COMPRISING A NATURAL LUNG, AN ARTIFICIAL LUNG

COMPRISING AN OXYGEN-CARBON DIOXIDE EXCHANGE MEMBRANE

The present invention refers to a computer program that simulates in real time a system comprising a natural lung, an artificial lung comprising an oxygen-carbon dioxide exchange membrane.

To date, to assist hypercapnic patients or patients suffering from acute respiratory failure (ARDS), use is made of ventilator supports that help the patient in the gas exchange at the lung level and/or extracorporeal systems that facilitate the oxygenation of the blood and the removal of carbon dioxide CO ₂ .

Pulmonary ventilators or Venturi or turbine flow generators are used to replace or augment spontaneous ventilation of a patient who has respiratory/ventilatory insufficiency owing to pathologies affecting the lung or chest pump.

Mechanical ventilation is mainly employed in acute respiratory failure. Less common is the use as a treatment aimed at controlling pathological conditions that chronically cause (such as diseases of the rib cage, neuromuscular diseases or COPD) a stable increase in carbon dioxide values and to remove excesses thereof from the body.

In such cases, it is preferred to proceed through non-invasive ventilations that help the patient in facilitating the gas exchange through flows provided at positive pressures that increase alveolar recruitment and therefore greater ease for the patient to remove excess CO ₂ and increase oxygenation. Both pulmonary ventilators and flow generators facilitate the gas exchange at the patient's alveolar level.

The problem found in recent years caused by the pulmonary ventilators, is the so-called Ventilator- Induced Lung Injury (VILI), i.e. lacerations/ruptures of the lung tissues caused by excessive pressure or volume of the gases supplied by the pulmonary ventilators in cases of patients that are intubated and not spontaneously breathing. Such high volumes or pressures are the result of severely compromised lungs that are overstressed by mechanical ventilation to ensure a minimum of alveolar exchange at the physiological level.

To avoid such stresses to the lung, the patient may be subjected, when the clinical picture allows it, to NIV (Not Invasive Ventilation) leaving the patient spontaneously breathing or with a minimum of respiratory assistance and maintaining a positive pressure inside the lung below the safety threshold, and at the same time helping the partial removal of CO ₂ through an extracorporeal circulation of blood (decapneization) in a gas-permeable membrane, thus assisting the activity of the natural lung. Decapneization means a therapy dedicated to removing CO ₂ from the blood by means of a medical-surgical device referred to as a decapneization device, inserted into an extracorporeal blood circuit capable of selectively extracting carbon dioxide (CO ₂ ) from blood by means of its passage through a filter membrane permeable to CO ₂ . Inside the decapneization device a flow of air more or less enriched with oxygen flows and through a membrane permeable to gases only, the oxygen carbon dioxide O ₂ -CO ₂ exchange takes place which is dictated by the difference in partial pressures of the individual gases in the two compartments.

The surface of the membrane is able to support an important removal of CO ₂ thanks to the connection with a source of O ₂ or of medical air that determines a pressure gradient of the individual gases within the fibres of the membrane itself.

Single-lumen or double-lumen catheters normally positioned in the femoral or jugular veins, i.e. in a lower or upper part of a patient's body respectively, are generally used for the removal and the reintroduction of blood into the patient's veins.

Intrapulmonary gas exchanges are the basis of the breathing mechanism that regulates both the diffusion of molecular oxygen (O ₂ ) from the alveoli to the arterial blood (oxygenation), and the elimination of molecular carbon dioxide (CO ₂ ). Gas exchanges depend, in addition to diffusion, also on the mechanical capacity of the respiratory system that allows the exchange of air in the lungs. Alterations in intrapulmonary gas exchanges may cause hypoxemia (insufficient oxygenation of the blood) or hypercapnia (inadequate elimination of CO ₂ from the blood).

Generally in a patient in pathological conditions a dysfunction of both the exchange of O ₂ and CO ₂ occurs, but more commonly prevailing impairments of either of them occur. In some pulmonary and/or systemic pathologies, the elimination of CO ₂ can only occur by resorting to mechanical ventilation, thus accepting the increased risk of possible complications. In fact, if after the failure of the non-invasive ventilation (NIV) techniques, the patient requires invasive ventilation methods, he will be faced with an increased probability of morbidity with an increased risk of mortality.

Extracorporeal gas exchange systems adapted to remove CO ₂ are for example ECCO ₂ -R (extracorporeal CO ₂ removers), ECC (Extracorporeal Circulation) system and systems referred to as ECMO (Extracorporeal Membrane Oxygenation) used in serious pathologies or lung transplants represent an additional opportunity for critical patients.

There is a clinical and experimental need to monitor a patient with acute respiratory failure treated with Extracorporeal Vein-Venous Membrane Oxygenation (ECMO) therapy. This therapy is increasingly used in Intensive Care and its intrinsic complexity poses great difficulties in clinical management, as the normal physiology of the patient is profoundly altered by the therapy itself.

Unfortunately it is difficult both to detect in real time and simultaneously data from the patient, and to simulate what happens in a system comprising natural lung, artificial lung and membrane once the physician changes a parameter of the system. Normally the CO ₂ data in the blood is detected with blood gas analysis every 6 or 8 hours, therefore when the doctor changes a parameter of the system he must rely on his empirical knowledge and experience to predict what could happen to the system in 6 or 8 hours, without the possibility of simulating what will happen within a few hours.

In the article by Christopher John Joyce et at, "A mathematical model of CO, O and N exchange during venovenous extracorporeal membrane oxygenation", Intensive Care Medicine Experimental (2018) 6:25, DOI: 10.1186/S40635-018-0183-4 disadvantageously only a blood flow from a lower part of the body is considered, which is directed towards an artificial lung, furthermore not all input values are calculated or measured, but are estimated.

Aim of the present invention consists in realizing a method implemented by a computer that simulates in real time a system comprising a natural lung, an artificial lung comprising an oxygen-carbon dioxide exchange membrane and that predicts how the system evolves over time, for example what happens by varying a mechanical ventilation and/or settings of an artificial lung.

In accordance with the invention this aim is achieved with a simulation method implemented on a computer according to claim 1.

Another aim of the present invention consists in realizing a computer program that simulates in real time a system comprising a natural lung, an artificial lung comprising an oxygen-carbon dioxide exchange membrane and that predicts how the system evolves over time, for example what happens by varying a mechanical ventilation and/or settings of an artificial lung.

In accordance with the invention this other aim is achieved with a computer program according to claim 9.

Other features are provided in the dependent claims.

The features and advantages of the present invention will become more apparent from the following description, which is to be understood as non-limiting example, with reference to the appended schematic drawings, in which: figure 1 is a schematic view of a flowchart of the method implemented by a computer program according to the present invention that simulates in real time a system comprising a natural lung, an artificial lung comprising an oxygen-carbon dioxide exchange membrane and that predicts what happens by varying a mechanical ventilation and/or settings of an artificial lung; figure 2 is a diagram of the functioning of the natural lung; figure 3 is a diagram of two compartments of an ideal pulmonary unit, the first compartment is referred to as dead space, the second compartment is properly referred to as venous admixture (and also referred to as, albeit improperly, shunt); figure 4 is a diagram of a pulmonary membrane in which part of the blood flow that exits the device, which is the artificial lung, can re-enter the device, depending on the anatomical positioning of the cannulas and on the quantity of a blood flow pumped through an ECMO circuit Q _EC measured in L/min; figure 5 is a graph showing how the percentage saturation of haemoglobin varies as a function of the partial pressure of oxygen in the blood PO ₂ measured in mmHg, two curves are represented, the former with dashed line is real and the latter with solid line is standard; figure 6 shows a flowchart of the method according to the present invention comprising a modelling part, a clinical part and a simulation part; fig. 7 shows a flowchart of the modelling part.

With reference to the cited figures there is described a computer program that simulates in real time a system comprising a natural lung, an artificial lung comprising an oxygen-carbon dioxide exchange membrane and that predicts what happens by varying a mechanical ventilation and/or settings of an artificial lung and which implements a simulation method 100.

The method 100 comprises a modelling part 200, a clinical part 300 and a simulator part 400.

The computer comprises at least one memory for storing the data and at least one processor for performing the actions of the program when the program that comprises instructions such that when the program is executed by the computer implement the method 100 for simulating the system.

Real time means that the method 100 receives input data at an initial time and through this input data it is able to simulate the evolution of the system at any future time chosen by taking a negligible time with respect to the time that would be required waiting for the evolution of the system, wherein this negligible time is the time it takes to the simulator to simulate the evolution of the system. The method simulates the evolution of the system over time means that the method simulates the evolution of the system at any future time starting from an initial time at which it receives input data.

The clinical part 300 of the program allows to enter patient data to measure or calculate key variables of clinical utility to monitor the evolution of the disease, for example advantageously avoiding performing invasive manoeuvres on the patient (e.g. pulmonary arterial catheter). For this, the ventilator configuration, a blood gas analysis (EGA) from the output of the membrane lung (ML), an arterial blood gas analysis EGA and the elimination of CO ₂ from the natural and artificial lungs are necessary as input. Blood gas analysis provides measured data.

The obtained data can be sent to an interface of the second part of the program which is the simulator 400. The simulator 400, given the previously calculated variables, allows to simulate how the system evolves in real time, allowing the doctor to choose different management strategies and to observe the expected response without taking any action on the patient. The simulator 400 can also be used alone, i.e. without the clinical part 300, as an educational tool to explain the complex interaction between the patient, the Extracorporeal Vein-Venous Membrane (ECMO) and all the physiological variables involved.

Through this analytical and numerical/iterative approach the program that implements the method is able to predict the most clinically useful blood parameters at every point of the ECMO system - patient even in impossible/difficult to collect sites.

Advantageously the invention provides a greater degree of safety to the fragile ECMO patient and a deep understanding to the doctor of the patient's specific physiological needs, taking a step forward in a personalized approach to the patient in intensive care.

Advantageously, the method allows a learning of the mechanisms that regulate the gas exchanges and helps the doctor to understand and define the actual state of gas exchange of the patient and to predict in real time what happens when the parameters vary, for example what happens if the mechanical ventilation and/or the settings of the artificial lung are modified. As shown in figure 1 the method 100 and the program comprise a modelling part 200 comprising three patterns or blocks 210, 220, 230.

Each model 210, 220, 230 integrates the description and the effects of the mechanical ventilation in the natural lung NL and the description and the effects of adding an extracorporeal blood flow ML, another component, which connects the natural lung NL to the artificial lung, is a model of the body metabolism B.

Generally referring to figure 1 the simulated system provides a first component A comprising a natural lung NL and a ventilator or more generally a flow generator, a second component B comprising the body metabolism, i.e. a tissue component, a third component C which is the artificial lung and comprises a pulmonary membrane ML i.e. any extracorporeal gas exchange system such as ECMO or ECCO ₂ -R.

For each block 210, 220, 230 we will provide the classical equations that describe the gas exchange and we will add some original solutions to widely recognized but yet unsolved problems in clinical practice 300.

These solutions of the clinical part 300 and of the simulation part 400 act synergistically with each other and constitute the heart of the invention.

Referring in particular to figure 1 the first model or block 210 is the model of the component A of the system, otherwise referred to as natural lung NL, also comprising the ventilator.

Referring to figure 1 the system comprises a multiplicity of connections in blood flow communication between the three compartments A, B and C, these connections are also referred to hereinafter as lines. Said multiplicity of connections comprise a first input connection 1 that transmits a total blood flow Qt to the first compartment A; a second input connection 2 that transmits a portion of blood flow QL to the input of the natural lung NL; a third input connection 3 that transmits a blood flow Q _s to non-aerated parts of the natural lung (NL); a fourth connection 4 at the exit from the natural lung (NL) and which connects with the third connection 3 towards a fifth connection 5.

Said fifth connection 5 receives the flows from the third 3 and from the fourth connection 4 of the first compartment A and transmits the total blood flow Qt towards the second compartment B.

Referring in particular to figure 2, the natural lung is simulated through the simulation program and the first block 210 can be imagined as a single pulmonary unit, in which the gases are uniformly distributed over space and time. In other words, this ideal pulmonary unit 215 has a constant blood input 211 and output 212 (corresponding respectively to the lines 1 and 5 of figure 1) and a constant gas input 213 and output 214. This unit 215 is the heart of the gas exchange in the natural lung (NL hereinafter), i.e. in this unit 215 a certain quantity of O ₂ is added by the gas to the blood that outflows from the lung and a certain quantity of CO ₂ is eliminated from the blood by the gas. The diagram is presented in figure 2.

Figure 2 shows at input 211 a capillary blood flow Q _c (L/min) that enters the ideal alveolus 215. Q _c is equal to a total blood flow Qt (L/min) minus a deviated blood flow Q _s (L/min), which does not enter the ideal pulmonary unit 215. Qt is the volume of blood pumped by the heart in the unit of time (L/min).

Q _s is the volume of blood that flows into the nonaerated parts of the lung per unit of time (L/min).

At input 211 an O ₂ content of venous blood entering the pulmonary unit 215 is C _v O ₂ (mL/100mL) and a CO ₂ content of venous blood entering the pulmonary unit is Cv CO ₂ (mL/100mL). Note that C _v O ₂ and C _v CO ₂ are also the gas concentrations in the derived blood.

In figure 2 at output 212 an O ₂ content of the capillary blood leaving the ideal alveolus 215 is C _c O ₂ (mL/100mL), while a CO ₂ content of the capillary blood leaving the ideal alveolus 215 is C _c CO ₂ (mL/100mL).

In figures 1 and 2, VO ₂ NL is the quantity of oxygen absorbed through the ideal pulmonary unit 215 in 1 min (mL/min) and VCO ₂ NL is the quantity of carbon dioxide eliminated through the ideal pulmonary unit in 1 min (mL/min).

The constitutive equations describing the relationship between VO ₂ , VCO ₂ and blood content at equilibrium are as follows:

The formulas are necessary to calculate the gas content in capillary, venous and arterial blood, respectively: C _c O ₂ = 1.39•Hb (g/dL) +

0.00314 (ml/10OmL•mmHg)-PA O ₂ (mmHg)

C _v O ₂ = 1.39-Kb (g/dL)•S _v O ₂ + 0.00314 (mL/10OmL•mmHg)-P _v O ₂ (mmHg)

C _a O ₂ = 1.39-Hb (g/dL)•S _a O ₂ + 0.00314 (mL/100mL mmHg)-P _a O ₂ (mmHg) where 1.39 is ml of O ₂ that binds 1g of Hb (where Hb stands for haemoglobin) and 0.00314 is the solubility coefficient for O ₂ in blood; PA O ₂ , Pv O ₂ and P _a O ₂ are the partial pressures of O ₂ in the alveolus, in the venous blood and in the arterial blood, respectively; S _v O ₂ and S _a O ₂ are venous and arterial saturations. In the ideal compartment, i.e. in the capillary blood, the saturation is assumed to be 100%.

According to Douglas equation the CO ₂ content is:

According to Kelman equation (Kelman GR. Digital computer procedure for the conversion of PCO ₂ into blood CO ₂ content. Respir Physiol. 1967 Aug;3 (1):111--5. doi: 10.2116/0034-5687 (67)90028-x. PMID: 6059098) the CO ₂ content is:

Doxygenated and D _reduced are, respectively, the ratio

[CO ₂ ]cells: [CO ₂ ]plasma under completely reduced and completely saturated blood conditions, as determined experimentally by Van Slyke and Sendroy (1928). Since this ratio is based on experimentally determined values, it automatically takes into account the carbon dioxide carried in the form of carbamine compounds. The ratio of the intermediate saturations was calculated by linear interpolation. where T is a temperature and Hct is the haematocrit content, i.e. a percentage of blood volume occupied by haematocrits: Hct = Hb * 3/100; in general pK= -logic(Ka), where Ka is an acid dissociation constant. In this case reference is made to the pK of carbonic acid (H ₂ CO ₃ ), which is 6.1.

We remind that O ₂ exchanged in the ideal pulmonary unit is equal to: and that the eliminated CO ₂ is equal to: where F _i O ₂ and FA O ₂ are fractions (e.g.: 0.30, 0.40 etc.) of oxygen respectively in the inspired (index i) and alveolar (index A) gas from the natural lung NL.

It follows that, at equilibrium, the quantity of gas absorbed by the blood (for O ₂ ) or eliminated from the blood (for CO ₂ ) is equal to the quantity given/removed with ventilation, as shown here for the oxygen:

The ratio of VCO ₂ to VO ₂ is known as the respiratory quotient (R):

If R = 1, it means that one mole of CO ₂ is produced for each mole of O ₂ consumed.

From the above equation it is possible to derive that F _A O ₂ , i.e. the fraction of oxygen in the ideal pulmonary unit:

To the ideal pulmonary unit, which takes full account of the exchange of VO ₂ and VCO ₂ , we can associate two other compartments: one ventilated and not perfused, and another perfused but not ventilated. The first is referred to as dead space and represents "wasted" ventilation, while the second is properly referred to as venous admixture and, albeit improperly, it is also referred to as shunt, and it represents "wasted" perfusion. The interaction of these two compartments with the ideal pulmonary unit is represented in figure 3.

In figure 3, VE is a minute ventilation at the input in the plant, VA is VE - VD where VA is the ventilation that reaches the ideal pulmonary unit 215, VD is the ventilation of the dead space that, being the not perfused compartment, does not participate in the gas exchange. Therefore, there is no difference in the composition of the gas entering and exiting the system (line 3 in figure 1).

In figure 3, F _i O ₂ is a fraction of oxygen in the inspired gas; F _A O ₂ /P _A O ₂ is a fraction pressure ratio of the oxygen present in the ideal pulmonary unit; F _A CO ₂ /P _A CO ₂ is a fraction pressure ratio of carbon dioxide present in the ideal pulmonary unit; F _E O ₂ /P _E O ₂ is a fraction-pressure ratio of the oxygen in the gas exiting the entire system, resulting from the gas mixture coming from the ideal pulmonary unit 215 (FA O ₂ ) and from the dead space; F _E CO ₂ /P _E CO ₂ is a fraction-pressure ratio of the carbon dioxide in the gas exiting the entire system, resulting from the gas mixture coming from the ideal pulmonary unit 215 (F _A CO ₂ ) and from the dead space.

In figure 3, Qt is a total blood flow (cardiac output) entering the system, divided into Q _c which is a perfusion that reaches the ideal pulmonary unit and Q _s which is a venous admixture, which represents the quantity of blood perfusing the unventilated alveoli. The composition of the blood exiting this compartment is the same as the one of the blood entering the compartment and will mix with the blood coming from the ideal pulmonary unit.

The dead space, defined as the quantity of gas that does not participate in the gas exchange, was initially calculated by Bohr (Bohr dead space) according to the following: it follows that

This is the fraction of gases that enters the system that reaches the ideal pulmonary unit 215, which is ventilated and perfused. Therefore, the complement to 1 of the above equation represents the fraction of gases that enters the ventilation system of the dead space compartment: P _E CO ₂ is calculated as the ratio of VCO ₂ NL to the total ventilation VE, while the alveolar partial pressure of carbon dioxide P _A CO ₂ is the ratio of VCO ₂ NL to the ventilation that reaches the alveoli VA, i.e.:

The number 863 is a constant factor that converts the volumes from BTPS to STPD and transforms the fractions into partial pressures.

The dead space calculated with the Bohr equation is also referred to as physiological dead space. The greatest limit of this equation is that it requires P _A CO ₂ , i.e. the partial pressure of carbon dioxide in the ideal pulmonary unit 215. Since this value cannot be measured, the Bohr equation was modified by Enghoff using P _a CO ₂ as a surrogate for P _A CO ₂ . This modification would be precise if the P _a CO ₂ value were a true surrogate of the partial pressure of CO ₂ in the capillary of the ideal pulmonary unit 215 (P _c CO ₂ ), which is in equilibrium with P _A CO ₂ . Unfortunately, the composition of the blood exiting the system is also affected by the venous admixture compartment, which modifies the P _a CO ₂ values. Therefore, the dead space calculated according to Enghoff's modification of the Bohr equation is falsely increased by any venous admixture effect.

The physiological dead space can be conceptually divided into two sections: the anatomical and the alveolar one.

For what concerns the alveolar dead space in the ideal pulmonary unit 215, ventilated and perfused, the following relationships can be derived:

Where VA _tot is the gas that enters the alveolar space, perfused or not perfused.

It follows that: this ratio represents the fraction of ventilated and perfused alveolar ventilation with respect to the total alveolar ventilation. Consequently, the complement of this relationship represents the alveolar dead space: where P _A CO ₂ is usually replaced by the arterial CO ₂ value (P _a CO ₂ ).

As far as the anatomical dead space is concerned it reflects the anatomical structures, including the mechanical ventilation apparatus where gas exchange is physically impossible.

An approximate estimate of the anatomical dead space is 1 ml per 1 pound of body weight (1 kg = 2.2 pounds). For example, in a 70 kg man the anatomical dead space will be 70 kg x 2.2 ml/kg = 154 ml.

According to Bohr, the anatomical dead space can also be derived as follows: it follows that: therefore, the anatomical dead space will be:

Referring in particular to figure 1 the second model or second block 220, is the model of the tissue compartment B.

Referring to figure 1, the second block 220 simulates the behaviour of an ideal tissue that is continuously perfused with a blood flow (Qt), consumes a certain quantity of oxygen and produces a certain quantity of CO ₂ . Under normal conditions, the quantity of O ₂ consumed will be equal to the flow multiplied by the difference between arterial and mixed venous O ₂ content, while the produced CO ₂ will be equal to the oxygen consumed multiplied by the respiratory metabolic quotient.

Under normal conditions, the partial pressure of CO ₂ in the ideal tissue is equal to the PCO ₂ in the mixed venous blood, i.e. the CO ₂ content exiting the ideal tissue compartment B is equal to the CO ₂ content in the mixed venous blood.

When an artificial blood is added to the system, the CO ₂ content leaving the tissue is different from the mixed venous blood content of CO ₂ . This will require an estimate of CO ₂ in the tissues. In addition, both O ₂ consumption and CO ₂ production, as well as blood flow, can be different in the upper and lower part of the body. This is absolutely relevant when the artificial lung C is added to the system, as the drainage cannula drains blood coming from specific districts of the body (usually the lower part of the body) whose gas composition is different from the weighted average concentration of gas found in the tissues.

To partially overcome this problem, we have divided the ideal tissue compartment into two sections: the upper one and the lower one.

We defined Q _up as the fraction of the cardiac output that perfuses the upper part 8 of the body and Q _low as the fraction that perfuses the lower part 9:

We defined f _c as the percentage difference in CO ₂ and O ₂ content between the upper and lower part of the body:

The model we adopted for the metabolic compartment is presented in figure 1 as second block 220.

The O ₂ and CO ₂ content of the ideal tissue was calculated as follows:

Said multiplicity of connections comprise a sixth connection 9 that transmits a blood flow Q _cath coming from the second compartment or component B. The blood flow Q _cath comes from the lower part 7 of the body and in part it could come from the upper part 8 of the body.

Said multiplicity of connections comprise a seventh connection 10 where the blood flow Qret of the upper part 8 of the body leaving the tissue component B flows and connects with the line 17 where the blood flow that arrives from the third component C flows reconnecting to the first connection 1 that enters the first component

A. Note that line 10 does not pass through the pulmonary membrane 230, in fact the blood flow coming from the lower part 7 of the body, comprising the blood flow coming from the femoral veins, has a higher pressure than the blood flow coming from the upper part 8 of the body, therefore the blood flow that comes from the upper part 8 of the body is sent directly to the natural lung NL 210 without passing through the lung membrane ML C, while only the blood flow that comes from the lower part

7 of the body ( and in part it could also come from the upper part 8 of the body) is directed towards the pulmonary membrane ML of the artificial lung C.

The blood flow of the lower body 7 has different values than the blood flow of the upper body 8.

Advantageously, by differentiating the two blood flows of the upper part 8 and the lower part 7 of the body, a greater precision of the simulation method 100 is obtained, also allowing the doctor a more correct clinical evaluation because it is based on data calculated or measured in real time and not on data estimated on the basis of samples taken once every 6 or

8 hours which do not differentiate the upper part 8 from the lower part 7 of the body as occurs in the state of the prior art.

The third model or third block 230 describes the artificial lung comprising the pulmonary membrane ML and its characteristics. The artificial lung, of which several models are available, is basically a device that allows the exchange of gases between two compartments: blood and gas. The material that separates them varies depending on the model and also the arrangement for the correspondence of blood and gas is different. The basic principles are the same as those adopted by the first block 210 for the natural lung NL: the material separating the two phases subrogates the alveolar- capillary barrier; the gas entering the gaseous compartment subrogates the total ventilation (VE _ML ) and the flow entering the pulmonary membrane (Q _EC ) through the line 12 subrogates the cardiac output.

The quantification of the gas composition in the pulmonary membrane ML and its correspondence with the blood encounters the same problems encountered with the natural lung NL. It is therefore convenient to approach the physiology of the pulmonary membrane ML like for the natural lung NL, defining in an analogous way to what has been done above for the natural lung an ideal compartment of the artificial lung to which the compartments of dead space and venous admixture of the artificial lung are added.

Ideal compartment: the ideal compartment in ML can be considered as a homogeneous section of the device in which all the exchange of oxygen and carbon dioxide takes place. Therefore, the correspondence of ideal blood flow and of the ideal gas flow is such that, at a given ideal P _oxy O ₂ and ideal P _oxy CO ₂ , the observed O ₂ input and CO ₂ removal can be fully explained.

Venous admixture compartment: the venous admixture compartment is calculated as follows:

Dead space: Bohr dead space of ML:

Where is the average PCO ₂ in output from the

ML (P _E CO ₂ ).

The physiological dead space of ML is calculated as:

As schematically shown in figure 4 another complication is present in the ML with respect to the NL: part of the blood flow exiting the device can re- enter the device, depending on the anatomical positioning of the cannulas and on the quantity of Q _EC . By device is meant the artificial lung. Even the artificial lung works like the natural lung shown in figure 2, in fact it is exchanged VCO _{2 ML} and VO _{2 ML} which respectively represent the amount of CO ₂ eliminated through the lung membrane ML and the amount of oxygen absorbed through the artificial lung unit ML, as shown more schematically in Figure 1.

Note that the blood flow coming from the lower body 7 is measured by hemo gas analysis, while the blood flow coming from the upper body 8 is measured by gas analysis. Advantageously, the gas analysis is carried out continuously and in real time.

Referring to figure 1 that shows the three blocks 210, 220, 230, consider: Qret is the blood flow of the upper part 8 of the body that goes directly from the tissue compartment B to the natural lung NL A following the line 10; Q _cath is the blood flow of the lower part 7 of the body from the tissue compartment B to the pulmonary membrane ML C following the line 9; Q _rc is the blood flow that recirculates through the pulmonary membrane ML following the line 11;

Q _ec is the extracorporeal blood flow that enters the pulmonary membrane C following the line 12, given by the sum of Q _cath and Q _rc ;

Q _ec is the total blood flow that exits the artificial lung ML C following the line 16 and connecting to the lines 11 and 17;

Q _oxy is the portion of Q _ec that enters the ideal ML compartment C following the line 13 and exits therefrom following the line 15;

Q _sec is the portion of Q _ec that enters the shunt compartment of the ML following the line 14;

Said multiplicity of connections also comprise the lines 11-17 shown in figure 11.

Q _gas (VEML) is the total gas flowing in the ML;

VA _oxy is the gas flow that ventilates the ideal compartment ML;

VDML is the ventilation of the dead space of the ML;

Coxy O ₂ and Coxy CO ₂ respectively represent the O ₂ and CO ₂ content in the ideal ML compartment C;

C _in O ₂ and C _in CO ₂ respectively represent the O ₂ and CO ₂ content of the blood entering ML C; C _out O ₂ and C _out CO ₂ respectively represent the O ₂ and CO ₂ content of the blood exiting ML C; P _oxy O ₂ and P _oxy CO ₂ represent the partial pressure of O ₂ and CO ₂ in the ideal compartment of ML C;

P _in O ₂ and P _in CO ₂ represent the partial pressure of O ₂ and of CO ₂ respectively in the blood entering the ML;

P _out O ₂ and Pout CO ₂ represent the partial pressure of O ₂ and of CO ₂ in the blood exiting the pulmonary membrane ML C, respectively.

More generally the method 100 comprises said modelling part 200 of the system that simulates the system as a simulated system by means of three models 210, 220, 230 which are the first model 210 that simulates a behaviour of the first component A, the second model 220 that simulates a behaviour of the second component B, the third model 230 that simulates a behaviour of the third component C.

The first model 210 comprises a first input line 1 that transmits a total blood flow Qt towards a natural lung NL; said natural lung NL comprising an aerated part that exchanges oxygen and carbon dioxide with a fraction of the total blood flow Qt which is a blood flow QL entering from the second line 2 and exiting oxygenated QL from the third line 4, a non-aerated part of the natural lung that transmits a remaining fraction of the total blood flow Qt which is the non-oxygenated blood flow Q _s that is transmitted from the fourth line 3; a fifth output line 5 that transmits a total blood flow Qt that sums the oxygenated blood flow QL of the third line

4 and the non-oxygenated blood flow Q _s that is transmitted from the fourth line 3.

The second model 220 comprises a first input line

5 which is the fifth output line 5 of the first model 210; the tissue component that exchanges oxygen and carbon dioxide with the total input blood flow Qt through the first line 5; a second output line 10 that transmits a blood flow Qret from the tissue component towards the first input line 1 of the first component A; a third output line 9 that transmits a blood flow Q _cath from the tissue component towards the third component C.

The third model 230 comprises a first input line 12 that transmits a total blood flow Q _EC towards the artificial lung; said artificial lung ML comprising the extracorporeal gas exchange system ML that exchanges oxygen and carbon dioxide with a fraction of the total blood flow Qt which is a blood flow Q _OXY entering from the second line 13 and exiting oxygenated Q _OXY from the third line 15, a non-aerated part of the artificial lung that transmits a remaining fraction of the total blood flow Qt which is the non-oxygenated blood flow Q _sEC that is transmitted by the fourth line 14; a fifth output line 16 that transmits a total blood flow Q _EC that sums the oxygenated blood flow Q _OXY of the third line 15 and the non-oxygenated blood flow Q _sEC of the fourth line 14; a recirculation line 11 that transmits a fraction of the total blood flow QEC exiting the fifth output line 16 and referred to as recirculation blood flow QRC and which connects to the first line 12 and to the second output line 9 of the second component B by mixing the recirculation blood flow QRC with the blood flow Q _cath coming from the tissue component to form the input blood flow Q _EC of the first line 12 to the artificial lung C; a transmission line 17 that transmits a fraction of the remaining blood flow Q _EC from the fifth output line 16 deprived of the recirculation blood flow QRC towards the first input line 1 of the first component A. Said transmission line 17 connects to the second output line 10 of the second component B to mix the remaining blood flow of the transmission line 17 with the blood flow Qret from the tissue component.

The clinical part 300 of the method 100 and of the program implementing the method 100 is designed to provide the doctor with a complete picture of the patient's clinical status and its interaction with the pulmonary membrane ML, using a limited number of input variables that can be implemented automatically. The concepts on which the clinical section 300 is built are the same as those of the simulator part 400 in that the simulator 400 predicts how the output parameters change once the input parameters provided by the clinical part 300 are modified.

The structure of the clinical section 300 is exactly the same as the one of the simulator section 400: we have the same three compartments: A natural lung NL comprising the ventilator, B tissue compartment, C artificial lung comprising the pulmonary membrane ML, connected as described above and depicted in particular in figure 1.

The biggest difference between the simulator 400 and the clinical instrument 300 is that in the latter P _A CO ₂ , PA O ₂ and the alveolar pH that must be estimated indirectly from the arterial blood gases, while they are calculated directly in the simulator 400. In the simulator 400, the most relevant variables of the ideal compartment, such as the venous admixture and the dead space, are calculated directly from the input variables used as input. In the clinical model 300 these technical characteristics are not primary variables to be estimated but are calculated. Therefore, the whole procedure must follow different steps.

The clinical part 300 needs initial measured input data to then calculate all input data needed for the simulation part 400.

More generally, the clinical part 300 provides in input for initial measured input data used by the clinical part 300 to calculate at least a part of input data for the simulation part 400. The remaining part of input data for the simulation part 400 are comprised among the initial input data of the clinical part 300. No input data is only estimated, but always either measured or calculated on the basis of measures. Note that calculating is different from estimating, because calculating implies having measured data to insert in a formula to calculate another data, while estimation means a probabilistic estimate affected by stochastic errors.

It is specified that the input data for the simulation part 400 are partly the initial input data also used by the clinical part 300 and partly are the data calculated by the clinical part 300 using the initial input data.

Referring to the arrows in figure 1 to establish pre- and post-pulmonary membrane ML C, the input variables for the clinical part 300 of the program and of the method are the initial input data and are divided in this manner.

General parameters: cardiac output (Qt), according to line 5 of figure

1; VCO _{2 ML} and VCO ₂ NL, which represent respectively the quantity of CO ₂ eliminated through the pulmonary membrane ML and the quantity of CO ₂ eliminated through the natural lung NL;

Ventilator setting parameters for the natural lung NL, part A: F _i O ₂ , which represents the fraction of oxygen in the gas inspired by the natural lung (number between 0 and 1);

RR respiratory rate, the number of breaths taken per minute; V _t , current or tidal volume, a quantity of air moving in or out of the lungs for each respiratory cycle L;

Arterial BGA blood gas analysis parameters:

P _a CO ₂ partial pressure of CO ₂ in the arterial blood measured in mmHg;

P _a O ₂ partial pressure of O ₂ in the arterial blood measured in mmHg; pH _art is the pH of the arterial blood;

Hb _art represents the concentration of haemoglobin in the arterial blood in g/dL;

Post EGA ML parameters:

Pout CO ₂ partial pressure of CO ₂ in the blood flowing out of the ECMO circuit measured in mmHg;

Pout O ₂ partial pressure of O ₂ in the blood flowing out of the ECMO circuit measured in mmHg; pH _out is the pH of the blood flowing out of the ECMO circuit;

Hb _out is the concentration of haemoglobin in the blood flowing out of the ECMO circuit, measured in g/dL.

Pulmonary membrane ML setting parameters of part C: Q _ec the volume of blood pumped through the ECMO circuit, per unit of time in L/min;

Q _gas is the volume of gas flowing in the ECMO circuit, per unit of time in L/min; F _i O _{2 ML} fraction of oxygen in the gas flowing in the pulmonary membrane, is a number comprised between 0 and 1;

Pre ML parameters:

S _pre O ₂ is the oxygen saturation in the haemoglobin in the blood flowing towards the ECMO circuit;

Tissue compartment parameters, part B:

ABE (v-a) is the difference in BE between tissue blood, i.e. venous blood not affected by extracorporeal circulation, and arterial blood; f _c is the percentage difference in O ₂ and CO ₂ content between the upper portion and the lower portion of the patient's body of the tissue compartment B; fq is the percentage fraction with respect to Qt between the upper and lower part of the body (e.g. percentage of Q _up with respect to Q _t , or percentage of Q _low with respect to Qt).

Consider that T=37°C is used in any formula that requires temperature.

The starting equations for the clinical part are: where Hct is the haematocrit content that is measured by a blood test that indicates the percentage of the blood volume occupied by the haematocrits.

Oxygen saturations are available directly from BGA blood gas analysis.

The clinical part 300 recalculates with coherence formulas all other saturations not directly available (e.g.: venous saturation).

Saturations for the arterial and post-ML blood are calculated from the input variables, respectively (pH, PO ₂ and PCO ₂ ).

As is done in the simulator part 400, a correction is applied for the parameters: temperature, PCO ₂ and pH. For this purpose we use the method proposed by Kelman (J. Appl. Fisio., 1966). Therefore, for each PO ₂ value we calculate a new value of virtual PO ₂ (virtual PO ₂ ) which has no clinical and biological significance, but when inserted into the standard saturation curve depicted in figure 5 it provides the same value of oxygen saturation of haemoglobin SO ₂ as the real curve with actual pH, PCO ₂ and PO _2n .

Virtual PO ₂ is calculated as:

This new value is inserted in place of the real PO ₂ in the tree equations described above (Severinghaus, Kelman, Ruiz) and the saturation is obtained in the current condition of pH, PCO ₂ and temperature:

Severinghaus: Kelman:

After calculating the haemoglobin saturation values, it is possible to calculate the basic excess BE of arterial and post-ML blood according to Zander equation:

From the pressures to the arterial and post-ML contents:

Oxygen: C _a O ₂ and C _out O ₂ are calculated as follows:

Carbon dioxide: C _a CO ₂ and C _out CO ₂ are calculated according to Douglas or Kelman formulas: CO ₂ content (according to Douglas eq.): CO ₂ content (according to Kelman eq.):

At this point the following variables are available for the arterial and post-ML blood: contents, pressures, pH, BE and saturations.

With regard to the oxygen in the pulmonary membrane ML an ideal compartment of pulmonary membrane ML is considered.

Since one of the input variables is the oxygen saturation of the blood entering the ML (pre ECMO saturation), we calculate the oxygen content C _in O ₂ as follows.

First of all, a conversion of the saturation in input to pressure (P _in O ₂ ) is performed with an inverse

Severinghaus equation:

It is important to point out that this calculation does not take into account the effect of pH, PCO ₂ and temperature on the haemoglobin dissociation curve; in fact, the P _in O ₂ calculated with inverse Severinghaus is the one that would be in equilibrium with the input saturation only if the pH was 7.40 and PCO ₂ was 40 mmHg. This limit is, however, clinically irrelevant as it is limited to no more than 3-4 mmHg.

If the pH and PCO ₂ of the input blood of the ML were known, however, it would be possible to add this additional correction.

In the second stage, the pre-ML blood oxygen content is calculated:

We can calculate now VO _{2 ML} and R _ML as follows:

It is assumed that the oxygen tension (P _oxy O ₂ ) in the blood flowing in the ideal ML compartment C is equal to the oxygen tension in the gaseous compartment. So: P _oxy O ₂ is then converted into virtual P _oxy O ₂ (using the pH and PCO ₂ post-ML values for correction) in order to calculate the corresponding haemoglobin saturation (S _oxy O ₂ ) with Severinghaus, Kelman or Ruiz equation.

At this point it is possible to calculate the oxygen content of this "ideal" compartment ML:

The shunt percentage of the compartment ML (line 14) with respect to Q _ec is then calculated with the usual shunt formula:

Therefore, it is possible to calculate the two components of the extracorporeal flow, namely the shunt flow (Q _sec ) (line 14 of figure 1) and the flow that perfuses the ventilated part of the ML ( Q _oxy ) (line 13 of figure 1):

With regard to the carbon dioxide in the pulmonary membrane ML, an ideal compartment of pulmonary membrane ML is considered. C _out CO ₂ has already been calculated from the input variables.

Gin CO ₂ is calculated as follows:

The CO ₂ content in the ideal compartment ML is instead calculated as follows:

Physiological dead space in the compartment of the pulmonary membrane ML:

As is evident from the formula, it is not enough to have an initial setup provided by a flow generator/lung ventilator to calculate physiological dead space.

With regard to the tissue compartment B, the section of the model 220 where all O ₂ is consumed and all CO ₂ is produced. Therefore, the arterial carbon dioxide content will be modified as follows:

A catheter draining the blood from the tissue compartment B may be inserted into the upper or lower part of a patient's body, where the distribution of the total flow may be different. It is therefore convenient to divide the tissue compartment B into two sections: the upper metabolic 8 and the lower metabolic 7 compartment.

The direct flow to the upper compartment 8 will be defined as:

Considering this, then the flow to the lower compartment 7 will be:

The concentration of carbon dioxide in the two compartments 7, 8 is different, as the metabolism may be different. In fact, gravity affects the upper body differently than it does the lower body. Therefore, the oxygen saturation of the blood leaving the upper 8 or lower 7 compartment is different. The percentage difference in the fraction of oxygen saturation between the upper 8 and lower 7 compartment is an input variable and is referred to as f _c .

It should be noted that the documents of the prior art however do not differentiate the blood flow coming from the upper part 8 of the body from the blood flow coming from the lower part 7 of the body.

In this step we must estimate how much flow from the tissue compartment reaches the pulmonary membrane ML and how much will return directly to the right heart. The following variables are then defined:

Qret is the blood flow that from the upper part 8 of the body goes directly from the tissue compartment B to the natural lung NL A following the line 10 of figure 1; Q _cath is the blood flow that from the lower part 7 of the body goes from the tissue compartment B to the pulmonary membrane C along the line 9 of figure 1; Q _rc is the blood flow that recirculates through the pulmonary membrane C, shown along the line 11 of figure 1;

Q _ec is the extracorporeal blood flow (line 12 of figure 1) that enters the pulmonary membrane C, given by the sum of Q _cath and Q _rc ;

Q _oxy is the portion of Q _ec that enters the ideal ML compartment C, see line 15 of figure 1; Q _sec is the portion of Q _ec that enters the shunt compartment of ML C, see line 14 of figure 1. In order to determine Q _cath , Q _rc and Qret it is necessary to understand how the blood exiting the tissue compartment B is drained in the extracorporeal circulation C. Two cases are possible:

Case 1: Q _cath ≤ Q _low

This occurs when Q _cath comes completely from the lower metabolic compartment 7;

Case 2: Q _cath > Q _low

This occurs when Q _cath receives blood from all the lower metabolic compartment 7 and from the upper one 8 (Q _{up cat} )•

When it is written that the blood flow of the lower part 7 of the body passes through line 9, it means that the blood flow of the lower part 7 of the body passes for the most part, but a part of the blood flow 8 of the upper part of the body can also pass in part as explained in the alternative case 2.

In line 10 of figure 1, on the other hand, only the blood flow of the upper part 8 of the body passes both in case 1 and in case 2.

In a first phase, we can assume that we are in the most complicated case, that is, in case 2. In this scenario, the following system of equations applies: from which, we can simply calculate Q _{up cath} and Q _rc :

If Q _{up cat} > 0: then case 2 is confirmed, the two values of Q _{up cath} and Q _rc are accepted and Q _cath can be calculated:

If Q _{up cat} 0, then case 2 is impossible and we return to case 1.

In this scenario, i.e. in case 1, the following system of equations applies: from which, we can simply calculate Q _cath and Q _rc :

In this step, regardless of the case, it is possible to calculate the recirculation rate as:

Advantageously to calculate the content of O ₂ in the upper 8 and lower 7 tissue compartments, it is necessary to know the recirculation flow, the flow of the catheter and the oxygen content of the blood entering and exiting the artificial lung C, this allows to calculate, with "inverse" sequence, the oxygen content in the tissue section B and its division in the two metabolic compartments 7, 8. In fact: it is then possible to calculate C _cath O ₂ , Cret O ₂ and C _v O ₂ . It is emphasized that these values are calculated and not estimated.

According to case 1:

As regards the role of carbon dioxide CO ₂ in the upper 8 and lower 7 tissue compartments, it is possible to calculate C _cath CO ₂ , Cret CO ₂ and C _v CO ₂ .

In case 1:

In case 2:

The basic excess BE of the arterial and post-ML blood has already been calculated in the earlier steps using Zander equation.

According to Zander, no difference should be found between arterial and venous BE. However, we leave the possibility to set ABE as input by the user.

P _in CO ₂ and pHin are calculated through the following iterative process in the pre-ML portion of figure 1. P _in CO ₂ is calculated according to the inverse Zander equation as a function of the increase in the pHin levels (starting from 6.5 with a 0.0001 step).

The calculated P _in CO ₂ is inserted into an equation of the CO ₂ content (either Douglas or Kelman). The iteration is interrupted when the calculated CO ₂ content is equal to the one given ( C _in CO ₂ ).

For all remaining compartments (tissue and mixed venous blood), saturation of PO ₂ , PCO ₂ , pH and O ₂ is derived from the content through the following iterative process .

A first step of the iterative process provides that PCO ₂ is calculated according to the inverse Zander equation as a function of the increase in pH levels (starting from 6.5, with 0.0001 step), starting from an oxygen saturation of 100%.

An appropriate BE value is used for each compartment: tissue compartment: BE _tiss mixed venous compartment: BE _V

The calculated PCO ₂ is inserted into an equation of the CO ₂ content (either Douglas or Kelman). The iteration is interrupted when the calculated CO ₂ content is equal to the one given (respectively C _tiss CO ₂ and C _v CO ₂ ).

A second step of the iterative process provides the PCCb/pH pair being used to calculate a PO ₂ /Sat pair through another iterative process. The PCO ₂ /pH pair is used to calculate PO ₂ virtual as a function of the increase in PO ₂ levels (starting from PO ₂ =1, e.g. with 0.01 step). PO ₂ virtual is then inserted into Severinghaus, Kelman or Ruiz equation to calculate a new oxygen saturation value, then the O ₂ content is calculated:

The process is interrupted when the calculated oxygen content is equal to the one given (respectively C _tiss O ₂ and C _v O ₂ ).

A third step of the iterative process provides that the PO ₂ /Sat pair obtained in the second step is inserted into the first step of the iterative process, to calculate a new PCO ₂ /pH pair, and so on.

The cycle of the three steps of the iterative process is interrupted when the last calculated pH is less than, for example, 0.00001 different from the previous one.

Alternatively it is possible to interrupt the cycle at different pH values.

As regards the first block 210 that models the natural lung NL.

At this point, the following calculations are possible:

As regards the oxygen in the natural lung NL, it is provided that PA O ₂ is calculated by assuming P _A CO ₂ = Pa CO ₂ :

Then, we determine the oxygen saturation (S _A O ₂ ) and the pH (pH _A ) of the capillary blood through iteration, in a similar way to what is done in the simulator 400.

Assuming P _A CO ₂ = Pa CO ₂ , we calculate BE through Zander equation, starting from S _A O ₂ = 1 and with increasing levels of pH _A (starting from pH 6.5 with increasing levels for example by a 0.0001 step), until the calculated BE is equal to the one given (BE _art ):

At this point the process is interrupted and the pH value _A is accepted. The pH _A is used to calculate PO ₂ virtual, along with PA O ₂ and P _a CO ₂ . P _virtual O ₂ is then inserted into Severinghaus, Kelman, or Ruiz equation to calculate a new oxygen saturation value. If the calculated value of S _A O ₂ differs from the previous one for example by more than 0.001, the cycle restarts from the beginning: the new saturation value is inserted into the initial Zander equation to calculate a new pH value, which will be used to find a new alveolar saturation value. The cycle continues until the last saturation value differs from the previous value less than, for example, 0.001. O ₂ capillary is calculated as:

With regard to the natural shunt of the lung (line 3 of figure 1):

With regard to the carbon dioxide of the natural lung NL:

With regard to the dead space of the natural lung

NL:

Owing to the approximations indicated some of the values calculated so far may be slightly inaccurate. To solve this problem, we recalculated some of the variables.

We recalculated S _A O ₂ and pH _A . TO do this, we repeated the cycle described above for the calculation of the oxygen in the natural lung NL, using the value P _A CO ₂ obtained in the calculation of the carbon dioxide for the natural lung NL.

Thus, a new value C _A CO ₂ can be obtained with the Kelman or Douglas equation.

We calculated a new C _a CO ₂ according to the following formula:

A new iteration starts. The following equations are solved in this order:

If the calculated C _a CO ₂ is different from the one calculated above in relation to the saturation calculation, see figure 5 for reference, the last value is used to restart the cycle. The iteration is interrupted when C _a CO ₂ is different from the previous one, for example 0.01.

More generally and summarizing what the clinical part 300 of the method 100 does, the clinical part (300) comprises at least one iterative calculation step for determining all the simulated system data starting from the initial input data.

Said at least one iterative calculation step comprises a multiplicity of calculation cycles for determining an evolution over time of both the initial input data and of the data calculated by the clinical part 300.

Referring to the arrows in figure 1 to establish pre- and post-pulmonary membrane ML C, the input variables for the simulation part 400 of the program are divided in this way.

General parameters: cardiac output (Qt), according to line 5 of figure 1, (it is also used for clinical part 300);

Hb : haemoglobin concentration in the involved blood streams; BE _art is the basic excess of arterial blood. The basic excess is defined as the quantity of base/acid that must be added to the blood to obtain a pH of 7.40, providing a partial pressure of carbon dioxide PCO ₂ of 40 mmHg and at a temperature of 37°C (mmmol/L).

Ventilator setting parameters for the natural lung NL, part A: F _i O ₂ , which represents the fraction of oxygen in the gas inspired by the natural lung (number between 0 and 1), (is also used for clinical part 300);

RR respiratory rate, the number of breaths taken per minute, (also used for clinical part 300); V _t , current or tidal volume, a quantity of air moving in or out of the lungs for each respiratory cycle L, (also used for clinical part 300);

V _{d phys} /V _t is the rate between V _d and Vd _Phys , where V _t is the total or tidal volume that represents the quantity of air moving in and out of the lungs at each respiratory cycle measured in L, while Vd _Phys is the total dead space, such as the volume of the ventilated but not perfused lung (measured in L).

Qs/Qt is the ratio between Q _s with respect to Qt, i.e. a number comprised between 0 and 1, where Q _s is the volume of blood flowing in the non-aerated parts of the lung, measured in unit of time, i.e. L/min.

VO ₂ tot represents the quantity of oxygen absorbed both through the natural lung NL and through the pulmonary membrane ML in 1 minute (mL/min).

VCO ₂ tot represents the quantity of carbon dioxide eliminated both through the natural lung NL and through the pulmonary membrane ML in 1 minute (mL/min).

Pulmonary membrane ML setting parameters of part C:

Q _ec the volume of blood pumped through the ECMO circuit, per unit of time in L/min; Q _gas is the volume of gas flowing in the ECMO circuit, per unit of time in L/min; F _i O _{2 ML} fraction of oxygen in the gas flowing in the pulmonary membrane, is a number comprised between 0 and 1;

VCO _{2 ML} is the quantity of CO ₂ eliminated through the pulmonary membrane ML, (also used for clinical part 300);

QRC/Q _EC is the QRC ratio with respect to Q _EC , where QRC is the part of Q _EC that recirculates through the pulmonary membrane (L/min);

Q _sec /Q _EC is the ratio of Q _sec with respect to Q _EC , where Q _sec is the part of Q _EC that flows into the non- ventilated parts of the pulmonary membrane ML (L/min);

Post ML parameter:

BEpostML is the basic excess of blood flowing out of the pulmonary membrane (mmmol/L).

Tissue compartment parameters, part B:

ABE (v-a) is the difference in BE between tissue blood, i.e. venous blood not affected by extracorporeal circulation, and arterial blood, (also used for clinical part 300); f _c is the percentage difference in O ₂ and CO ₂ content between the upper portion and the lower portion of the patient's body of the tissue compartment B, (also used for clinical part 300); fq is the percentage fraction with respect to Qt between upper and lower part of the body (e.g. percentage of Q _up with respect to Qt, or percentage of Q _low with respect to Qt), (also used for clinical part 300).

Consider that T=37°C is used in each formula of the simulation part 400 requiring temperature, as also happens for clinical part 300. The clinical part 300 introduces said input data set forth above into the simulator part 400.

Said simulator part 400 simulates an evolution of said simulated system starting from said input data by means of the three models 210, 220, 230.

More generally and summarizing what the simulator part 400 does, the simulation part 400 comprises at least one iterative calculation step for determining all the simulated system data starting from the input data provided by the clinical part 300, wherein said at least one iterative calculation step of the simulation part 400 comprises a multiplicity of calculation cycles for determining an evolution over time of both the input data provided by the clinical part 300 and of the data calculated by the simulation part 400 starting from said input data provided by the clinical part 300.

More specifically, the following initial equations are used for the simulation part 400: for the blood flowing in the natural lung A, i.e. the shunt flow Q _s line 3 of figure 1 and total flow Qt: for the blood flowing in the pulmonary membrane ML C, i.e. shunt flow Q _sec line 14 of figure 1, Q _oxy line 13 of figure 1 and recirculation flow Q _rc line 11 of figure 1:

The distribution of Qt from the tissue compartment B to the artificial lung ML C, i.e. Q _cath line 9 of figure 1, Qret line 10 of figure 1, Q _oxy line 17 of figure 1:

Other formulas used to calculate the other data needed for the simulation: where FR is a respiratory rate, i.e. a number of respiratory acts performed in one minute (acts/min).

With regard to the simulation of the natural lung NL: ideal compartment A, the following passages are implemented in sequence.

The first step is the determination of the alveolar partial pressure of carbon dioxide P _A CO ₂ :

The second step is the determination of the alveolar partial pressure of oxygen P _A O ₂ according to the following formula:

Note that, in this initial step, we consider RNL =1 where RNL is the rate of VCO _2NL with respect to VO _2NL , which are respectively the quantity of CO ₂ eliminated through the natural lung in 1 minute and the quantity of oxygen absorbed by the natural lung in 1 minute. P _B is a barometric pressure of 760 mmHg, while P _H20 is a saturated vapour pressure corresponding to 47 mmHg.

The third step consists in determining the saturation of the alveolar oxygen (Sat _a iv) and the alveolar pH (pH _alv ) of the capillary blood by iteration as described below.

By definition, the PO 2 of capillary blood (P _c O ₂ ) is equal to the ideal pulmonary unit PO ₂ . Since pH is a function of both basic excess and oxygen saturation, an iterative process is used to find the pH of the alveolar compartment. The reference equation is a modified Zander equation, which calculates BE: Given a BE input (assumed equal to BE _art which is the basic excess of arterial blood), the iterative process starts calculating the alveolar pH assuming a 100% alveolar saturation. Increasing pH levels (starting from pH 6.5 with increasing levels e.g. by a 0.0001 step) are inserted into Zander equation until the calculated BE is equal to the given one. At this point the process is interrupted and the pH value is accepted. Then, the pH is used to calculate the actual alveolar saturation.

It is possible to calculate the saturation of haemoglobin as a function of P _A O ₂ through Severinghaus, Kelman or Ruiz equation:

Severinghaus :

Ruiz :

It is important to point out that the equations listed above refer to a dissociation curve of the oxygen saturation measured at pH 7.40, PCO ₂ of 40 mmHg and temperature T of 37°C. A correct correction is therefore preferable when referring to the clinical scenario, with different pH and PCO ₂ values.

For this purpose we used a method proposed by Kelman (J Appl Fisio, 1966). The rationale behind the use of this equation is the generally accepted fact that all three factors alter the scale of the PO ₂ axis, but do not alter the shape of the dissociation curve. It is thus possible to make the standard dissociation curve applicable to different temperatures and acid-base states by calculating a new value of virtual PO ₂ (PO ₂ virtual). This new value has no clinical and biological significance, but when inserted into the standard saturation curve it provides the same SO ₂ value as the real curve with the actual pH, PCO ₂ and PO ₂ values (see figure 5).

This new value is inserted into place of the PO ₂ real in the tree equations described above (Severinghaus, Kelman, Ruiz) and saturation is obtained under the actual conditions of pH, PCO ₂ and temperature.

If the calculated alveolar saturation value differs from the previous one by more than for example 0.001, the cycle restarts from the beginning: the new saturation value is inserted into the initial Zander equation to calculate a new pH value, which will be used to find a new alveolar saturation value. The cycle continues until the last saturation value differs from the previous one by less than 0.001, for example.

More generally, this step of iterative calculation of said simulation part 400 can be summarized as comprising a first step that calculates the alveolar partial pressure of carbon dioxide P _A CO ₂ ; a second step that calculates the alveolar partial pressure of oxygen P _A O ₂ ; a third step saturation of alveolar oxygen (Sat alv) and of the alveolar pH (pHalv) of the capillary blood by means of an iterative process comprising calculating the alveolar pH starting from an alveolar saturation value and varying it step by step, using the alveolar pH calculated in the previous step and calculating the actual alveolar saturation under actual conditions of pH, PCO ₂ and temperature.

For what concerns a calculation of the gas content, we divide the problem by carbon dioxide and oxygen. With regard to the carbon dioxide, we calculate the capillary content (C _c CO ₂ ).

It is possible to choose which equation can be used between two different options: Douglas equation or Kelman equation. The input variables are: P _A CO ₂ , alveolar saturation and capillary blood pH.

For CO ₂ Content (Douglas eq.):

For CO ₂ Content (Kelman eq.):

For mixed venous blood (Cv CO ₂ ):

For arterial blood (C _a CO ₂ ):

For oxygen the capillary content (C _c O ₂ ): For what concerns the second tissue component B and for carbon dioxide the blood flow is divided into the upper and lower parts of the tissue compartment according to fq:

The CO ₂ content in the ideal tissue is calculated as follows: CO ₂ concentrations in the upper (C _up CO ₂ ) and lower part (C _low CO ₂ ) of the body can be calculated according to the following system of equations:

It follows that:

At this point it is necessary to consider the characteristics of the input blood, which can originate in proportions different from the upper and lower metabolic compartments:

In case 1: Q cat Q low this occurs when the catheter Q comes completely from the lower metabolic compartment;

In case 2: Q cat > Q low this occurs when Q _cath receives blood from all of the lower metabolic compartment and part of the upper one.

For what concerns case 1, since Q _cath comes only from the lower metabolic compartment, C _cath CO ₂ in this case it is equal to C _low CO ₂ .

In contrast, Qret is composed of blood coming from both the upper and lower metabolic compartments, and it is calculated as follows:

C _in CO ₂ , Coxy CO ₂ and C _out CO ₂ from the ML artificial lung are calculated through a matrix as follows:

For what concerns case 2, C _r et is only composed of blood coming from the upper metabolic compartment, so C _ret CO ₂ = Cup CO ₂ .

On the other hand, Q _cath is composed of blood coming from the upper and lower metabolic compartments and is calculated as follows:

C _in CO ₂ , Coxy CO ₂ and C _out CO ₂ from the artificial lung ML are calculated through a matrix as follows:

With regard to the ideal compartment of the pulmonary membrane ML. For further calculations it is useful to calculate P _oxy CO ₂ and P _oxy O ₂ . P _oxy CO ₂ is calculated through an iterative process, assuming Sat _oxy =1 and BE _oxy = BE _art .

P _in CO ₂ is calculated according to the inverse Zander equation as a function of the increase in pH levels (starting from 6.5, e.g. 0.0001 step):

Each calculated P _in CO ₂ is inserted into an equation of the CO ₂ content (either Douglas or Kelman). The iteration is interrupted when the calculated CO ₂ calculated is equal to the one given (Coxy CO ₂ .

Then, assuming RML =1, it is possible to calculate:

For what concerns the tissue compartment B, the problem is divided into two cases 1 and 2.

With regard to case 1 we can find C _a O ₂ , C _v O ₂ , C _U p O ₂ , C _low O ₂ , Cin O ₂ and C _out O ₂ by solving the following system of equations through a matrix:

Since Q _cath only comes from the lower metabolic compartment, C _cath O ₂ in this case is equal to Ci _O w O ₂ .

In contrast, Qret is composed of blood coming from both the upper and lower metabolic compartments, and it is calculated as follows:

As regards case 2, we can find C _a O ₂ , C _v O ₂ , C _U p O ₂ , Glow O ₂ , Cin O ₂ and C _out O ₂ by solving the following system of equations through a matrix:

In this case, Cret is only composed of blood coming from the upper metabolic compartment, so Cret O ₂ = C _up O ₂ .

On the other hand, Q _cath is composed of blood coming from the upper and lower metabolic compartments and is calculated as follows:

Once this system of equations is solved, the O ₂ content of the blood entering and exiting the natural lung NL and the artificial lung ML can be calculated. It is then possible to calculate the quantity of O ₂ added to the blood from each lung with the following formulas: consequently, since VCO ₂ and VO ₂ are available for both lungs, it is possible to calculate RNL and RML:

For accuracy purposes, it is now possible to recalculate P _A O ₂ with the correct RNL:

It is possible to calculate BE according to Zander. No difference should be found between arterial and venous BE, however, we leave the possibility to set ABE as input by the user.

PO ₂ , PCO ₂ , pH and saturation can now be calculated for all compartments A, B and C.

For all compartments dealt with above (arterial, mixed venous, pre-ML, post-ML and tissue blood), PO ₂ , PCO ₂ , pH and O ₂ saturation are derived from the contents through the following iterative process:

In the first stage, PCO 2 is calculated according to the inverse Zander equation as a function of the increase in pH levels (starting from 6.5, for example with 0.0001 step), starting from an oxygen saturation of 100%

An appropriate BE value is used for each compartment: Arterial: BE _art Mixed venous: BE _V Pre-ML, Post-ML and tissues: BE _tiss •

The calculated PCO ₂ is inserted into an equation of the CO ₂ content (either Douglas or Kelman). The iteration is interrupted when the calculated CO ₂ content is equal to the one given (C _a CO ₂ , C _v CO ₂ , C _in CO ₂ , C _out CO ₂ and C _tiss CO ₂ , respectively).

In the second stage, the PCO ₂ /pH pair is used to calculate a PO ₂ /Sat pair through another iterative process. The PCO ₂ /pH pair is used to calculate virtual PO ₂ virtual (as discussed above) as a function of the increase in PO ₂ levels (starting from P02=l, e.g. with step 0.01).

P _virtual O ₂ is then inserted into Severinghaus, Kelman or Ruiz equation to calculate a new oxygen saturation value, then the O ₂ content is calculated:

The process is interrupted when the calculated oxygen content is equal to the one given (respectively C _a O ₂ , C _v O ₂ , C _in O ₂ , C _out O ₂ and C _tiss O ₂ )• In the third stage, the PO ₂ /Sat pair obtained in the second stage described above is inserted into the first stage, to calculate a new PCO ₂ /pH pair, and so on. The cycle is interrupted when the last calculated pH is lower than, for example, 0.00001 different from the previous one.

Alternatively, it is possible to choose other steps, with respect to those mentioned so far in the implementation example.

As far as the artificial lung dead space is concerned, it is possible to calculate it as the Bohr dead space of the ML: where is the average PCO ₂ in output from the ML

(PECO ₂ ).

The physiological dead space of the ML is calculated as:

Alternatively and more generally it is possible to provide that in place of ECMO any extracorporeal gas exchange system such as ECCO ₂ -R is used.

Alternatively and more generally the pulmonary ventilator is a flow generator.

Alternatively and more generally initial input data for the clinical part 300 comprises: the total input blood flow Qt through the first line 5 of the first component (A); the quantity of CO ₂ VCO _{2 ML} eliminated through the extracorporeal gas exchange system (ML); the quantity of CO ₂ VCO ₂ NL eliminated through the natural lung (NL); the oxygen fraction in the gas inspired by the natural lung (NL) F _i O ₂ ; the respiratory rate RR of the natural lung (NL); the tidal volume V _t of the natural lung (NL); the partial pressure of CO ₂ in an arterial blood P _s CO ₂ ; the partial pressure of O ₂ in the arterial blood P _a O ₂ ; the pH of the arterial blood pH _art ; the haemoglobin concentration in the arterial bloodH _art r the partial pressure of CO ₂ in the blood P _out CO ₂ flowing out of the third component (C); the partial pressure of O ₂ Pout O ₂ in the blood flowing out of the third component (C); the pH of the blood pH _out flowing out of the third component (C); the concentration of haemoglobin Hb _out in the blood flowing out of the third component (C). the blood flow Q _ec pumped through the third component (C); the volume of gas Q _gas flowing in the third component (C); the fraction of oxygen F _i O _{2 ML} in the gas flowing in the extracorporeal gas exchange system (ML); the oxygen saturation S _pre O ₂ in the haemoglobin in the blood flowing towards the third component (C); a basic excess difference ABE (v-a) between tissue blood and arterial blood; a percentage difference f _c of O ₂ and CO ₂ content between an upper portion and a lower portion of the second component (B); a percentage fraction f _q with respect to Qt between the upper and lower part of the second component (B).

Alternatively and more generally input data for the simulation part 400 comprises: the total input blood flow Qt through the first line 5 of the first component (A); the concentration of haemoglobin Hb in the blood flows of the simulated system; the basic excess of the arterial blood BE _art ; the oxygen fraction in the gas inspired by the natural lung (NL) F _i O ₂ ; the respiratory rate RR of the natural lung (NL); the tidal volume V _t of the natural lung (NL); the rate Va _Phys /V _t between a tidal volume V _p and a total dead space volume V _{d Phys} ; the Qs/Qt ratio between a volume of blood flowing in non-aerated parts of the natural lung Q _s with respect to the total blood flow Qt; the quantity of oxygen absorbed VO ₂ tot both through the natural lung (NL) and through the extracorporeal gas exchange system (ML); the quantity of carbon dioxide eliminated VCO ₂ tot both through the natural lung NL and through the extracorporeal gas exchange system (ML); the volume of blood Q _ec pumped through the third component (C); the volume of gas Q _gas flowing in the third component (C); the fraction of oxygen F _i O _{2 ML} in the gas flowing in the extracorporeal gas exchange system (ML); the quantity of CO ₂ VCO _{2 ML} eliminated through the extracorporeal gas exchange system (ML); the QRC/Q _EC ratio of the recirculation blood flow QRC with respect to the blood flow Q _EC in the third component (C); the Q _sec /Q _EC ratio of the blood flow flowing in the non-ventilated parts of the extracorporeal gas exchange system (ML) Q _sec with respect to Q _EC ; a basic excess difference ABE (v-a) between tissue blood and arterial blood; the percentage difference f _c of O ₂ and CO ₂ content between an upper portion and a lower portion of the second component (B); the percentage fraction f _q with respect to Qt between the upper and lower part of the second component (B).

Advantageously, the present invention implements the method 100 implemented by the computer which simulates in real time the system comprising the natural lung NL, the artificial lung ML comprising the oxygen carbon dioxide exchange membrane and which predicts how the system evolves over time, for example what happens by varying a mechanical ventilation and/or artificial lung settings.

Advantageously, method 100 does not estimate the values, but as input it has measurements or calculations made on measurements and as output method 100 has calculations performed on the input measurements and/or calculations obtained which are repeated iteratively.

The invention thus conceived is susceptible to many modifications and variants, all falling within the same inventive concept.