WO2019079838A1

WO2019079838A1 - Method and system for controlling an exchange rate of a permeate

Info

Publication number: WO2019079838A1
Application number: PCT/AT2018/060259
Authority: WO
Inventors: Alen KARABEGOVIC; Margit GFÖHLER
Original assignee: Technische Universität Wien
Priority date: 2017-10-25
Filing date: 2018-10-25
Publication date: 2019-05-02

Abstract

A method for controlling an exchange rate of a permeate from a source fluid (3) across a first membrane (2) and across a second membrane (11), wherein the membranes (2, 11) are connected by a circulation (6) of a sweep fluid (5) and the circulation (6) comprises a circulator pump (12), by controlling the circulator pump (12) according to an exchange model, which estimates the permeate exchange rate across the first membrane (2) depending on a determined flow rate of the source fluid (3), a determined flow rate of the sweep fluid (5) and a determined amount of permeate removed from the sweep fluid (5) at the second membrane (11) into a washing fluid (10), to achieve a reference permeate exchange rate.

Description

Method and system for controlling an exchange rate of a permeate

The present invention relates to a method and a system for con^¬ trolling an exchange rate of a permeate to achieve a reference permeate exchange rate from a source fluid across at least one membrane .

One preferred use of the invention is to control the carbon di^¬ oxide (C02) gas quantity in blood inside the human body, where C02 and oxygen (02) are exchanged across the at least one mem^¬ brane, which is in contact with the blood.

In their article "The Relationship Between Oxygenator Exhaust P_Co2 and Arterial P_Co2 During Hypothermic Cardiopulmonary Bypass" (Anaesth Intensive Care 2005; 33: 457-461), Graham et al disclose a method to estimate carbon dioxide in oxygenator arterial blood from the partial pressure of gas exhausting from the oxy^¬ genator. This method applies to a cardiopulmonary bypass situa^¬ tion, where the lung is replaced by a membrane oxygenator. In this situation, the exchange happens in an extracorporeal de^¬ vice, i.e. the blood is temporarily removed from the body.

Therefore, the amount of C02 removed from the blood can be de^¬ termined immediately from an analysis of the exhaust gas.

WO 2017/064285 Al discloses a device and method for supporting C02 exchange in addition to the functioning of the lungs. An intravascular membrane catheter is provided and connected to an extracorporeal membrane oxygenator via a circulation of sweep fluid, that is used as a transport medium for transporting C02 out of the body. It is not described, how the disclosed device can be operated and controlled in detail.

An objective of the present invention is to provide a system and method that allow to control the exchange rate of the permeate without knowledge of or possibility to measure a permeate con^¬ centration in the source fluid.

In order to achieve the objective mentioned above, the present invention provides a method as defined in the outset, for con^¬ trolling an exchange rate of a permeate to achieve a reference permeate exchange rate from a source fluid across a first mem^¬ brane and across a second membrane,

wherein the first membrane and the second membrane are con^¬ nected by a circulation of a sweep fluid, wherein said circula^¬ tion comprises a circulator pump,

wherein the first membrane is arranged in a cross-flow con^¬ figuration between a flow of the source fluid and the circula^¬ tion of the sweep fluid, and

wherein the second membrane is arranged in a cross-flow con^¬ figuration between the circulation of the sweep fluid and a flow of a washing fluid, the method comprising the steps of:

- determining a source flow rate of the source fluid past the first membrane;

- determining a sweep flow rate of the sweep fluid within the circulation;

- determining a removed amount of permeate contained in the washing fluid downstream the second membrane;

- removing the permeate from the sweep fluid at the second membrane; and

- controlling the circulator pump according to an exchange model, which estimates the permeate exchange rate across the first membrane depending on the determined source flow rate, sweep flow rate and removed amount of permeate, to achieve the reference permeate exchange rate.

In order to achieve the objective mentioned above, the present invention further provides a system as defined in the outset, for controlling an exchange rate of a permeate to achieve a ref^¬ erence permeate exchange rate, the system comprising:

a first membrane,

a second membrane,

a circulation connecting the first membrane and the second membrane and comprising a circulator pump,

a source flow sensor configured to determine a source flow rate of a source fluid past the first membrane,

a sweep flow sensor configured to determine a sweep flow rate of a sweep fluid within the circulation,

a permeate content sensor configured to determine a removed amount of permeate contained in a washing fluid downstream the second membrane, and a controller connected to the circulator pump, the source flow sensor, the sweep flow sensor and the permeate sensor and configured to control the circulator pump according to an ex^¬ change model, which estimates the permeate exchange rate across the first membrane depending on the source flow rate, sweep flow rate and removed amount of permeate, to achieve the reference permeate exchange rate.

In principle, each of the membranes (first and second membrane) may be any membrane allowing the passage of the permeate. Re^¬ garding the preferred use of the invention, at least the first membrane may be cylindrical in shape in order to minimize pres^¬ sure losses and improve flow profiles when placed for example in the vena cava (which may be regarded as a type of a cylindri^¬ cal pipe) . Examples of such membranes are known from the Intra^¬ venous Oxygenator (IVOX) or Hattler catheter placed in a cylindrical pipe, or any other cylindrical membrane used as a gas filter/purifier that permeates same or similar gases as those found in blood. There are several ways of modelling such mem^¬ branes, with many examples known to the skilled person. Some of them are listed below, with the list extending to referenced documents as well:

McKee, S., Dougall, E. A., & Mottram, N. J. (2016) . Analytic solutions of a simple advection-diffusion model of an oxygen transfer device. Journal of Mathematics in Industry, 6(1), 3.

Hewitt, T. J., Hattler, B. G., & Federspiel, W. J. (1998) . A mathematical model of gas exchange in an intravenous membrane oxygenator. Annals of biomedical Engineering, 26(1), 166-178.

Federspiel, W. J., Hewitt, T. J., & Hattler, B. G. (2000) . Experimental evaluation of a model for oxygen exchange in a pul^¬ sating intravascular artificial lung. Annals of biomedical engineering, 28(2), 160-167.

Manap, H. H., Wahab, A. K. A., & Zuki, F. M. (2017, June) . Mathematical Modelling of Carbon Dioxide Exchange in Hollow Fi^¬ ber Membrane Oxygenator. In IOP Conference Series: Materials Science and Engineering (Vol. 210, No. 1, p. 012003) . IOP Publi^¬ shing .

Hormes, M., Borchardt, R., Mager, I., Schmitz-Rode, T., Behr, M., & Steinseifer, U. (2011) . A validated CFD model to predict 02 and C02 transfer within hollow fiber membrane oxygen- ators . The International journal of artificial organs, 34(3), 317-325. and

Zierenberg, J. R., Fujioka, H., Hirschl, R. B., Bartlett, R. H., & Grotberg, J. B. (2007) . Pulsatile blood flow and oxygen transport past a circular cylinder. Journal of biomechanical en^¬ gineering, 129(2), 202-215.

The second (e.g. extracorporeal) membrane may be of any size and shape. It may be a cylindrical membrane as the first membrane or e.g. a typical oxygenator. Examples of suitable models are well researched and known in literature - therefore these can be readily identified and applied by the skilled person.

The reference permeate exchange rate may be a direct reference variable or it may be derived from a permeate content in the source fluid and a reference permeate content in the source flu^¬ id. The invention is not limited to methods and systems where the reference permeate exchange rate is provided directly and explicitly .

The source flow sensor and/or the sweep flow sensor can be any sensing or measuring means suitable to determine the source flow rate of a source fluid past the first membrane or the sweep flow rate respectively. The invention does not require a dedicated flow sensor in the form of a separate device for the specific purpose of determining the respective flow rate. Rather each of the flow sensors can either use a dedicated sensor or an estima^¬ tion technique using other available measurements, for example based on a rotational speed of a pump moving the source fluid or the sweep fluid. The flow sensor can be integrated with such a pump (e.g. as a current sensor) . The rotational speed can be de^¬ rived from variations of a drive current or using a Hall sensor. Similarly, the permeate content sensor refers to any sensing or measuring means suitable to determine an amount of permeate con^¬ tained in the washing fluid. In particular this may be a perme^¬ ate content analyser. For example, the concentration of permeate (e.g. C02 ) in the sweep fluid exiting the second (e.g. extracor^¬ poreal) membrane (exhaust) can be acquired using established sensors on the market, such as NDIR sensors. The invention is based on the finding, that the amount of perme^¬ ate crossing the first membrane and even the permeate content in the source fluid upstream the first membrane can be estimated from the source flow rate, the sweep flow rate and the amount of permeate removed from the sweep fluid, together with constant system characteristics that can be predetermined, e.g. in a cal^¬ ibration measurement. This estimation is based on an exchange model, which defines the relation between the above-mentioned process variables as follows:

^-source f t> tfsweep,toti ^source,tot' ^wash,permeate where c_SOUrce is the permeate content in the source fluid upstream of the first membrane, q_SWee_P,tot it is the total volumetric flow rate of the sweep fluid in the circulation, q_SOurce,tot is the total volumetric flow rate of the source fluid past the first mem^¬ brane, m_wash,permeate ίs the mass flow rate of permeate contained in the washing fluid, and k is a constant specific to the first membrane .

In the case first membrane is a hollow fibre membrane, expres^¬ sion for the permeate content in the source fluid upstream of the first membrane becomes

Qsource.tot ^wash.perme te

^(■source ~ 7 ϊ J \ ^~

1— ^~k r, + , . tot

p \*< source, tot Hsweepfot'H sweep while the constant k can be calculated as follows:

where D is a diffusion constant determined by the membrane mate^¬ rial, permeate type and the properties of the source fluid and the sweep fluid, R_out and Ri_n are the outer and inner radius of a single fibre, Nf_ib(memb is the number of fibres making up the first membrane, and L is the length of the fibres (and hence the mem^¬ brane) in a direction of flow of the source fluid. This assumes that the fibres are swept with the sweep fluid parallel to the flow of the source fluid outside the fibres.

The above exchange model makes several assumptions and simplifi^¬ cations, to which the invention shall not be limited. In detail, it is assumed that the fibres are arranged perfectly parallel to the flow of the source fluid and sweep fluid, have the same di^¬ mensions and same local cross-sectional area for the entire flow of source fluid in the vicinity. It is further assumed that the effects of viscosity and shape of the source fluid flow and sweep fluid flow can be neglected and a constant flow velocity along the first membrane is assumed. Moreover, no radial flow of the fluids is taken into account, i.e. perfectly straight flow directions are assumed. Finally, it is assumed that the flow path and exchange process are not affected by the geometry of the surroundings of the membrane.

The model presented above is only one of many possible ways to describe the relation shown in equation [1] . The final determination of parameters and fine-tuning of the model can be per^¬ formed routinely by the skilled person. As a matter of course, the different flow rates are a time-dependent and consequently the exchange rates are as well. The dependency on time involves the system's transient times and delays due to system dimen^¬ sions, sensors' positions and response times. These are all identified individually by the skilled person and can be imple^¬ mented into the control system using established principles of control theory.

Based on the above equation and assuming that the flow rate of the sweep fluid can be influenced by controlling the circulator pump, the system input of the circulator pump can be controlled such that a desired reference permeate exchange rate correspond^¬ ing to a desired permeate content in the source fluid downstream the first membrane is achieved. For example, a measured error may be the reference permeate exchange rate minus an estimated exchange rate. The relation between c_source and the exchange rate of the permeate is described in more detail later in connection with the exemplary embodiments. The system input can be a pump speed or a drive current of the circulator pump. Preferably, the present method comprises controlling a source pump, which is configured to move the source fluid along the first membrane, according to the exchange model to achieve the reference permeate exchange rate. In this case, the flow rate of the source fluid past the first membrane can be influenced by controlling the source pump. Consequently, a multi-input multi- output control system is established that allows to optimise the time response of the control such that a desired steady-state can be reached faster than by controlling only the circulator pump. The models of all components of the system are the part of the control system. The model of the complete system (nonlinear in nature) can be controlled either directly using a nonlinear controller or be linearized and used with various controller types, most straightforward of which is a PID controller (or its types) . The development of the controller can be based on well- known models of major interaction systems and is within the expertise of the skilled person.

Correspondingly, the present system may comprise a source pump, which is configured to move a source fluid past the first mem^¬ brane, wherein the controller is connected to the source pump and configured to control the source pump according to the ex^¬ change model to achieve the reference permeate exchange rate.

The source pump may be for instance an axial or radial pump (e.g. inserted into the blood stream) that may be directly at^¬ tached to the first membrane. In connection with the preferred use, it may be driven by a motor that can be arranged inside a patient's body. Examples of pumps able to operate within an in- tracorporeal catheter are the Abiomed Impella and Thoratec

Heartmate PHP, both existing on the market for several years. It is within the experience and routine of the skilled person to identify the behaviour of any pumping and drive units. The pump^¬ ing unit is completely described through a range of experiments using blood or liquid of same viscosity in order to obtain pres^¬ sure-flow dependency. Drive unit's (motor's) current-torque char^¬ acteristic is also known ahead, which enables a conventional de^¬ sign of a motor speed controller, which can be applied within the present method. Conventional measures in this respect may include an integrated rotational speed sensor or estimator using other available measurements essentially opaque to the present disclosure. Both characteristics can be obtained in experiments well described in literature and routinely performed by the skilled person in this technology.

Especially with regards to applications where the first membrane obstructs the flow of the source fluid, it can be advantageous if the controlling of the source pump respects a constraint de^¬ fining a required pump power of the source pump. For instance, this allows to exactly define the required rotational speed or drive current or power of the source pump. When the present method controls a pumping unit of an intravascular catheter, this requirement corresponds to the blood flow requirement that (at least) compensates any influence that the membrane would have on the physiological pressures in the blood vessel (e.g. the vena cava) . In cases where the source pump is driven by transferring flow energy from the sweep fluid, the above requirement puts an additional constraint on the control of the circulator pump. Preferably, said constraint may be a lower boundary of the pump power, i.e. allowing for (temporary) higher pump powers than the required pump power (or minimum pump power) .

Correspondingly, the controller of the present system may be configured to respect a constraint defining a required pump pow^¬ er of the source pump.

Therefore, it is favourable, if the present method comprises controlling the flow rate of the washing fluid depending on the determined sweep flow rate and removed amount of permeate, to remove essentially all permeate from the sweep fluid at the sec^¬ ond membrane. The system input for controlling the flow rate of the washing fluid can be determined using a stored set of char^¬ acteristic curves defining the relation of the sweep flow rate and the flow rate of the washing fluid in order to achieve com^¬ plete removal of the permeate from the sweep fluid. These curves can be determined empirically (e.g. by experiment and measure^¬ ment) . In this process, the sweep fluid upstream the second mem^¬ brane can be saturated with permeate in order to obtain a con^¬ servative characteristic. Generally, it is not required to set the permeate in sweep fluid after the second membrane to zero (i.e. remove all permeate from the sweep fluid), but only par^¬ tial removal of the permeate from the sweep fluid can be used to optimise an energy consumption of the system. This could happen if the power required to achieve a certain flow rate of the washing fluid (washing flow rate, e.g. keep the valve of a mass flow controller open, including the required power in the internal electronics) becomes higher than the power required to achieve a certain sweep flow rate (e.g. spin an external pump for creating the required q_sweep ) · For such cases, the initial concentration of permeate in the sweep fluid upstream the first membrane (c_sweep, i_ni_ti_al ) can be determined even if it is not known, combining the mass conservation law of the permeate in the complete system and the exchange model presented above. Further^¬ more, the impact of a change in the sweep flow rate compared to the impact of a change in the washing flow rate would have on the removed permeate depends on the second membrane's character^¬ istic curves. In general, the power levels of both actuators (valve or pump) , as well as these characteristic curves, are un^¬ known, thus a general optimisation strategy applies a cost- benefit algorithm.

Correspondingly, the present system may comprise a wash flow control device for controlling the flow rate of a washing fluid past the second membrane, wherein the controller is connected to the wash flow control device and configured to control the flow rate of the washing fluid depending on the sweep flow rate and removed amount of permeate, to remove essentially all permeate (or a maximum amount of permeate subject to constraints defined by the second membrane and the sweep fluid) from the sweep fluid at the second membrane.

In a preferred embodiment, the flow rate of the washing fluid can be controlled with a single or multiple mass flow regula^¬ tor (s) . I.e. the reference value (s) of at least one mass flow regulator are determined as one of the system inputs together with the input of the circulator pump. Alternatively, the flow rate of the washing fluid may be controlled e.g. with a valve or pump . As pointed out in the outset, the present invention is particu^¬ larly suited for controlling an exchange of carbon dioxide.

Therefore, the present method is preferably characterized in that the permeate is carbon dioxide.

The removed amount of permeate contained in the washing fluid may be determined using a gas analyser arranged downstream the second membrane. The gas analyser is preferably an infrared gas analyser. The permeate content determination can also be performed with any other type of permeate detection sensor, such as gas chromatographers , mass spectrometers or chemical sensors. In the current state of art, the optical gas analysers (e.g. based on an infrared spectrum of the washing fluid downstream the second membrane) are the fastest option.

Correspondingly, the permeate sensor of the present system may be a gas analyser, which is arranged to analyse a washing fluid downstream the second membrane, preferably an optical gas ana^¬ lyser or - more specifically - an infrared gas analyser.

In a preferred embodiment of the present invention the first membrane is a hollow fibre membrane. Hollow fibre membranes pro^¬ vide an exceptional volume-surface ratio and are therefore par^¬ ticularly well-suited for applications where space requirement is an issue (e.g. inside a blood vessel) .

With regard to the preferred application in a system supporting a lung function, the first membrane may preferably be part of an intravascular membrane catheter and the second membrane a part of an extracorporeal gas exchange unit. The sweep fluid can be a gas, a gas mixture or a liquid; it is preferably a liquid, e.g. PFC.

Referring now to the drawings, wherein the figures are for pur^¬ poses of illustrating the present invention and not for purposes of limiting the same,

Fig. 1 schematically a preferred application of the present invention in a system for removing carbon dioxide from blood using an intravascular membrane catheter;

Fig. 2 schematically a signal flow in a system according to Fig. 1;

Fig. 3 schematically a closed control loop illustrating the control method according to the invention;

Fig. 4a a diagram of a membrane characteristic curve of the relation between the flow rate of the washing fluid and the concentration of the permeate in the sweep fluid upstream the sec^¬ ond membrane (i.e. the "final" concentration in sweep fluid af^¬ ter it passes the first membrane) at various sweep flow rates, for which the concentration of the permeate in the sweep fluid downstream the second membrane (i.e. the "initial" concentration in sweep fluid before it meets the first membrane) equals zero; and

Fig. 4b an operating window of a single point on the curve shown in Fig. 4a, while the "initial" concentration in the sweep fluid is not zero.

The invention encompasses a system and underlying principle of control of a permeate quantity in a source fluid (e.g. C02 in blood inside the human body) without direct measurement of the permeate content in the source fluid.

The described system and method can be used in combination with intracorporal medical devices as for example an intravascular membrane catheter 1 for C02 reduction as shown in Fig. 1. In comparison to other existing blood C02 control systems that pre^¬ dominantly interact with blood extracorporeally, i.e. require the blood to exit the patient only to be released into the sys^¬ temic circulation after passing the external oxygen- ator/degasser, the proposed system is the first of its kind that controls the C02 level in blood in combination with an intracorporal system. By using estimation techniques for determination of blood flow and C02 level in blood and adaptive algorithms to control the speed of C02 removal the blood can stay in the human circulation at all times, resulting in a significantly lower invasiveness of the system and, consequently, minimizing the nega^¬ tive impact on the patient.

The intracorporal device can for example be an intravascular membrane catheter 1 as described in WO 2017/064285 Al and comprising a first membrane 2 having fibres ordered in a defined shape that improves the C02 transfer from blood forming the source fluid 3 inside the vessel 4 into a sweep fluid 5 inside a circulation 6, a pumping unit or source pump 7 that improves the blood flow through the catheter 1 and past the first membrane 2 and a drive unit 8, which is either a DC motor or a fluid tur^¬ bine .

The system comprises a controller 9 (see Fig. 2) that assumes existence of an external sweep fluid circulation 6 which is able to independently control the flow of blood through the porous membrane structure, flow of sweep fluid in the blood-sweep fluid interface, and flow of a washing fluid 10 (e.g. a washing gas) in a sweep fluid-washing fluid interface comprising a second membrane 11. These parameters are manipulated using the source pump 7 (as a blood flow actuator) , a circulator pump 12 (as a sweep fluid flow actuator in the blood-sweep fluid interface) and a wash flow control device 13 (as washing gas flow actuator in the sweep fluid-sweep gas interface), e.g. a mass flow con^¬ troller. In the following, the source pump 7, the circulator pump 12 and the wash flow control device 13 are referred to as a DC motor, an external pump and a gas valve, respectively.

Measurements on the system acquired extracorporeally, such as a partial pressure of C02 in the sweep fluid at the entry and exit to the first membrane 2, flow of sweep fluid 5 and washing fluid 10, permeate content in the washing fluid 10 downstream the sec^¬ ond membrane 11 (e.g. streaming out of the extracorporeal oxy- genator/degasser ) , as well as the pressures at several points in the extracorporeal system, are used to calculate the C02 content in venous blood according to an exchange model as described above. The exchange model can be derived from a system of mutu^¬ ally dependent partial differential equations that determine the dynamic behaviour of the permeate exchange process. The basis of these partial differential equations are the advection-diffusion equations applied to the permeate concentration in the source and sweep fluids interacting with each other over a single fiber : ^so rc source, tot ^ ^sourc _>_ ^ >,

■a_* ~ A a₇ ⁺ A \¾ource ^c sweep)

UL ft-tofv ^u - ^Atofv- c sweep _ sweep, tot ^c sweep k - .

with A_t0fv being the total cross-sectional area of the outer-fibre volume inside the membrane and A_tif_V is the total cross-sectional area of the inner-fibre volume inside the membrane. The equa^¬ tions describe the effects of change in certain parameters on the rest of the system states, among them crucial being the val^¬ ue of the concentration of permeate in the source fluid (e.g. C02 in venous blood) and the value of the concentration in the sweep fluid (e.g. C02 in PFC) . The concentration of permeate in the source fluid or sweep fluid is equivalent to a partial pres^¬ sure of permeate as described by Henry's law, where the Henry's constant for the permeate (e.g. a specific gas) is known for the source fluid or the sweep fluid (e.g. PFC) . For the equations to be correct it is assumed that all constants in the system are known, such as the properties of the fibre material of the first membrane 2 and the properties of the sweep fluid 5, or the stat^¬ ic characteristics of the first (porous) membrane 2, the intra- corporal source pump 7, the external circulator pump 12, the second membrane 11, etc. The constants and static properties of components can be measured in stationary conditions during pre^¬ paratory identification experiments. The estimation algorithm implements the acquisition of the latest measurements, and to^¬ gether with their historic development, solves the partial dif^¬ ferential equations, resulting in the latest estimated value of permeate in the source fluid.

The estimate of the flow rate of the source fluid through the first membrane is determined using sensory fusion principle from the latest values of the source pump' s 7 rotational speed, motor current and optionally pressure difference in front and after the membrane catheter 1. These are combined with previously measured static characteristics to provide the current value of the flow rate. The controller 9 reads out the reference of the permeate content in the source fluid 3 that is manipulated by the outside user, e.g. a doctor, via a graphical user interface 14 (see Fig. 2) . The reference is compared to the estimated value of permeate currently present in the source fluid 3, e.g. venous blood. The controller 9 observes the historic progression of the permeate content in the source fluid 3 and optimizes the outputs to down^¬ stream controllers interacting with the actuators 15 in the sys^¬ tem, i.e. the source pump 7, the circulator pump 12 and the wash flow control device 13. In order to estimate the permeate con^¬ tent in the source fluid and/or the exchange rate of the perme^¬ ate, the controller 9 is connected to a first source flow sensor 16 transmitting the drive current of the source pump 7, to a second source flow sensor 17 transmitting the rotation speed of the source pump 7, a first sweep flow sensor 18 directly measur^¬ ing the flow inside the circulation 6 and transmitting the flow rate of the sweep fluid, and a second sweep flow sensor 19 transmitting the rotation speed of the circulator pump 12. Moreover, the controller 9 is connected to multiple pressure sen^¬ sors: two source pressure sensors 20, 21 measuring and transmit^¬ ting the pressure at the inlet and outlet respectively of the first membrane 2, two circulator pump pressure sensors 22, 23 measuring and transmitting the pressure at the inlet and outlet respectively of the circulator pump 12, two sweep pressure sen^¬ sors 24, 25 measuring and transmitting the pressure at the inlet and outlet respectively of the second membrane 11, and multiple wash pressure sensors 26 measuring and transmitting the pressure of one or more washing fluid sources 27. In practice, the two source pressure sensors 20, 21 measuring and transmitting the pressure at the inlet and outlet respectively of the first mem^¬ brane 2 are optional, as the first (e.g. intracorporal ) membrane would need them only, if the estimation of the source flow rate from a source pump controller (e.g. a DC motor's current) is not possible or feasible.

In the application shown in Fig. 1 the washing fluid sources 27 are gas pressure bottles containing different gases (e.g. nitro^¬ gen or oxygen) . The washing fluid 10 is prepared in a mixer 28 according to either a predetermined or a dynamically controlled gas mixture. Said mixture is chosen such as to optimally remove the permeate from the sweep fluid 5 and to charge the sweep flu^¬ id 5 with particles that should be transported into the catheter 1. The second membrane 11 is part of an extracorporeal gas ex^¬ change unit 47. In a downstream section 29 of the washing fluid pipe a gas analyser 30 is arranged. The gas analyser 30 determines the composition of the washing fluid 10 downstream the second membrane 11 and transmits at least a determined permeate content to the controller 9.

Fig. 3 illustrates the control logic implemented by the control^¬ ler 9. The shown control loop 31 receives as a reference a ref^¬ erence permeate exchange rate 32 (as mass transfer rate) , or a reference permeate content (or partial pressure) of the source fluid, or a reference change of permeate content (or partial pressure) of the source fluid, or another equivalent reference. From the reference permeate exchange rate 32 and estimated per^¬ meate exchange rate 33 (or other estimated output, e.g. con^¬ tent/concentration or partial pressure of permeate in the source fluid, change of content/concentration or partial pressure in the source fluid, etc.) is subtracted to obtain a measured error 34. The master controller 35 determines a reference source flow rate 36, a reference sweep flow rate 37 and a reference wash flow rate 38 (i.e. the reference flow rate of the washing fluid) from the measured error 34 together with some or all sensory outputs 39 of the device (see Fig. 2), including those sensory outputs that are required to determine the working point for achieving c_sweep, i_ni_ti_ai⁼0 (zero permeate content in the sweep flu^¬ id) . The master controller 35 transmits those references 36-38 to secondary controllers 40-42 (or "subcontrollers") . The sec^¬ ondary controllers include a source flow control loop 43, a sweep flow control loop 44 and a wash flow control loop 45 (e.g. implemented by the wash flow control device 13) . The secondary controllers 40-42 can be implemented by a standard design, e.g. a PID-control, sliding mode control, etc. The secondary control^¬ lers 40-42 receive a measured error determined from the respec^¬ tive references 36-38 and measurements or estimates of the con^¬ trolled output. The source flow is estimated with a source flow estimator 46 connected to a first source flow sensor 16 and a second source flow sensor 17 integrated in the source pump 7 ; the sweep flow is measured with a first sweep flow sensor 18; the flow of the washing fluid is measured with a wash fluid flow sensor 47. The remaining quantity of the washing fluid in the washing fluid sources 27 is supervised by the pressure sensors 26. The secondary controllers 40-42 control the input current 48 of the source pump 7, the input current 49 of the circulator pump 12 and the input 50 of the wash flow control device 13 (e.g. MFC) and thereby determine the system inputs 51, 52, 53 for the permeate exchange system 54 comprising the first mem^¬ brane 2, the second membrane 11 and the circulation 6. The sen^¬ sory outputs 39 of the permeate exchange system 54 include the removed amount of permeate contained in the washing fluid 10 as determined by the gas analyser 30. From this removed amount to^¬ gether with an estimated source flow rate available from the source flow control loop 43 and a sweep flow rate available from the sweep flow control loop 44 the estimator 55 determines the estimated permeate exchange rate 33 according to the exchange model embedded in the estimator 55. The controller 9 as shown in Fig. 2 preferably comprises at least the master controller 35 and the estimator 55. In addition, any or all of the secondary controllers 40, 41, 42 may be implemented in the controller 9. A required pump power of the source pump 7 may be implemented as a constraint in the source flow control loop 43 and/or in the mas^¬ ter controller 35.

In order to give the user an additional level of control in con^¬ nection with the exemplary application described in connection with Fig. 1, the control system enables them to adjust both the desired amount of energy consumption from the actuators in the system, as well as the criticality level or the shape of the C02 removal from the blood. A cost function is therefore created that is based on the nonlinear state space system calculated from the partial differential equations that calculates the new settings of the secondary controllers in the actuator control loops downstream, as well as the new references for the same control loops. Such an adaptive controller can optimize the bat^¬ tery consumption when the system is not connected to a current source while still providing enough support to the patient. In this case, minimum energy consumption may be achieved by the controller setting the reference source flow to a predetermined constraint (e.g. according to a minimum source flow to compen- sate a pressure difference between the beginning and the end of the first membrane) , setting the reference mass flow rate of the washing fluid to a value that is sufficient to remove essential^¬ ly all permeate from the sweep fluid even when it is saturated, wherein the setting naturally depends on the flow rate of the sweep fluid, and setting the reference sweep flow to a value that is just sufficient to achieve the reference permeate ex^¬ change rate. Depending on the energy consumption of the involved actuators and controllers, a different setting (e.g. a reference source flow above a predetermined constraint) may achieve the minimum energy consumption.

Determination of permeate content in the sweep fluid

The reference mass flow rate of the washing fluid that is suffi^¬ cient to remove essentially all permeate from the sweep fluid can be determined from characteristics recorded during static experiments with the second membrane (e.g. an external oxygen^¬ ator) . These characteristics correspond to a 3D surface con^¬ structed from 3D points ( q_Swee_P,tot, m_wash, c_sweep, final) measured at a moment when the content c_sweep, initial in the sweep fluid downstream the second membrane becomes zero at increasing washing fluid flow rate (m_wash) , while the permeate concentration in the sweep fluid ( Csweep, final) and the sweep flow rate (q_SWee_P,tot) being the same .

The recorded curve of a single pass experiment may look like the diagram shown in Fig. 4a.

The idea here is to reuse the information recorded during such individual experiments to determine the following:

1. find the range of m_wash where the content c_sweep, initial becomes 0 using the 3D surface

2. calculate the concentration c_source after bringing the content csweep, initial to 0

3. calculate csweep, initial from the values of concentration csource r mass flow of permeate in exhaust gas m_wash,permeate, and sweep flow rate q_SWee_P,tot

The instant c_sweep,initai reaches zero can be recognized in that Ac_p = c_s„eep, final - c_sweep, initial = const., i.e. no further changes in Csweep, initial will be possible. In signals that can be measured in the system this would be observed as m_wash,permeate remaining con^¬ stant, as well as independent of m_wash, since the maximum amount of permeate would already be removed from the sweep fluid.

Therefore, in order to ensure that c_sweep, initial becomes zero during operation with an outside current source, for recording the characteristics of the second membrane, one needs to manipulate the m_wash signal and record whether m_wash(Permeate changes or not: if it remains constant, we know that c_sweep,initai has become zero.

The graph in Fig. 4b depicts two curves describing the change of Csweep, initial at changing m_wash, keeping c_sweep, final and q_SWeep,tot con^¬ stant. Assuming that the system shall operate at c_sweep,initai^>0

(higher than zero) means that on the curve shown in Fig. 4b it would operate at a nonzero point, i.e. above the horizontal ax^¬ is. At this moment, m_wash(Permeate, i can be measured. The equation

[5] represents the relationship of c_sweep, initial to other variables measured at the same point:

— ^w h_^perrne t ,! [5]

Csweep, initial,! ~ ^ sweep, final,! ^"~ " ^"~

"sweep,tot

By increasing m_wash one can observe the change of m_wash(Permeate until it reaches m_wash,permeate, 2 which remains constant since

At this point, the values are related to each other as:

_ ^mwash,permeate,2 [ 6 ] t-sweepjinai i ^{~~ ~}

"sweep.tot

The condition

permits the calculation of c_source using equation [2] . With the value of c_SOUrce_/ and using the following expression for c_sweep, final, ι :

^so rce ^' : : ½weej>,!»iti«i.l _r _ _r , , . ·, { ¹ , \ _T c .... , , = ^ wr £ m ^c!2*SSB 2&e ¾«»_Αί¾5) ^L [ 7 1 one can finally calculate csweep, initial, 1 aS.

s.we pMUiaii'l [8]

Thus, by knowing the characteristic curve at a given q_SWee_P,tot, one can extract the c_sweep, initial value based on manipulating m_wash and observing changes in m_wash(Permeate ·

The speed of this control method is dependent on dead and tran^¬ sient times in the sweep circulation, i.e. a change in the per^¬ meate concentration in the sweep fluid takes some time to reach the first membrane, interact in it and finally be led back to the second membrane, where it is analysed in the exhaust washing fluid. This can easily be compensated for using available tech^¬ niques from the systems theory.

Finally, by changing c_sweep, initial we are fundamentally influencing the exchange process at the first membrane. Simply put, we change the c_sweep, final (the permeate content downstream the first membrane) . However, since we have the model that directly ex^¬ presses c_sweep, final and c_sweep,initial (see equations [7] and [8]), and having a method now to estimate/determine c_sweep, initial, we can es^¬ timate the Csweep, final change during the process. In order for this to work, the permeate content in the source fluid c_source has to be known. One can achieve that in periodic intervals (e.g. every 30 minutes) by bringing c_SWeep, initial to zero (according to the above-discussed characteristics) and applying equations [2],

[5]- [8] .

Calculation of permeate mass transfer rate

As the concentration levels of permeate in the source fluid and the sweep fluid, using the model in combination with the meas^¬ urement of m„ash, permeate, are assumed to be known, the question comes down to how the concentration change of permeate in the source fluid (Ac_SOurce) reflects in the changing permeate mass transfer rate m_pemeate. The equation is derived from the ideal gas law and describes how the partial pressures of permeate in the source fluid correlate with the change of permeate mass in the confined volume of the membrane : jn«„H-u.r „„

-^ permeate ' tofv,memb 1 ~~ j

permeate where Ap_permeate signifies the difference of partial pressures of permeate in the source fluid in front and after passing the mem^¬ brane, V_t0fv,membi represents the total volume of outer-fibre volume inside the membrane 1, Am_permeate is the total mass of permeate transferred from the source fluid into the sweep fluid, M_permeate is the molecular mass of the permeate, R is the universal gas constant, and T is the temperature of the source fluid (e.g.

temperature of blood inside the body) .

Using Henry's law the change of permeate 's concentration Acsource relates to Ap_permeate as:

^■source =

[10] with H_b(Permeate being the Henry's constant (Henry solubility de^¬ fined via concentration) for the sweep fluid (e.g. liquid Per- fluorcarbone, PFC) . Including the transport time of the sweep fluid between the membrane 1 and membrane 2, as well as includ^¬ ing the dimensions of the two membranes while assuming that

, one can finally express the mass rate of the perme^¬ ate taken from the source fluid m_permeate and released into the at^¬ mosphere as m_wash,_permeate:

Here the N_fib(membi is the number of fibres in the membrane 1,

A_t0fv,membi ίs the total cross-sectional area of the outer-fibre volume inside the membrane 1, Nfib,_memb2 is the number of fibres in the membrane 1, and A_tif_V,memb2 is the total cross-sectional area of the inner-fibre volume inside the membrane 2, with the assump- tion that source fluid flows outside and sweep fluid inside the fibers of membrane 1, while washing fluid flows outside and sweep fluid inside of membrane 2.

The equation [11] shows that the mass transfer rate of the per^¬ meate in the static case directly correlates to the concentra^¬ tion change of the permeate in the source fluid, and can be di^¬ rectly manipulated by changes in the membrane dimensions or the sweep flow.

This procedure also demonstrates that any of the three parame^¬ ters :

- permeate concentration change in the source fluid,

- permeate partial pressure change in the source fluid, and

- permeate mass transfer rate from the source fluid

can be used in the control loop as the reference value inter^¬ changeably, without the need for any modification in the control principle .

Alternative control objectives

An alternative control objective might be to minimise the con^¬ sumption of washing fluid (e.g. where one or more washing fluid sources must be carried in a mobile application) . In this case, the controller might again set the reference source flow to the predetermined constraint as above, set the reference sweep flow to a maximum value supported by the circulator pump 12 and circulation 6, and set the reference mass flow rate of the washing fluid 10 to a value that is just sufficient to remove of a mini^¬ mum amount of permeate from the sweep fluid to achieve the ref^¬ erence permeate exchange rate.

In optimising the time development of the system inputs to reach a desired steady-state as fast as possible, the controller will consider predetermined time constants of the different transfer functions for each of the secondary control loops 38, 39, 40 and the primary control loop 32. For instance, a temporary peak of the sweep flow rate can be useful to quickly react to changes of the reference permeate exchange rate.

Claims

Claims :

1. A method for controlling an exchange rate of a permeate to achieve a reference permeate exchange rate from a source fluid

(3) across a first membrane (2) and across a second membrane

(11) ,

wherein the first membrane (2) and the second membrane (11) are connected by a circulation (6) of a sweep fluid (5), wherein said circulation (6) comprises a circulator pump (12),

wherein the first membrane (2) is arranged in a cross-flow configuration between a flow of the source fluid (3) and the circulation (6) of the sweep fluid (5), and

wherein the second membrane (11) is arranged in a cross-flow configuration between the circulation (6) of the sweep fluid (5) and a flow of a washing fluid (10), the method comprising the steps of:

- determining a source flow rate of the source fluid (3) past the first membrane (2);

- determining a sweep flow rate of the sweep fluid (5) with^¬ in the circulation (6);

- determining a removed amount of permeate contained in the washing fluid (10) downstream the second membrane (11);

- removing the permeate from the sweep fluid (5) at the sec^¬ ond membrane (11) ; and

- controlling the circulator pump (12) according to an exchange model, which estimates the permeate exchange rate across the first membrane (2) depending on the determined source flow rate, sweep flow rate and removed amount of permeate, to achieve the reference permeate exchange rate.

2. A method according to claim 1, characterized in that the method comprises controlling a source pump (7), which is configured to move the source fluid (3) along the first membrane (2), according to the exchange model to achieve the reference perme^¬ ate exchange rate.

3. A method according to claim 2, characterized in that the controlling of the source pump (7) respects a constraint defin^¬ ing a required pump power of the source pump (7) .

4. A method according to one of claims 1 to 3, characterized in that the method comprises controlling the flow rate of the wash^¬ ing fluid (10) depending on the determined sweep flow rate and removed amount of permeate, to remove essentially all permeate from the sweep fluid (5) at the second membrane (11) .

5. A method according to claim 4, characterized by controlling the flow rate of the washing fluid (10) with a single or multi^¬ ple mass flow regulator (s) .

6. A method according to one of claims 1 to 5, characterized in that the permeate is carbon dioxide.

7. A method according to claim 6, characterized in that the re^¬ moved amount of permeate contained in the washing fluid (10) is determined using a gas analyser (30) arranged downstream the second membrane (11) .

8. A method according to one of claims 1 to 6, characterized in that the first membrane (2) is a hollow fibre membrane.

9. A system for controlling an exchange rate of a permeate to achieve a reference permeate exchange rate, the system compris^¬ ing :

a first membrane (2),

a second membrane (11),

a circulation (6) connecting the first membrane (2) and the second membrane (11) and comprising a circulator pump (12),

a source flow sensor (16, 17) configured to determine a source flow rate of a source fluid (3) past the first membrane (11) ,

a sweep flow sensor (18, 19) configured to determine a sweep flow rate of a sweep fluid (5) within the circulation (6),

a permeate content sensor configured to determine a removed amount of permeate contained in a washing fluid (10) downstream the second membrane (11), and

a controller (9) connected to the circulator pump (12), the source flow sensor (16, 17), the sweep flow sensor (18, 19) and the permeate sensor and configured to control the circulator pump (12) according to an exchange model, which estimates the permeate exchange rate across the first membrane (2) depending on the source flow rate, sweep flow rate and removed amount of permeate, to achieve the reference permeate exchange rate.

10. A system according to claim 9, characterized in that the system comprises a source pump (7), which is configured to move a source fluid past the first membrane (2), wherein the control^¬ ler (9) is connected to the source pump (7) and configured to control the source pump (7) according to the exchange model to achieve the reference permeate exchange rate.

11. A system according to claim 10, characterized in that the controller (9) is configured to respect a constraint defining a required pump power of the source pump (7) .

12. A system according to one of claims 9 to 11, characterized in that the system comprises a wash flow control device (13) for controlling the flow rate of a washing fluid past the second membrane (11), wherein the controller (9) is connected to the wash flow control device (13) and configured to control the flow rate of the washing fluid depending on the sweep flow rate and removed amount of permeate, to remove essentially all permeate from the sweep fluid at the second membrane (11) .

13. A system according to one of claims 9 to 12, characterized in that the permeate content sensor is a gas analyser (30), which is arranged to analyse a washing fluid downstream the sec^¬ ond membrane (11) .

14. A system according to one of claims 9 to 13, characterized in that the first membrane (2) is a hollow fibre membrane.

15. A system according to one of claims 9 to 14, characterized in that the first membrane (2) is part of an intravascular mem^¬ brane catheter (1) and the second membrane (11) is part of an extracorporeal gas exchange unit (47) .