Innocor Inert Gas Rebreathing Method Guide Issue A Rev 9 July 2013

Innocor® Inert Gas Rebreathing Method

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1

INERT GAS REBREATHING METHOD

1.1

SCOPE

The purpose of this section is to give an introduction to the Inert Gas Rebreathing Method used in Innocor. This section applies to distributors and end-users of Innocor with only limited experience in gas exchange measurements. For more detailed information about the rebreathing method, please contact Innovision A/S or simply look in medical article databases.

1.2

INTRODUCTION

Inert Gas Rebreathing is an old technique introduced by August Krogh back in 1912. Since the introduction the method has been validated through numerous medical publications. Despite the indisputable scientific value of the method, inert gas rebreathing has until now only gained little propagation. The main reason is that the equipment required to perform the measurements has been expensive and difficult to maintain. With the introduction of Innocor, Inert Gas Rebreathing has become a simple and easy-to-use method for measuring important cardiopulmonary parameters. Innocor is a small and portable device and it requires only little maintenance. This document will enable the reader to understand the cardiopulmonary parameters measured by Innocor and the way they are determined.

1.3

REBREATHING PARAMETERS

The parameters measured by a fully equipped Innocor are: Symbol CO CI PBF VL HR SV SI VO2 VO2/kg SpO2 SvO2 %A-V O2 Shunt SYS DIA MAP SVR SVRI

Name Cardiac Output (1 Cardiac Index (1 Pulmonary Blood Flow Lung Volume Heart Rate Stroke Volume (1 Stroke Index (1 Oxygen uptake (2 Oxygen uptake pr kg body weight (2 Oxygen saturation in arterial blood Oxygen saturation in mixed venous blood (2 Arterio-venous oxygen saturation difference (2 Shunt fraction (2 Systolic blood pressure (3 Diastolic blood pressure (3 Mean Arterial blood Pressure (3 Systemic Vascular Resistance (3 Systemic Vascular Resistance Index (3

Unit l/min l/min/m2 l/min l (BTPS) 1/min ml ml/m2 l/min (STPD) ml/min/kg (STPD) % % % % mmHg mmHg mmHg mmHg/(l/min) mmHg·m2/(l/min)

1) In case of a significant shunt the oxygen sensor option is required to calculate the parameter. 2) Requires the oxygen sensor option. 3) Requires the NIBP option (blood pressure).

All the listed parameters will be explained in detail in this section. July 2013

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1.4

THE REBREATHING MODEL

Calculations of the cardiopulmonary parameters are based on a single-alveolar lung model, and assumptions included in the model are: • Complete and instantaneous mixing of all gases in the volume consisting of alveolar and dead space air and bag volume. • Instantaneous equilibration of the soluble gas between the alveoli and blood, and between alveoli and tissue, respectively. • Constant pulmonary blood flow (PBF) and constant volume of lung tissue (Vt). • Negligible mixed venous concentration of soluble gas throughout the rebreathing period. For this assumption to be true, it is required that no recirculation occurs within the rebreathing period, and that repeated determinations are carried out with a sufficient washout period of e.g. 5 minutes in between. 1.4.1

Total systemic volume (Vs,tot)

Inert gas rebreathing allows the total systemic volume to be determined with high accuracy. Vds Vds,rb

Vrb VL

Figure 1.4.1-1 Systemic volumes. The total systemic volume is defined as: Vs,tot = VL + Vds + Vds,rb + Vrb

where VL Vds Vds,rb Vrb

= = = =

Lung volume at the end of an expiration Dead space volume of rebreathing valve (RVU) Residual volume of bag when empty Volume of rebreathing bag

During the rebreathing period the concentration of insoluble gas (SF6) decreases from the initial value in the bag (Fi0) to a final equilibrium (Fi,eq) value practically obtained after a few breaths (figure 1.4.1-2). Since the volume of the rebreathing bag is known, the total systemic volume can be determined simply from the dilution of the insoluble gas. A typical SF6 curve from a rebreathing manoeuvre is shown in figure 1.4.1-2. July 2013

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Insoluble gas

Fi 0

Fi,eq

t=0

Figure 1.4.1-2 Insoluble gas concentration during rebreathing. The total systemic volume is not constant during a rebreathing manoeuvre. Initially the volume increases due to a constant oxygen uptake and an increased excretion of carbon dioxide. Normally the rebreathing manoeuvre is performed at slightly forced ventilation. Since the pulmonary blood flow is assumed to be constant, the increased ventilation causes a lower alveolar partial pressure of carbon dioxide. The higher gradient (CO 2) between the alveoli and the capillaries causes a rise in carbon dioxide excretion and hereby also an increase in systemic volume. The increased excretion of carbon dioxide lasts only short. As the carbon dioxide quickly builds up in the lungs and bag, the gradient between the alveolar and capillary (mixed venous) CO 2 concentrations falls. This decreases the carbon dioxide excretion. The oxygen uptake is still constant. The result is therefore a shrinkage in the total systemic volume. The total systemic volume, referred to in this document, is the volume at the time “zero”. Time “zero” is defined as the middle of the first inspiration. This volume is difficult to measure directly since the volume measurements require the insoluble gas to be perfectly mixed. At the time zero this is not the case. Therefore the volume is determined by back extrapolation by drawing a straight line through the expiratory points of the insoluble gas where adequate mixing is obtained. The insoluble gas concentration at time “zero” is then determined as the point where the extrapolated line crosses time “zero” - see figure 1.4.1-2 (Fi,eq). The total systemic volume at time “zero” is calculated using the following formula:

Vs,tot =

Fi 0  Vrb Fi,eq

where Vs,tot = Total systemic volume Fi0 = Initial concentration of insoluble gas in the rebreathing bag Fi,eq = Equilibrium concentration of insoluble gas (back extrapolated to t = 0)

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Example: Total systemic volume How to calculate the total systemic volume from the data in figure 1.4.1-2: The following data is assumed: VRB = 2 l PB = 763 mmHg ta = 23 °C RH = 24% Data from figure 1.4.1-2: Initial concentration of SF6 in the rebreathing bag, Fi0 = 0.114% Equilibrium concentration of SF6, Fi,eq = 0.053% (back extrapolated to t = 0) The total systemic volume can now be calculated:

Vs,tot (ATP) =

Fi0  VRB (ATP) Fi,eq

where ATP = Ambient temperature, pressure and humidity Example:

Vs,tot (ATP) =

0.114  2 l = 4.30 l 0.053

The Vs,tot is converted to STPD (see section 1.4.22) for further calculations: RH PB −  PH2O (t a ) 273 100% Vs,tot (STPD) =   Vs,tot (ATP) 273 + t a 760 Example: 273 Vs,tot (STPD) =  273 + 23

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763 −

24  21.1 100  4.30 l = 3.96 l 760

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1.4.2

Innocor® Inert Gas Rebreathing Method

Pulmonary Blood Flow (PBF)

PBF is the blood flow that perfuses the ventilated part of the alveoli. During rebreathing an amount of the soluble gas disappears from the alveoli due to solution in tissue and blood. An initial nearly instantaneous disappearance of soluble gas is ascribed to solution of the gas in lung tissue, while the later gradual decrease is due to washout into the blood flowing through the capillaries. Figure 1.4.2-1 shows a typical washout curve for soluble gas (N2O) during a rebreathing manoeuvre.

Soluble gas

Figure 1.4.2-1 Soluble gas concentration during rebreathing. The disappearance rate is proportional to the pulmonary blood flow. Assuming a constant PBF and a constant total systemic volume, the disappearance curve for the soluble gas describes a monoexponentially decreasing function of time, since the rate of absorption is also proportional to the alveolar gas concentration. The exponentially decaying concentration of soluble gas can be represented by a rectilinear disappearance in a semi logarithmic plot. Figure 1.4.2-2 shows a semi logarithmic plot of soluble gas concentrations (normalised) during a rebreathing manoeuvre.

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Ln(F’s)

Regression line through expiratory points

Ln(F’s,1)

Ln(F’s,2)

Time [s]

Ts,1

Ts,2

Figure 1.4.2-2 Semilogarithmic plot for soluble gas (N2O). The pulmonary blood flow can be calculated using the following formula:

PBF = −β 

Vs,tot  C1 + C 2 αb

where PBF = Vs,tot = C1 = C2 = αb = αt = Vt = PB =

Pulmonary Blood Flow Total systemic volume (STPD) 760/(PB - 47) αt∙Vt, Constant to account for the disappearance of soluble gas into lung tissue. Bunsen solubility coefficient in blood [ml STPD/ml/atm @ 37°C] (αb,N2O = 0.412). Bunsen solubility coefficient in tissue [ml STPD/ml/atm @ 37°C] (αt,N2O = 0.407). Lung tissue volume (default 600 ml) Ambient pressure in mmHg

As mentioned in section 1.4.1, the total systemic volume shrinkage occurs mainly due to the continuing oxygen uptake and decreasing excretion of carbon dioxide. Therefore, and in order to compensate for incomplete mixing, concentrations of soluble gas are corrected prior to any of the calculations, according to the changes in concentration of insoluble gas (normalisation). The regression line, with slope  (Figure 1.4.2-2), is drawn through the expiratory points of the logarithmic normalised soluble gas concentrations. 

= Slope of line through the expiratory points of:  F ( t )  Fi 0   ln(F's ( t )) = ln  s  F (t)  F 0  s   i

where F’s(t)= Fs(t) = Fi,0 = Fi(t) = Fs0 =

Normalised fractional concentrations of soluble gas Fractional soluble gas concentration as a function of time Initial fractional insoluble gas concentration in the rebreathing bag Fractional insoluble gas concentration as a function of time Initial fractional concentration of soluble gas in the rebreathing bag

The insoluble gas is hereby used as an indicator of the size of the volume the soluble gas

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disappears from and to estimate the degree of “incomplete mixing”. Having the total systemic volume defined, the pulmonary blood flow can be estimated directly from the slope of the regression line shown in figure 1.4.2-2. “The steeper the slope, the higher the pulmonary blood flow”. Example: Pulmonary blood flow: Estimation of pulmonary blood flow from the data in figure 1.4.2-2:

PBF = − 

Vs,tot  C1 + C 2

b The slope of the regression line through the expiratory points: =

ln(F's, 2 ) − ln(F's,1 )

T2 − T1 From figure 1.4.2-2: ln(F’s,2) = ln(F’s,1) = T2 = T1 =

=

-0.223 -0.164 14.2 sec. 9.1 sec.

−0.223 − (−0.164 ) / min = −0.694 / min (14.2 − 9.1) / 60

Given data: Vs,tot(STPD) = 3.96 l C1 = 1.06 C2 = 0.600•0.407 l = 0.244 l αb = 0.412

PBF = −( −0.694) 

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3.96  1.06 + 0.244 l / min = 7.45 l/min 0.412

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1.4.3

Oxygen uptake (Vo2)

With the Oxygen Analyser option included, it is possible to measure oxygen uptake. The measurement is based on the assumption that the alveolar partial pressure of O 2 is higher than 100 mmHg throughout the rebreathing period so that the blood perfusing the ventilated alveoli is fully saturated with oxygen. Figure 1.4.3-1 shows an oxygen-rebreathing curve.

Oxygen

FO2,ET

Figure 1.4.3-1 Oxygen rebreathing curve. If the oxygen uptake, VO2, during the rebreathing period is constant, the slope of the disappearance curve for O2 is proportional to the oxygen uptake: Vo 2 = −β  Vs,tot (STPD)

where Vs,tot = Total systemic volume (STPD) Due to the volume shrinkage, and in order to compensate for incomplete mixing, concentrations of oxygen are corrected prior to any of the calculations, according to the changes in concentration of insoluble gas (normalisation). The regression line, with slope  (Figure 1.4.3-2), is drawn through the expiratory points of the normalised oxygen concentrations. 

= Slope of line through the expiratory points of: Fi,eq F' O 2 ( t ) = (FO 2 ( t ) − FO 2,ET )  + FO 2,ET Fi ( t )

where F’O2(t) FO2(t) FO2,ET Fi,eq Fi(t)

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= = = = =

Normalised fractional concentrations of oxygen Fractional oxygen concentration as a function of time End-tidal fractional oxygen concentration prior to rebreathing Equilibrium concentration of insoluble gas (back extrapolated to t = 0) Fractional insoluble gas concentration as a function of time

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F’O2

Regression line through expiratory points

F’O2,1

F’O2,2

Time [s]

T1

T2

Figure 1.4.3-2 Oxygen rebreathing curve, normalised. Example: Oxygen uptake Oxygen uptake calculated from the data in figure 1.4.3-2. The slope of the regression line through the expiratory points:

=

F' O 2, 2 −F' O 2,1 T2 − T1

From figure 1.4.3-2: F’O2,2 = F’O2,1 = T2 = T1 =

=

0.162 0.181 14.2 sec. 9.1 sec.

0.162 − 0.181 / sec = −0.224 / sec . (14.2 − 9.1) / 60

Given data: Vs,tot(STPD) = 3.96 l. Result: Vo2 = -(-0.224) · 3.96 l/min = 0.89 l/min

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1.4.4

Oxygen uptake pr kg body weight (Vo2/kg)

The oxygen uptake in proportion to body weight:

Vo 2 / kg = 1000 

Vo 2 [ml/min/kg] Weight

Example: Weight = 75 kg Vo2/kg = 1000 · 0.89 / 75 = 11.9 ml/min/kg 1.4.5

Lung Volume (VL)

In the literature FRC is defined as the gas volume in the lungs at the end of expiration (at rest). In stress test and in measurements at rest with increased ventilation (for better mixing) the measured VL is not the “true FRC” but rather something between the Functional Residual Capacity (FRC) and Residual Volume (RV). Residual volume is the volume left in the lungs after a maximal expiratory effort. The VL can be determined by the equation from section 1.4.1: VL = Vs,tot − (Vrb + Vds,rb + Vds )

When BTPS, STP and STPD conditions are used the equation becomes: VL(BTPS) = [Vs,tot(STPD) – (Vrb(ATP)+Vds,rb(ATP)) · C1] · C2 – Vds(BTPS) where Vs,tot = Vrb = Vds = Vds,bag = C1 = C2 =

Total systemic volume, STPD Volume of rebreathing bag, ATP Dead space volume of rebreathing valve (RVU), BTPS (containing expired air) Residual volume of bag when empty, ATP Conversion from ATP to STPD, see section 1.4.22 Conversion from STPD to BTPS, see section 1.4.22

Example: Vs,tot(STPD) = Vrb(ATP) = Vds,rb(ATP) = Vds(BTPS) = PB = ta = RH = 273 C1 =  273 + 23

C2 =

3.96 l 2l 0.013 l 0.102 l 760 mmHg 23 °C 24% 763 −

24  21.1 100 = 0.916 760

273 + 37 760  = 1.205 273 763 − 47

VL(BTPS) = (3.96 – (2.0+0.013) · 0.916) ·1.205 – 0.102 l = 2.45 l

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1.4.6

Arterial Oxygen Saturation (%SpO2)

The oxygen saturation of haemoglobin in arterial blood (%SpO2) is determined by pulse oximetry. Oxygen saturation is determined by the pulse oximeter as an estimate of the proportion of haemoglobin which is present in a reduced form by comparing the absorption of infrared light at two different wavelengths where the absorption for oxygenated and reduced haemoglobin is the same and very different, respectively. 1.4.7

Cardiac Output (CO)

Cardiac Output (CO) is defined as the output of the left ventricle pr unit time. The CO is not necessary equal to the PBF, which is the blood flow that perfuses the ventilated part of the alveoli. The difference is the Shunt flow, Q’s – see figure 1.4.7-1.

CcO2

CaO2 CvO2

Figure 1.4.7-1 CO, PBF and shunt flow. Three equations can be written. Based on simple mass conservation: CO = PBF + Q’s

(1)

where CO = Cardiac Output [l/min] PBF = Pulmonary blood flow Q’s = Shunt flow [l/min] From Fick’s principle: Vo 2 [l/min] CO = C aO 2 − C vO 2 where Cao2 = Oxygen content in arterial blood [litres STPD/litre]

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(2)

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= = = = =

0.000139 · Hb · %SPO2 Arterial oxygen saturation [%], as defined in section 1.4.6 Haemoglobin concentration [g/dl] Oxygen content in mixed venous blood Oxygen uptake [l/min]

Fick’s principle used on the pulmonary circulation:

PBF =

Vo 2 C cO − C vO 2

[l/min]

(3)

2

where Cco2 Cco2 %Sco2 %Sco2

= = = =

Oxygen content in end-capillary blood [litres STPD/litre] 0.000139 · Hb · %SCo2 End-capillary oxygen saturation [%] 98% (assumed)

The three equations contain three unknown parameters (CO, Q’s and Cvo2) and can be solved as:

CO =

1 1 Ca O 2 − Cc O 2 + PBF Vo 2

Example: PBF = %Spo2 = Hb = Cao2 = Cco2 = Vo2 =

CO =

7.45 l/min 97 % 15 g/dl 0.000139 · 15 · 97 = 0.2022 0.000139 · 15 · 98 = 0.2043 0.89 l/min

1 l / min = 7.58 l / min 1 0.2022 − 0.2043 + 7.45 0.89

The calculation of cardiac output and shunt requires that both the pulse oximeter (SpO2) and Oxygen Analyser (Vo2) are installed and used.

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1.4.8

Shunt fraction

The shunt fraction is defined as the proportion between the shunt flow and the total blood flow from the left ventricle (see figure 1.4.7-1):

Shuntfraction =

Q' s  100 % CO

where Q’s = Shunt flow [l/min] CO = Cardiac Output [l/min] If the cardiac output is known (see section 1.4.7), the shunt fraction can be calculated using the formula:

Q's  PBF  = 1 −   100 % CO  CO  where PBF = Pulmonary Blood Flow Example: PBF = 7.45 l/min CO = 7.58 l/min Shuntfraction = (1 – 9.0/9.38) · 100% = 1.7%

1.4.9

Mixed venous oxygen saturation (%SvO2)

The mixed venous oxygen saturation is the oxygen saturation of haemoglobin in mixed venous blood returning to the lungs for oxygenation. The calculation of %SvO2 is based on the %ScO2, Vo2, PBF and Hb: Vo 2 [%] %S v O 2 = %S C O 2 − PBF  0.000139  Hb where %ScO2 = End-capillary oxygen saturation [%] %ScO2 = 98% (assumed) Vo2 = Oxygen Uptake [l/min] PBF = Pulmonary blood flow [l/min] Hb = Haemoglobin concentration [g/dl] Example: %ScO2 = Vo2 = PBF = Hb =

98% 0.89 l/min 7.45 l/min 15 g/dl

0.89   %S v O 2 =  98 − % = 41% 7 . 45  0.000139  15  

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1.4.10 %A-V oxygen difference (%A-V O2) The %A-V oxygen difference is the difference in oxygen saturation in arterial blood compared to mixed venous blood: %A-V O2 = %SpO2 - %SvO2

[%]

Example: %A-V O2 = (97 – 41)% = 56% 1.4.11 Heart Rate (HR) The number of heart beats per minute. Measuring HR requires only the standard pulse oximeter. Calculated as 1/RR, where RR is the peak-peak interval determined from a pulse oximeter plethysmogram. 1.4.12 Body Surface Area (BSA) The total surface area of the body is used to calculate indices. BSA is calculated from the equation: BSA = 0.007184 · W 0.425 · H0.725 [m2] where W H

= Weight of patient [kg] = Height of patient [cm]

Example: W = 75 kg H = 175 cm BSA = 0.007184 · 750.425 · 1750.725 m2 = 1.90 m2 The data is taken from the patient database. If patient’s height and weight are not typed into the database, the indices will not be calculated. 1.4.13 Cardiac Index (CI) Cardiac Index is defined as the amount of blood ejected from the left ventricle into the aorta (systemic circulation) per unit time seen in proportion to body size (surface area):

CI =

CO  l   2 BSA  min m 

where CO = Cardiac Output [l/min] BSA = Body Surface Area [m 2] Example: CO = 7.58 l/min BSA = 1.90 m2 CI = 9.38/1.90 l/min/m2 = 3.99 l/min/m2

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1.4.14 Stroke Volume (SV) Stroke volume [ml] is defined as the amount of blood ejected by the left ventricle into the aorta per heart beat.

SV =

CO  1000 [ml] HR

where CO = Cardiac Output [l/min] HR = Heart Rate [1/min] Example: CO HR SV

= 7.58 l/min = 73 /min = 7.58/73∙1000 ml = 104 ml

1.4.15 Stroke Index (SI) The stroke volume in proportion to the body surface area (BSA):

SI =

SV [ml/m2] BSA

Example: SV = 104 ml BSA = 1.90 m2 SI = 104/1.90 ml/m2 = 54.7 ml/m2 1.4.16 Blood Pressure (DIA, SYS, MAP) If the NIBP option is included, the blood pressure parameters can be measured [mmHg]. The diastolic blood pressure (DIA) is defined as the lowest pressure during diastole. The systolic blood pressure (SYS) is defined as the highest pressure during systole. The mean arterial blood pressure (MAP) is calculated by the NIBP module, but can be estimated from the systolic and diastolic blood pressures:

MAP = DIA +

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(SYS − DIA) [mmHg] 3

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1.4.17 Systemic Vascular Resistance (SVR) The resistance to blood flow in the systemic blood circulation, i.e. the average resistance that the left ventricle works against when delivering the stroke volume into the aorta.

SVR =

MAP − CVP  mmHg   l / min  CO  

where MAP = Mean Arterial Pressure [mmHg] CVP = Central Venous Pressure [mmHg] As CVP is not measured it is set to 4.6 mmHg by default. CO = Cardiac Output [l/min] Example: MAP = 113 mmHg CO = 7.58 l/min SVR = (113-4.6)/7.58 mmHg/(l/min) = 14.3 mmHg/(l/min) 1.4.18 Systemic Vascular Resistance Index (SVRI) The resistance to blood flow in the systemic blood circulation seen in proportion to body surface area

SVRI =

MAP − CVP ( MAP − CVP)  BSA  mmHg  m 2  =   CI CO  l / min 

where MAP = Mean Arterial Pressure [mmHg] CVP = Central Venous Pressure [mmHg] As CVP is not measured it is set to 4.6 mmHg by default. CI = Cardiac Index [l/min/m 2] CO = Cardiac Output [l/min] BSA = Body Surface Area [m 2] Example: MAP = CO = SVR = BSA = SVRI =

113 mmHg 7.58 l/min 14.3 mmHg/(l/min) 1.90 m2 (113-4.6)∙1.90/7.58 mmHg∙m2/(l/min) = 27.2 mmHg∙m2/(l/min)

1.4.19 Cardiac Power Output (CPO) Cardiac Power Output is a measurement of the cardiac pumping capability. CPO = CO ∙ MAP ∙ 0.0022 [watt] where CO = Cardiac Output [l/min] MAP = Mean Arterial blood Pressure [mmHg] Example: MAP = 113 mmHg CO = 7.58 l/min CPO = 7.58 ∙ 113 ∙ 0.0022 Watt = 1.88 Watt

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1.4.20 Cardiac Power Index (CPI) Cardiac Power Index is a measurement of the cardiac pumping capability seen in proportion to body size (surface area). CPI = CI ∙ MAP ∙ 0.0022 [W/m2] where CI = Cardiac Index [l/min/m2] MAP = Mean Arterial blood Pressure [mmHg] Example: CI = 3.99 l/min/m2 MAP = 113 mmHg CPI = 3.99 ∙ 113 ∙ 0.0022 W/m2 = 0.99 W/m2 1.4.21 Haemoglobin Concentration (Hb) Hb is the haemoglobin concentration in blood. The parameter is determined by an analysis of a blood sample. The unit can either be in [g/dl] or in [mmol/l]. 1 g/dl = 0.62 mmol/l 1 mmol/l = 1.61 g/dl A normal value is 7-10 mmol/l for female and 8-11 mmol/l for male subjects.

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1.4.22 Conversion between ATP, STPD and BTPS The volume of a number of moles (n) of gas molecules depends on the thermodynamic temperature (T) and the ambient pressure (P). The following relationship holds for dry gas: V = n·R·T/P where R = gas constant, and T is expressed in Kelvin (K = 273.2 + ºC). Air and expired gas are made up of gas molecules and water vapour. In a gas mixture saturated with water vapour and in contact with water (such as occurs in the lung) the number of water molecules in the gas phase varies with temperature and pressure. As the number of molecules is not constant, the above gas law should be applied to dry gas. This also holds outside the lung when gas saturated with water vapour is compressed or cools down. BTPS:

In respiratory physiology lung volumes and flows are standardised to barometric pressure at sea level, body temperature, saturated with water vapour: body temperature and pressure, saturated. Measured at ambient temperature, pressure, saturated with water vapour (e.g. expired gas, which has cooled down): ambient temperature and pressure, saturated. Like ATPS, but not saturated with water vapour (e.g. room air). Like ATPS, but dry (e.g. from a gas bottle). Oxygen consumption and carbon dioxide delivery are standardised to standard temperature (0 ºC), barometric pressure at sea level (101.3 kPa / 760 mmHg) and dry gas: standard temperature and pressure, dry.

ATPS: ATP: ATPD: STPD:

Correction from ATP to STPD. Multiply the ATP-value by:

273  273 + t a

PB −

RH  PH 2O ( t a ) 100 760

Correction from BTPS to STPD. Multiply the BTPS-value by:

P − 47 273  B 273 + 37 760 where ta PB RH PH2O(ta) Temperature [°C] 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

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= = = =

ambient temperature in °C barometric pressure in mmHg relative humidity in % saturated water vapour pressure in mmHg at temperature ta, see table below

Water vapour pressure [mmHg] 4.7 5.2 5.6 6.1 6.5 7.0 7.4 7.9 8.3 8.8 9.2 9.8 10.5 11.2 12.0

Temperature [°C] 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

Water vapour pressure [mmHg] 12.8 13.6 14.5 15.5 16.5 17.5 18.7 19.8 21.1 22.4 23.8 25.2 26.7 28.3 30.0

Temperature [°C] 30 31 32 33 34 35 36 37 38 39 40

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Water vapour pressure [mmHg] 31.8 33.7 35.7 37.7 39.9 42.2 44.6 47.1 49.7 52.4 55.3

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