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 CO_{2} production (VCO_{2}) to O_{2} utilisation (VO_{2})) 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 CO_{2} 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 CO_{2} and O_{2} over the tissues. This simulation is being performed until the arterialised oxygen saturation matches the arterial oxygen saturation measured by a pulse oximeter.

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: pH_{v}, p_{v}CO_{2}, p_{v}O_{2}, Hb_{v}, S_{v}O_{2}, methaemoglobin (fMetHb_{v}) and carboxyhaemoglobin (fCOHb_{v}) and the arterial oxygen saturation measured by a pulse oximeter. fMetHb_{v} and fCOHb_{v} 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, p_{v}CO_{2}, p_{v}O_{2}, S_{v}O_{2}, Hbv, fMetHb_{v}, and fCOHb_{v} are used to calculate the total CO_{2} concentration (t_{v}CO_{2}), total O_{2} concentration (t_{v}O_{2}), base excess (BE_{v}), and the concentration of 2,3-diphosphoglycerate (2,3-DPG_{v}) in the venous blood for which the oxygen dissociation curve passes through the measured venous pO_{2},v and SO_{2},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 (tNBB_{p}), the concentration of 2,3-DPG and BE are the same in arterial and venous blood:

tHb_{a }= tHb_{v}

tNBB_{p,a }= tNBB_{p,v}

2,3-DPG_{a }= 2,3-DPG_{v}

BE_{a }= BE_{v}

**Step 4**: Calculation of the total concentration of O_{2} and CO_{2} in arterial blood is then performed by simulating addition of a concentration of O_{2} (ΔO_{2}), to the venous blood and removing a concentration of CO_{2} (ΔCO_{2}, where ΔCO_{2} = RQ ΔO_{2}) from the venous blood:

tO_{2,a}= tO_{2,v}+∆O_{2,}

tCO_{2,a}= tCO_{2,v}- RQ * ∆O_{2}

Calculated values of arterialised blood tCO_{2}^{-}(B)_{a},c; tO_{2}^{-}(P)_{a},c; Hb_{a}; BE_{a},c; t_{a}NBBp and DPG_{a} are then used to calculate the remaining variables describing arterialised blood, i.e. pH_{a,}c, p_{a}CO_{2},c, p_{a}O_{2},c and S_{a}O_{2,}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 S_{a}O_{2} is then compared with that measured by the pulse oximeter (SpO_{2}). The difference between the two giving an error = S_{a}O_{2}−SpO_{2}. By varying the value of ΔO_{2} and repeating steps 4, a value of ΔO_{2} can be found for which the error is zero. At this point, the ΔO_{2} represents the concentration of O_{2} added, and RQ multiplied by ΔO_{2} the concentration of CO_{2} removed, so as to transform venous to arterialised blood. For this value of ΔO_{2}, calculated values of all variables describing arterialised blood should be equal to measured arterial values.

The calculated arterial output blood gas values include pH_{a},c, p_{a}CO_{2},c, p_{a}O_{2},c (up to 10 kPa), HCO_{3}^{-}(P)_{a},c, Base Excess (BE_{a},c), tO_{2}^{-}(P)_{a},c and tCO_{2}^{-}(B)_{a},c.

Optional feature: If FiO_{2} is entered on the blood gas analyser, the v-TAC™ software will calculate the PaO_{2}/FiO_{2} 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

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 CO_{2}, O_{2} and binding effects to haemoglobin (oxygen carrying and non-oxygen carrying) and the relationship between values of pO_{2} and SO_{2} 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 pH_{p}= 7.4, at a pCO_{2} = 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 O_{2} 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