OBI Medical

Principles of the method

The v-TAC™ software calculates arterial blood gas values from a venous peripheral blood gas measurement, combined with arterial oxygen saturation, using algorithms and mathematical models that simulates the transport of blood back through the tissues.


To perform this simulation two assumptions are required:

First it is assumed that the amount of strong acid added to the blood on its passage through the tissues is small or zero, such that a change in base excess (BE) from the venous sampling site to the arterial site (ΔBEav) is approximately zero. For peripheral venous blood, this is likely to be true if the peripheral limb has a clearly recognizable arterial pulse, a normal capillary response, and a normal colour and temperature. For central or mixed venous blood this assumption is less likely to be true, as the different organ systems can add different and substantial amounts of acid into the blood circulation in situations with e.g. anaerobic metabolism.

In addition, it is assumed that the respiratory quotient (i.e. the rate of CO2 production (VCO2) to O2 utilisation (VO2)) over the tissue sampling site, cannot vary outside the range 0.7 and 1.0. RQ of the tissue cells can only vary between 0.7 and 1.0, being 0.7 in aerobic metabolism of fat and 1.0 in aerobic metabolism of carbohydrate. Whilst R, the respiratory exchange ratio, measured at the mouth, may vary outside this range, the RQ over the tissue sampling site can only do so if there is a rapid flow of acid, base or CO2 in or out of the tissues where peripheral venous sampling occurs. This may occur in situations involving rapid disturbance of acid–base status, such as in exercise. However, in a warm, well perfused extremity this rapid re-distribution is less likely. This means that anaerobically sampled venous blood can be “arterialised” mathematically by simulating the removal/addition, respectively, of a constant ratio (RQ) of CO2 and O2 over the tissues. This simulation is being performed until the arterialised oxygen saturation matches the arterial oxygen saturation measured by a pulse oximeter.


The v-TACTM software step-by-step

v-TAC™ uses an approximation of RQ=0.82 for the conversion.

The principle steps of the software are illustrated in the figure below and the details of this mathematical transformation now follow:

First an anaerobic venous blood sample is drawn to provide values of the acid-base and oxygen status of the peripheral venous blood.

As input, the v-TAC™ software uses the following values: pHv, pvCO2, pvO2, Hbv, SvO2, methaemoglobin (fMetHbv) and carboxyhaemoglobin (fCOHbv) and the arterial oxygen saturation measured by a pulse oximeter. fMetHbv and fCOHbv are optional and can be replaced by constants through configuration.

Step 1: v-TAC™ performs an input check on the venous blood gas values calculated by the blood gas analyser. Read more about the v-TAC™ input check - Learn more

Step 2: The venous measurements pHv, pvCO2, pvO2, SvO2, Hbv, fMetHbv, and fCOHbv are used to calculate the total CO2 concentration (tvCO2), total O2 concentration (tvO2), base excess (BEv), and the concentration of 2,3-diphosphoglycerate (2,3-DPGv) in the venous blood for which the oxygen dissociation curve passes through the measured venous pO2,v and SO2,v. These calculations are performed by using an acid-base mass action and mass balance simulator.

Step 3: We assume that the concentration of haemoglobin (tHb), the total concentration of plasma non-bicarbonate buffer (tNBBp), the concentration of 2,3-DPG and BE are the same in arterial and venous blood:

tHb= tHbv

tNBBp,a = tNBBp,v

2,3-DPG= 2,3-DPGv


Step 4: Calculation of the total concentration of O2 and CO2 in arterial blood is then performed by simulating addition of a concentration of O2 (ΔO2), to the venous blood and removing a concentration of CO2 (ΔCO2, where ΔCO2 = RQ ΔO2) from the venous blood:

tO2,a= tO2,v+∆O2,

tCO2,a= tCO2,v- RQ * ∆O2

Calculated values of arterialised blood tCO2-(B)a,c; tO2-(P)a,c; Hba; BEa,c; taNBBp and DPGa are then used to calculate the remaining variables describing arterialised blood, i.e. pHa,c, paCO2,c, paO2,c and SaO2,c also using the acid-base mass action and mass balance simulator described below, but in a reverse of the process.

Step 5: The calculated arterialised oxygen saturation SaO2 is then compared with that measured by the pulse oximeter (SpO2). The difference between the two giving an error = SaO2−SpO2. By varying the value of ΔO2 and repeating steps 4, a value of ΔO2 can be found for which the error is zero. At this point, the ΔO2 represents the concentration of O2 added, and RQ multiplied by ΔO2 the concentration of CO2 removed, so as to transform venous to arterialised blood. For this value of ΔO2, calculated values of all variables describing arterialised blood should be equal to measured arterial values.

The calculated arterial output blood gas values include pHa,c, paCO2,c, paO2,c (up to 10 kPa), HCO3-(P)a,c, Base Excess (BEa,c), tO2-(P)a,c and tCO2-(B)a,c.

Optional feature: If FiO2 is entered on the blood gas analyser, the v-TAC™ software will calculate the PaO2/FiO2 ratio, which is required for calculation of the SOFA score.

Step 6: Before the mathematical process is completed, v-TAC™ performs several output checks on the calculated arterial blood gas values.

Find a list of all input and output parameters in the v-TAC™ Product Description here


The acid-base mass-action and mass-balance simulator

What makes the v-TAC™ algorithm possible is the use of mathematical models of acid-base and blood chemistry based on Siggaard-Andersen and extended by Rees and Andreassen. The combined model is a comprehensive set of connected mass action and mass balance equations, to keep track of the masses of CO2, O2 and binding effects to haemoglobin (oxygen carrying and non-oxygen carrying) and the relationship between values of pO2 and SO2 in the blood, known as the oxygen dissociation curve. It represents plasma bicarbonate and non-bicarbonate buffers and the buffering on the amino end and side chains of the haemoglobin molecule. The model accounts for the Bohr-Haldane effects.

It should be noted that in this model, BE is defined as the concentration of strong acid necessary to titrate fully oxygenated blood to a pHp= 7.4, at a pCO2 = 5.33 kPa. In the conventional definition (called Actual Base Excess (ABE)), BE is defined without fully oxygenating the blood. Because of Bohr-Haldane effects, ABE values therefore depend upon oxygen level and are not the same in arterial and venous blood, even in the absence or addition of acid or base in to the blood from the tissue. In the definition of BE used here, values of BE are independent of O2 level and will only change if strong acids or bases are added and the model therefore accounts for the Bohr-Haldane effects.

For all details of the science behind the method please read the published articles – Learn more