq. 3) to eliminate the denominator (CvCO₂—CcCO₂) and so the need for invasive measurements of venous blood content. Rearranging Fick's equations for EPP (Eq. 2B), the denominator in Berggren's equation (Eq. 3) can be expressed as:

(CvCO2-CcCO2)=VCO2EPP(Eq.9)

Combining equation 9 with the CO₂-based Berggren equation (Eq. 3) yields:

shunt(%)=EPP*(CaCO2-CcCO2)VCO2(Eq.10)

Another important aspect of the invention is the estimation of capillary CO₂content from alveolar partial pressure, concentration or volume of CO₂in order to replace the term CcCO₂in the numerator of the CO₂-based Berggren equation (Eq. 3) with quantities that are either known or directly derivable from the CO₂measurements on the expiration gas exhaled by the subject.

This is achieved according to a preferred embodiment of the invention by utilizing the fact that a value of alveolar partial pressure of CO₂(PACO₂) substantially corresponding to the capillary partial pressure of CO₂(PcCO₂) of the subject can be determined as a CO₂value found at or near the midpoint of the alveolar slope of a volumetric capnogram directly obtained through said CO₂measurements, and the fact that the capillary CO₂content (CcCO₂) of the subject can be estimated from capillary partial pressure of CO₂(PcCO₂) by using the following relationship:

CxCO₂═S*PxCO₂+B  (Eq. 11)

where S is the CO₂solubility, PxCO₂is the partial pressure of CO₂and CxCO₂is the content of CO₂in blood and B is the intercept of the straight line relating CO₂partial pressure (PxCO₂) and content (CxCO₂) over a physiological range to be considered. This equation assumes that the CO₂content is linearly related to the partial pressure of CO₂, something that is true over the physiological range to be considered¹⁵.

Considering equation 11 and the fact that the capillary partial pressure of CO₂(PcCO₂) can be replaced by the PACO₂value obtained from the volumetric capnogram as described above, the term CcCO₂can be expressed as:

CcCO₂═S*PcCO₂+B═S*PACO₂+B  (Eq. 12)

where S is the CO₂solubility in blood and B is the constant relating PcCO₂to CcCO₂over the physiological range to be considered.

Again considering equation 11, the arterial CO₂content (CaCO₂) of the subject relates to the arterial partial pressure of CO₂as:

CaCO₂═S*PaCO₂+b  (Eq. 13)

where S is the CO₂solubility in blood and b is a constant representing the intercept of the straight line relating PaCO₂to CaCO₂over the physiological range to be considered.

Now starting from equation 10 and combining this equation with equations 12 and 13, and assuming that the constants b and B for arterial and capillary blood are equal, shunt can be calculated as:

shunt(%)=EPP(CaCO2-CcCO2)VCO2=EPP((S*PaCO2+b)-(S*PACO2+B))VCO2=S*EPP(PaCO2-PACO2)VCO2(Eq.5)

Thus, by studying the arterial to capillary CO₂content difference (C(a-c)CO₂), and taking the steps of: 1) replacing the arterial CO₂content (CaCO₂) with a known value of CO₂solubility in blood S, a value of arterial partial pressure of CO₂(PaCO₂), and a constant b representing the intercept of the straight line relating PaCO₂to CaCO₂over the physiological range to be considered; 2) replacing the capillary CO₂content (CcCO₂) with a known value of CO₂solubility in blood S, a value of alveolar partial pressure of CO₂(PACO₂) representing a value of capillary partial pressure CO₂(PcCO₂) and directly derivable from the CO₂measurements of expiration gas, and a constant B representing the intercept of the straight line relating PaCO₂to CaCO₂over the physiological range to be considered; and 3) assuming that the constants b and B are equal over the physiological range to be considered, the arterial to capillary CO₂content difference can be replaced by an arterial to alveolar CO₂partial pressure difference multiplied by a value S of CO₂solubility in blood. Or, from another point of view, the arterial partial pressure of CO₂and the alveolar partial pressure of CO₂, the latter being directly derivable from the CO₂measurements on expiration gas, can be used to estimate the arterial to capillary difference of CO₂content using the CO₂solubility in blood S, thus eliminating the need for determining not only the capillary CO₂content (CcCO₂) but also the arterial CO₂content (CaCO₂) of the subject.

The CO₂elimination (VCO₂) of the subject may be calculated based on the CO₂measurements on the expiration gas exhaled by the patient, and preferably based on volumetric capnography as:

VCO₂=VTCO_2,br*RR  (Eq. 14)

where VCO₂is the elimination CO₂per minute derived non-invasively from the area under the curve of the VCap (VTCO_2,br) multiplied by the respiratory rate (RR) of the subject.

Furthermore, considering that the shunt value calculated through equation 5 is the fraction of the cardiac output not participating in blood gas exchange, i.e. that:

shunt(%)=QSQT(Eq.15)

where Q_Sis the shunt flow of blood not participating in blood gas exchange, and the fact that the cardiac output (Q_T) of the subject is the sum of the shunt flow (Q_S) and the effective pulmonary perfusion (EPP), i.e. that:

Q_T=EPP+Q_S  (Eq. 16)

Then, by replacing EPP with (Q_T−Q_S) in equation 5 and solving the equation for shunt, i.e. Q_S/Q_T, the following expression can be obtained:

shunt(%)=S(PaCO2-PACO2)S(PaCO2-PACO2)+VCO2QT(Eq.4)

The proposed principle for calculating shunt does not require any arterial or capillary CO₂content to be calculated in absolute terms. Instead, by looking only at the difference in the arterial and capillary CO₂content (C(a-c)CO₂), replacing the difference in arterial and capillary contents of CO₂with the difference in arterial and capillary partial pressures of CO₂(P(a-c)CO₂), and by replacing the capillary partial pressure of CO₂with a corresponding alveolar partial pressure of CO₂that can be determined from non-invasive CO₂measurements on expiration gas, the present invention allows shunt to be calculated based on CO₂measurements on expiration gas, a value of EPP or Q_T, a value of arterial CO₂content and a value of CO₂solubility in blood.

An advantage of these formulas is that shunt can be estimated without having to use a PAC by for example using volumetric capnography, a method for obtaining Q_Tor EPP, and an arterial blood sample to determine PaCO₂. The formula avoids complications and hospital costs related to the use of PAC. Furthermore, it is less dependent on the effects of differences in FiO₂during shunt determination than other known formulas for shunt estimation. Yet further, the proposed CO₂based approach for calculating shunt has several advantages compared to known O₂based approaches for calculating shunt, as previously described in the summary of the invention.

Currently there are several described methods for non-invasive estimation of Q_T. These methods could enhance the usefulness of the above formula without increasing the need of invasive devices in clinical practice. Some of these methods are based on the application of the Fick principle to expired CO₂analysis. However, as CO₂delivery from blood to the alveolar gas requires the presence of effective capillary-alveolar exchange, these methods are closer to effective pulmonary perfusion (EPP) than to total cardiac output. Since these methods together with the proposed method for calculating shunt are based on capnography analysis and PaCO₂of the subject, it could be advantageous to use equation 5 instead of equation 4 in the calculation of shunt.

One method that is particularly suitable for determination of Q_Tor EPP is a non-invasive capnodynamic method described in EP 2 641 536, which method is based on a capnodynamic equation describing how the fraction of alveolar carbon dioxide (FACO2) varies between different respiratory cycles. This method is advantageous not only because it is non-invasive but also because Q_Tor EPP can be determined only based on CO₂measurements and calculations of CO₂related parameters. Other methods that may also be employed for non-invasive determination of Q_Tor EPP within the scope of this invention are described in the background of EP 2 641 536, in U.S. Pat. No. 6,042,550, and in Peyton et al⁸.

As previously mentioned, the proposed method for shunt calculation may be completely non-invasive if a value of PaCO₂is derived without an arterial blood sample. Therefore known surrogates of PaCO₂, such as partial pressure of end-tidal CO₂(PetCO₂), may be used instead of PaCO₂in the shunt calculation although use of such PaCO₂surrogates reduces the accuracy in the shunt calculation. In the future, if a method for estimating PaCO₂non-invasively becomes available, or if transcutaneous PCO₂measurements become more reliable, clinicians will potentially have both a fully non-invasive and reliable method for estimating shunt at the bedside.

FIG. 4 illustrates a method for estimating shunt of a subject according to the principles of the invention. The method will be described with simultaneous reference to the previously described drawings.

In a first step S1, measurement values from CO₂measurements on expiration gas exhaled by the subject are obtained by the apparatus 1A, 1B. These values typically include values of the flow or the volume of expiration gas exhaled by the subject and the partial pressure, concentration or volume of CO₂in the expiration gas, measured by the capnograph 13 and transmitted to the apparatus 1A, 1B where they are received and used by the processing unit 21 in the calculation of shunt.

In a second step S2, a first value relating to alveolar CO₂of the subject is obtained by the processing unit 21. Typically, said first value relating to alveolar CO₂is obtained by the processing unit 21 by determining, based on the CO₂measurements obtained in step S1, a value of alveolar CO₂partial pressure, concentration or volume substantially corresponding to a capillary CO₂partial pressure, concentration or volume of the subject. In a preferred embodiment, the alveolar CO₂related value is a value of alveolar partial pressure of CO₂(PACO₂) determined by the processing unit 21 based on the capnographic data received from the capnograph 13. Preferably, the PACO₂value is determined based on a CO₂value found at or near the midpoint of an alveolar slope (phase III) of a volumetric capnogram 23 derivable by the processing unit 21 based on the capnographic data.

In a third step S3, a second value related to arterial CO₂of the subject is obtained by the processing unit 21, typically in form of a value of arterial CO₂partial pressure (PaCO₂), concentration or volume. Preferably, the arterial CO₂value is determined through analysis of blood gases in an arterial blood sample and input to the apparatus 1A, 1B, e.g. in form of a PaCO₂value, via the user interface 31, whereupon it is received by the processing unit 21 and used in the determination of shunt.

In a fourth step S4, a third value related to the cardiac output (Q_T) or effective pulmonary perfusion (EPP) of the subject is obtained. As discussed above, the Q_Tor EPP-related value may be determined by the processing unit 21 based on the CO₂measurements obtained in step S1, e.g. based on the capnographic data received from the capnograph 13, or be received by the processing unit 21 through manual input of a Q_Tor EPP-related value via the user interface 31 of the apparatus 1A, 1B.

In a fifth step S5, a fourth value related to CO₂elimination (VCO₂) in the subject is obtained. Preferably, this value is determined by the processing unit 21 based on the CO₂measurements obtained in step S1, e.g. based on the capnographic data received from the capnograph 13.

In a sixth and last step S6, the shunt of the subject is calculated by the processing unit 21 based on the first value related to alveolar CO₂of the subject obtained in step S2, the second value related to arterial CO₂of the subject obtained in step S3, the third value related to Q_Tor EPP of the subject obtained in step S4, and the fourth value related to VCO₂of the subject obtained in step S5. As discussed above, the calculation of shunt preferably involves the step of combining a modified version of Berggren's equation where O₂is replaced by CO₂(Eq. 3) with Fick's equation for Q_Tor EPP (Eq. 2A and 2B, respectively) in order to eliminate the need for determining a venous CO₂content of the subject. Furthermore, the calculation of shunt preferably involves the step of using the first and second values obtained in steps S2 and S3 to eliminate the need for determining a capillary CO₂content of the subject. This may be achieved by using said first and second values to estimate a difference in arterial to capillary CO₂content (C(a-c)CO₂), which has the further advantage of eliminating the need for determining an arterial CO₂content of the subject. In a preferred embodiment, the calculation of shunt involves the steps of replacing, the arterial to capillary CO₂content difference (C(a-c)CO₂) in the numerator of said CO₂-based Berggren equation (Eq. 3) with a difference in arterial to capillary partial pressure of CO₂(P(a-c)CO₂), and using the first value related to alveolar CO₂obtained in step S1 as a measure of capillary partial pressure of CO₂of the subject. The replacement of the difference in arterial to capillary CO₂content (C(a-c)CO₂) with the difference in arterial to capillary partial pressure of CO₂(P(a-c)CO₂) further requires the CO₂solubility in blood to be introduced and used in the calculation of shunt. Thus, in a preferred embodiment of the invention, the shunt of the subject is calculated based on the first to fourth values obtained in steps S2 to S5, and a value of CO₂solubility in blood.

Preferably, the above described method is performed repetitively, e.g. on a breath-by-breath basis, in order to continuously monitor the shunt of the subject 3. That the method is repeated on a breath-by-breath basis here means that step S6 and at least one of the steps S2-S5 are repeated on a breath-by-breath basis in order to calculate an updated shunt value for each breath of the subject.

It should be noted that although the invention has herein been described as a method using a value of cardiac output (Q_T) or effective pulmonary perfusion (EPP) and a value of CO₂elimination (VCO₂) of the subject in the calculation of shunt, it should be appreciated that the above described principles of using the alveolar CO₂partial pressure, concentration or volume of the subject to eliminate the need for determining the capillary CO₂content of the subject may be advantageously used also in existing or future methods for calculating shunt without using values of Q_T, EPP or VCO₂. Thus it should be appreciated that according to one aspect of the invention, there is provided a method for estimating shunt of a subject, comprising the steps of:

• • obtaining, from CO₂measurements on expiration gas exhaled by said subject, a first value related to alveolar CO₂of said subject;
  • obtaining a second value related to arterial CO₂of said subject, and
  • calculating the shunt of the subject based on said first and second values,
    wherein said first value related to alveolar CO₂is determined as a value of alveolar partial pressure, concentration or volume of CO₂substantially corresponding to a capillary CO₂partial pressure (PcCO₂), concentration or volume of the subject, and wherein said first value related to alveolar CO₂is used in the calculation of shunt in a way that eliminates the need for determining a capillary CO₂content (CcCO₂) of the subject.

As discussed above, said first value related to alveolar CO₂may be a value of alveolar CO₂partial pressure [PACO₂], concentration or volume, and said second value related to arterial CO₂may be a value of arterial CO₂partial pressure [PaCO₂], concentration or volume, which first and second values may be used together with a known value of CO₂solubility in blood to estimate a difference in arterial to capillary CO₂content (C(a-c)CO₂), thereby eliminating the need for determining the CcCO₂of the subject.

Although the present invention has been described in connection with the specified embodiments, it should not be construed as being in any way limited to the presented examples. The scope of the present invention is to be interpreted in the light of the accompanying claim set. In the context of the claims, and other parts of the description, the terms “comprising” or “comprises” do not exclude other possible elements or steps.

Also, the mentioning of references such as “a” or “an” etc. should not be construed as excluding a plurality. The use of reference signs in the claims with respect to elements indicated in the figures shall also not be construed as limiting the scope of the invention. Furthermore, individual features mentioned in different claims, may possibly be advantageously combined, and the mentioning of these features in different claims does not exclude that a combination of features is not possible and advantageous.

alveolar dead space Ventilated alveoli not perfused by blood, i.e. alveoli for which the V/Q ratio approaches infinity
anatomic shunt The fraction of blood bypassing the alveoli of the lungs through anatomic channels
BP Barometric pressure
CaCO₂Arterial content of CO₂
CaO₂Arterial content of O₂
cardiac output The volume of blood leaving the left (or right) ventricle each minute
CcCO₂Capillary content of CO₂
CcO₂Capillary content of O₂
CvCO₂Venous content of CO₂
CvO₂Venous content of O₂
Dead space The portion of ventilation not participating in gas exchange
EPBF Effective pulmonary blood flow
EPP Effective pulmonary perfusion
FiO₂Inspired oxygen fraction
PAC Pulmonary artery catheter
PaCO₂Arterial partial pressure of CO₂
PaO₂Arterial partial pressure of O₂
PACO₂Alveolar partial pressure of CO₂
PCO₂Mixed expired partial pressure of CO₂of an entire breath
PH₂O Water vapour pressure
pulmonary shunt The fraction of blood perfusing the alveoli of the lungs not participating in gas exchange due to insufficient ventilation, i.e. shunt caused by zero or low V/Q ratio; corresponding to venous admixture pure shunt The fraction of pulmonary shunt caused by a V/Q ratio of zero
Q_TCardiac output
RR Respiratory rate
shunt The (total) fraction of blood not involved in gas exchange; the sum of anatomic shunt and pulmonary shunt
VCap Volumetric capnography
VCO₂Eliminated volume of CO₂per minute (CO₂elimination); sometimes referred to as CO₂production since it corresponds to the litres of CO₂produced by the tissues per minute
VD_Bohr/VT True dead space or Bohr's dead space; calculated as the gradient between mean alveolar (PACO₂) and mixed expired partial pressure of CO₂(PECO₂) over PACO₂
VD_B-E/VT Bohr-Enghoff's surrogate of dead space; calculated as the gradient between arterial partial pressure of CO₂(PaCO₂) and mixed expired partial pressure of CO₂(PECO₂) over PaCO₂
venous admixture See pulmonary shunt
V/Q heterogeneity simultaneous presence of areas of the lung with low (non-zero) and high V/Q ratios
V/Q ratio ventilation-perfusion ratio; the ratio of the amount of air reaching the alveoli to the amount of blood reaching these alveoli
VT tidal volume
VTCO_2,brthe area under the curve of the capnogram or the amount of CO₂eliminated per breath, or minute CO₂elimination divided by respiratory rate

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