Microfluidic device and method for collecting droplets

Abstract

The invention relates to a microfluidic device, comprising a fluidic main line (10) having a flow direction (81), and further comprising a plurality of catching structures (41) for droplets (70), which are arranged in the main line (10). The catching structures (41) are each designed as a recess (42) in a wall of the main line (10), wherein the recess (42) has a fluidic secondary line (43, 43a-b) which opens into the main line (10) downstream of the recess (42). In a method for collecting droplets (70) in the microfluidic device, droplets (70) are produced at the intersection point, the droplets (70) are introduced into the catching structures (41), and the droplets (70) are collected in the recesses (42) of the catching structures (41).

Description

[0001] R. 412692

[0002] - 1 -

[0003] Description

[0004] title

[0005] Microfluidic device and method for collecting droplets

[0006] The present invention relates to a microfluidic device. It also relates to a method for collecting droplets in the microfluidic device.

[0007] State of the art

[0008] 3D cell culture is used, for example, in drug testing, personalized medicine, basic research, organoid culture from stem cells, and cancer research.

[0009] One method for producing tumor organoids involves taking individual cells or tissue fragments from a cancer patient's primary tumor and culturing them. During this process, these cells or tissue fragments differentiate and multiply, eventually self-organizing into three-dimensional structures. The resulting tumor organoids are therefore 3D cell agglomerates that exhibit a composition and architecture similar to the patient's primary tumor tissue.

[0010] Depending on the application and time horizon, the cells are supported in their 3D growth with different scaffolds to enable the formation of the most informative cell models possible. One approach is the cultivation of cells in droplets. These are small, spatially well-defined, usually spherical structures. They are generally located in a liquid from which they are separated by a phase boundary or shell. Such droplets can form a closed microenvironment for a single cell or a cell cluster of several cells. This environment can be replicated in a similar form for many cells using such droplets. R. 412692

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[0012] EP 3 711 855 A1 describes a method for the production and dispensing of cells enclosed in droplets within a microfluidic chip. The chip has an oil reservoir and an inlet for an aqueous cell sample. This sample is first passed through a straight channel and then through a coiled delay channel. The cells can initially be collected in a collection container before being examined in a detection cell and then brought into contact with the oil from the oil reservoir near an outlet of the device, resulting in the formation of droplets.

[0013] Disclosure of the invention

[0014] In one aspect, a microfluidic device is provided which has a fluidic main line with a flow direction. The microfluidic device specifically comprises a pneumatic layer, a fluidic layer, and a membrane, which is partially arranged between the pneumatic and fluidic layers. A fluidic layer is defined as a layer that has chambers and channels and is configured to transport a sample and react it with reagents. The main line, for example, runs within this fluidic layer. A pneumatic layer is defined as a layer that has channels which adjoin the membrane at one end and can be connected to a pneumatic manifold at the other end.By generating overpressure in the channels of the pneumatic layer, the membrane can be deflected into the fluidic layer, and conversely, by generating underpressure in the channels of the pneumatic layer, the membrane can be deflected into the pneumatic layer. This allows for the manipulation of fluid flows within the fluidic layer. The fluidic and pneumatic layers are preferably made of a plastic, which simplifies their fabrication. A particularly preferred plastic is transparent polycarbonate (PC). The membrane is preferably made of thermoplastic polyurethane (TPU). Due to its high elasticity, this material is particularly well-suited for the membrane. Furthermore, its thermoplasticity allows it to be laser-welded to polycarbonate. R. 412692.

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[0016] According to the invention, the device has at least one trapping structure for droplets. This structure is arranged in the main line. The at least one trapping structure is designed as a recess in a wall of the main line. The recess has at least one fluidic branch line that opens into the main line downstream of the recess.

[0017] The invention is described below using a plurality of trapping structures for droplets; however, it can also be meant that only one trapping structure for droplets is present.

[0018] This device enables the production and collection of droplets in a microfluidic environment. Depending on the dimensions of the trapping structures, each structure can hold one or more droplets. This allows for the cultivation of biological cells contained within the droplets in the trapping structures. The fluidic bypass channels allow the fluid flow in the main channel to be manipulated so that droplets transported along the main channel are drawn into the recesses. Furthermore, the bypass channels allow the droplets to be flushed out of the trapping structures by passing a fluid through the main channel against the flow direction.

[0019] In particular, the microfluidic device is designed as a disposable cartridge intended for use in a microfluidic analysis system.

[0020] To ensure reliable transport of the droplets in the main line, it preferably has a width in the range of 200 pm to 1,000 pm. Furthermore, it is preferred that this width is at most twice the diameter of the droplets for whose generation the intersection point is designed. The secondary lines each preferably have a width in the range of 50 pm to 800 pm. This ensures, on the one hand, that a sufficiently strong flow can be generated in the depressions to draw in droplets or to remove them from the R. 412692

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[0022] To flush out depressions, and on the other hand, to prevent droplets from passing through the secondary lines.

[0023] It is preferred that the main conduit has several sections running parallel to each other along a first axis. Within each of these sections, several trapping structures are arranged such that branch lines of several sections lie on a common second axis, which is orthogonal to the first axis. Thus, when a fluid flows through the main conduit along the flow direction, it flows along the first axis within the sections and deviates from this direction only in an arc-shaped transition from one section to the next. Simultaneously, several further flow paths are formed, each running along a second axis.In this process, the fluid flows through the auxiliary channels, with a portion of the fluid deviating from the main flow direction along the first axis, flowing into the recess of a trapping structure in one section, and exiting through the auxiliary channel of that recess in the fluidically subsequent section of the main channel. The device can, in particular, have at least 30 trapping structures. Preferably, it has at least ten sections, each containing at least ten trapping structures. In this way, at least 100 droplets can be collected in the microfluidic device in a space-saving manner.

[0024] The recesses have a semicircular cross-section. If each recess is to accommodate a droplet, the diameter of the semicircle is preferably twice the diameter of the droplets for whose production the intersection point is designed.

[0025] A junction point in the main line is configured to generate droplets. This junction point can be configured as a T-junction, where a channel enters the main line laterally. Alternatively, the junction point can be configured as a focusing unit, where two channels entering the main line laterally are positioned opposite each other. Alternatively, the junction point can be configured as nested channel structures or co-flowing structures. A R. 412692 is located at the junction point.

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[0027] The cross-section of the main line is preferably reduced, at least in sections, compared to the cross-section of the main line upstream and downstream of the crossing point, in order to promote droplet formation. The trapping structures for droplets are arranged downstream of the crossing point. The main line preferably terminates downstream of the trapping structures at a branch point located between the crossing point and the trapping structures, and then flows back into itself. A fluid that has passed through the trapping structures can thus be reintroduced upstream of the trapping structures into the main line. It can therefore be passed through the trapping structures multiple times in a cycle, so that droplets which were not captured in one of the trapping structures during the first passage are transported by the fluid back to the trapping structures to be fixed there during one of the subsequent passages.

[0028] Furthermore, it is preferred that an outlet line branches off from the main line. This outlet line leads into an outlet section. In the outlet section, droplets that are to be sorted out after their generation at the intersection point, but before being introduced into the trapping structures, can be diverted out of the microfluidic device. The outlet section can also be used to divert droplets that are released from the trapping structures after cultivation is complete.

[0029] To enable the release of droplets from the trapping structures, it is preferred that a flushing line connects to the main line downstream of the trapping structures. This flushing line is connected to a flushing fluid reservoir. The flushing fluid can be introduced into the trapping structures against the flow direction of the main line. By reversing the flow direction, some of the flushing fluid flowing through the main line is forced into the secondary lines, thereby flushing out any droplets trapped in the depressions.

[0030] To enable the generation of droplets at the crossing point, it is preferred that the main line upstream of the crossing point has a R. 412692

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[0032] The microfluidic device has an inlet for a first fluid for droplet generation. At the intersection point, it preferably has two opposing inlets for a second fluid for droplet generation. The first fluid is, in particular, a mixture of a cell suspension with a matrix solution. In one embodiment of the microfluidic device, this mixture is introduced into the inlet for the first fluid from outside the microfluidic device. In another preferred embodiment, the inlet is a mixing point where the cell suspension supplied from the first reservoir and the matrix supplied from the second reservoir are mixed together. The second fluid is, in particular, a hydrophobic liquid. The two inlets for the second fluid are preferably connected to a common reservoir for the second fluid, from which both inlets are supplied.By having a stream of the first fluid meet two converging streams of the second fluid at the intersection point, droplets can be advantageously created.

[0033] Upstream of the inlet for the first fluid, the main conduit preferably has a delay section in which the main conduit is particularly meandering. Decelerating the fluid flow in the delay section facilitates mixing of the cell suspension with the matrix solution before they reach the intersection point.

[0034] For some matrix materials, it is advantageous if droplet generation takes place below room temperature, while droplet curing occurs above room temperature. Therefore, it is preferred that a cooling element is arranged at the intersection point and a heating element is arranged downstream of the intersection point.

[0035] Between the intersection point and the trapping structures, in particular between the heating element and the trapping structures, at least one sensor is arranged to enable the examination of the droplets before they are introduced into the trapping structures. Droplets that do not meet at least one predefined criterion can be diverted to the outlet area of ​​the microfluidic device. For this purpose, the main line is provided with at least one deflector to remove droplets from the R. 412692

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[0037] to deflect the flow direction towards the outlet area. The deflection device is specifically selected from the group consisting of a dielectrophoresis field generator (DEP), an ultrasonic transducer, a pressure pulse generator, and a fluidic sorter.

[0038] Another heating element is preferably arranged on the trapping structures to allow the droplets to be tempered during their cultivation in the trapping structures.

[0039] In another aspect, a method for collecting droplets in the microfluidic device is provided. In this method, droplets are first generated at the intersection point. The generated droplets are then introduced into the trapping structures. Finally, the droplets are collected in the recesses of the trapping structures.

[0040] To generate the droplets, two fluids are first provided and combined at the intersection point. The first fluid comprises a matrix solution and biological cells and / or cell clusters suspended within the matrix solution. The matrix solution is specifically selected from the group of hydrogels and can be of synthetic or natural origin, consisting of a basement membrane-like matrix, cellulose, collagen, and polymers. If cell clusters are used instead of individual cells, each cell cluster preferably contains a maximum of 25 cells, so that pronounced organoid growth occurs only in a later process step. The second fluid is specifically a hydrophobic liquid, such as an oil. Preferably, the second fluid also contains a surfactant to promote droplet formation with the first fluid.

[0041] The intersection point is preferably dimensioned such that the generated droplets have a diameter in the range of 100 pm to 500 pm. This ensures, on the one hand, that the droplet provides sufficient space for organoid growth and, on the other hand, that it can be securely held within the capture structures. Smaller droplets can also be used, but this must then be taken into account in the dimensioning of the channel structures. The design of an R. 412692

[0042] - 8 - The microfluidic cartridge is adapted for a corresponding, narrow size range of the droplets.

[0043] It is preferred that, after the droplets are generated and before being introduced into the trapping structures, they undergo a curing treatment. This curing treatment is carried out particularly in the delay zone of the main conduit. It can be achieved, for example, by heating the droplets or by irradiating them to trigger photopolymerization.

[0044] After any necessary curing treatment and before introducing the droplets into the trapping structures, the droplets are preferably analyzed. Droplets that do not meet at least one predefined criterion are directed to an outlet area of ​​the microfluidic device and thus disposed of. The criterion can, for example, be that the droplets contain a predefined minimum and maximum number of cells and / or cell clusters. The analysis can be performed, in particular, using an optical sensor.

[0045] After the droplets have been collected in the depressions, they can be stored there in an organized manner. This preferably allows for the cultivation of organoids within the droplets while they are stored in the depressions. During cultivation, at least one cultivation fluid is preferably supplied to the droplets via the main line. This fluid can, in particular, contain glucose as a nutrient. To monitor the cultivation, the cultivation fluid exiting the trapping structures can be analyzed for parameters such as its oxygen content, carbon dioxide content, pH value, glucose content, and / or lactate content. Further investigations of the droplets can be carried out, in particular, by optical, fluorescence, and / or luminescence-based analyses within the trapping structures. For this purpose, these structures are preferably transparent.Image analysis is preferably performed using AI.

[0046] Preferably, at least one analysis fluid is fed to the droplets via the main line during or after cultivation. (R. 412692)

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[0048] The analytical fluid can consist of dyes, active ingredients, or reagents. The effect of the analytical fluid on the organoids can be analyzed optically or by sensory means.

[0049] Further cultivation of the organoids can be passive, controlled, or optionally regulated. In the passive case, the microfluidic device containing the droplets would be stored under suitable conditions that promote growth. These conditions include, in particular, predetermined values ​​for temperature, humidity, and the composition of the gas atmosphere. In the controlled case, the nutrient and gas supply would be ensured by suitable pumping mechanisms. This may involve exchanging or circulating the cultivation fluid and, if necessary, introducing at least one gas into the cultivation fluid. In particular, pre-planned variations of the conditions may be provided. In the regulated case, one or more of the aforementioned parameters in the droplets or the supplying medium would be monitored, and further cultivation would then be adjusted accordingly.

[0050] Once the specified cultivation period has been reached or an endpoint of cultivation has been identified through monitoring, the process can proceed in various ways.

[0051] Once cultivation is complete, the droplets are preferably removed from the wells by passing at least one rinsing fluid through the main line against the flow direction. This rinsing fluid can, in particular, contain at least one substance designed to dissolve the droplet shell and thereby release the organoids contained therein into the rinsing fluid.

[0052] The droplets or released organoids are then preferably flushed with the rinsing fluid into an outlet area of ​​the microfluidic device for further analysis. For these analyses, they can, for example, be stained. R. 412692

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[0054] In one embodiment of the method, the organoids are extracted from the droplets and subsequently split into cells and / or cell clusters. This splitting can be performed enzymatically or mechanically. The cells and / or cell clusters are then reintroduced into the device to be introduced into new droplets at the intersection point. For this purpose, the device can be designed to include additional elements beyond the outlet area to automate the splitting of the organoids and their reintroduction upstream of the intersection point.

[0055] Brief description of the drawings

[0056] Exemplary embodiments of the invention are shown in the drawings and are explained in more detail in the following description.

[0057] Figure 1 schematically shows a microfluidic device according to an embodiment of the invention.

[0058] Figure 2 shows a flowchart of a method according to an embodiment of the invention.

[0059] Figure 3 shows an isometric representation of several capture structures of a device according to an embodiment of the invention.

[0060] Figure 4 shows a cutaway isometric view of a trapping structure, illustrating how droplets can be trapped in a trapping structure in an embodiment of the method according to the invention.

[0061] Figure 5 shows a cutaway isometric view of two trapping structures, illustrating how droplets can be released from the trapping structures in an embodiment of the inventive method.

[0062] Exemplary embodiment of the invention R. 412692

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[0064] Figure 1 shows components of a microfluidic device according to an embodiment of the invention, arranged in a fluidic layer of a device designed as a microfluidic cartridge. The device has a main line 10 with a diameter of, for example, 600 pm. A mixing point serves as an inlet 11 for a first fluid. For this purpose, it is connected to a first reservoir 21 for a cell suspension. A second reservoir 22, which contains a hydrogel, is connected to the inlet 11 via two lines 31a and 31b. At the inlet 11, the cell suspension is therefore exposed to the second fluid from two sides. The cell suspension thus obtained then flows through a delay structure 12, in which the main line 10 meanders to mix the cells of the hydrogel even more thoroughly. A further reservoir 23 contains, for example, a mixture of an oil and a surfactant.This fluid is guided through two inlets 32a, 32b to two opposing positions at a crossing point 13 of the main line, where it merges with the cell suspension. The two inlets 32a, 32b have the same length and essentially the same fluidic resistance. The crossing point 13 is designed as a focusing element. At the crossing point 13, the main line 10 is constricted such that droplets with a diameter of, for example, 300 pm are formed from the cell suspension and the oil. The main line 10 then runs through a trapping structure system 40, which has a plurality of trapping structures 41 with branch lines 43. At the outlet of the trapping structure system 40, the main line 10 is connected at a first branch point 14 to a flushing line 33, which leads into a flushing fluid reservoir 24. At the second junction point 15, an outlet pipe 34 branches off from it, which leads into an outlet area 25.The main line 10 ends at a third branch point 16, where it flows back into itself upstream of the trap structure system 40.

[0065] In addition to the elements shown, the microfluidic device includes valves (not shown) and microfluidic pump chambers to transport and direct fluids in the piping system of the fluidic layer.

[0066] The sequence of an embodiment of the method according to the invention is shown in Figure 2. First, a hydrogel solution 51 is introduced into the R. 412692

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[0068] Reservoir 22 and an input 52 of cells or cell clusters into the cell reservoir 21. This is followed by mixing 53 of these starting materials in the inlet 11 and the delay structure 12. The oil 54 is then fed into reservoir 23. Droplets 55 are generated at the junction 13 by combining the cell suspension and the oil there. The droplets are then stabilized 56 downstream of the junction 13 in the main line 10. During this process, the droplets can be tempered or exposed to light by components of the microfluidic device not shown. Upstream of the third branch point 16, the droplets are analyzed 57 by means of a sensor not shown. Droplets that do not meet the quality criteria of the analysis are discharged from the microfluidic device 58.For this purpose, they are diverted at the third branch point 16 towards the second branch point 15 through the outlet pipe 34 into the outlet area 25. It is also possible at the beginning of droplet generation to divert all droplets into the outlet area 25 for a predefined period until droplet generation has stabilized. The remaining droplets are introduced into the trapping structure system 40 59.

[0069] While the trapping structure system 40 in Figure 1 is shown in a simplified form, Figure 3 shows a complex trapping structure system 40 for receiving one hundred droplets. The main conduit 10 runs in ten parallel sections 17 along an x-axis. The sections 17 are each connected to one another by an arc-shaped portion of the main conduit 10. In each section 17, ten trapping structures 41 are arranged one behind the other. Ten trapping structures 41 from different sections 17 are also arranged one above the other along the y-axis.

[0070] Figure 4 shows how a droplet 70 is trapped in a trapping structure 41. The fluid flowing along a flow direction 81 through the trapping structure system 40 carries the droplets 70 along with it. Each trapping structure 41 is designed as a recess 42 in the wall of the main conduit 10. This recess 42 has a semicircular cross-section with a diameter of, for example, 600 pm. At its deepest point, the recess 42 has a secondary conduit 43a with a width of, for example, 65 pm. In Figure 4, R. 412692

[0071] - 13 - shows that in the area of ​​the trap structure 41, a secondary channel 43a connects the depression 42 with the downstream section 17 of the trap structure system, and simultaneously, a secondary channel 43b opposite this connects the main channel 10 with a depression 42 in the upstream section 17 of the trap structure system. Part of the fluid does not flow along the flow direction 81, but along a secondary flow direction 82 through the secondary channel 43a. This draws one of the droplets 70 into the depression 42 along a suction direction 83.

[0072] The trapping structure system 40 enables the orderly storage 61 of, for example, one droplet in each of the trapping structures 41. There, the cells or cell clusters within the droplets 70 are then cultivated 62 to form organoids. For this purpose, a nutrient solution is introduced into the main line 10 through the inlet 11 and circulated between the trapping structures, the first branch point 14, the second branch point 15, and the third branch point 16. The cultivation process 63 can be monitored by chemical analysis of the nutrient solution leaving the trapping structure system 40 and by optical inspection of the trapping structure system 40. Used nutrient solution can be directed to the outlet area 25 and replaced with fresh nutrient solution.

[0073] When monitoring 63 indicates that cultivation is complete, the droplets are removed from the trapping structures 41. For this purpose, a rinsing fluid is introduced from the rinsing fluid reservoir 24 through the rinsing line 33 and past the first branch point 14, against the flow direction 61, into the trapping structure system 40. Figure 5 illustrates, using two trapping structures 41 as examples, that the rinsing fluid not only flows in a direction 84 opposite to the flow direction 81, but that the flow direction is also reversed by the branch lines 43a and 43b. The rinsing fluid thus flows through these branches along a flow direction 85 and pushes the droplets 70 along a direction 86 into the rinsing fluid flow in the main line 10. The droplets 70 are then directed to the third branch point 16.Using the same means provided there to direct droplets 70 into the outlet area 25 in process step 58 before they reach the trap structure system 40, the R. 412692.

[0074] - 14 - Droplets 70 released from the capture structure system 40 are now also directed into the outlet area 25. Some of the droplets 70 can now be subjected to tests 64. This can also include staining 65 of the organoids in the droplets 70. In particular, staining to determine the viability of the organoids, i.e., the number of dead and living cells or the organoids' ability to divide, can still take place in the droplets to inform decisions regarding their further use. Another portion of the droplets 70 is chemically digested or dissolved by the addition of enzymes, or via a temperature gradient, to release the organoids from the droplets 70 66. Some of the released organoids are subjected to further tests 67 and can also be immunohistochemically stained 68 to visualize specific biomarkers. Other organoids are split 69 to obtain cells or cell clusters again.These can be reintroduced into the cell reservoir 21. Elements of the microfluidic device (not shown) can be arranged in a fluidic path between the outlet area 25 and the cell reservoir 21 to automate the steps of extraction 66, splitting 69, and reintroduction 52 into the cell reservoir 21 within the microfluidic device. For splitting the organoids, structures and methods such as those described in DE 10 2021 214 276A1 can be used, for example.

Claims

R. 412692 - 15 - Claims 1. Microfluidic device comprising a main conduit (10) with a flow direction (81), wherein at least one trapping structure (41) for droplets (70) is arranged in the main conduit (10), wherein the at least one trapping structure (41) is designed as a recess (42) in a wall of the main conduit (10) and wherein the recess (42) has at least one fluidic secondary conduit (43, 43a-b) which opens into the main conduit (10) downstream of the recess (42).

2. Microfluidic device according to claim 1, wherein the main conduit (10) has a width in the range of 200 pm to 1,000 pm and the secondary conduits (43, 43a-b) each have a width in the range of 50 pm to 80 pm.

3. Microfluidic device according to claim 1 or 2, wherein the main conduit (10) has several sections (17) running parallel along a first axis (x), wherein in each of these sections (17) several trap structures (41) are arranged such that secondary conduits (43, 43a-b) of the trap structures (41) of several sections (17) lie on a common second axis (y) which runs orthogonally to the first axis (x).

4. Microfluidic device according to one of claims 1 to 3, wherein the fluidic main line (10) has a crossing point (13) which is configured to generate droplets (70), wherein the at least one trapping structure (41) for droplets is arranged downstream of the crossing point (13).

5. Microfluidic device according to one of claims 1-4, wherein the main line (10) downstream of the at least one trapping structure (41) at a third branching point (16) which lies between the intersection point (13) and the at least one trapping structure (41) flows back into itself, so that a circuit is formed. R. 412692 - 16 - 6. Microfluidic device according to one of claims 1 to 5, wherein an outlet line (34) branching off from the main line (10) opens into an outlet area (25).

7. Microfluidic device according to one of claims 1 to 6, wherein downstream of the at least one trapping structure (41) a flushing line (33) which is connected to a flushing fluid reservoir (24) opens into the main line (10).

8. Microfluidic device according to one of claims 1 to 7, wherein the main line (10) has an inlet (11) for a first fluid for droplet generation upstream of the crossing point (13) and has two opposing inlets (32a-b) for a second fluid for droplet generation at the crossing point (13).

9. Method for collecting droplets (70) in a microfluidic device according to any one of claims 1 to 8, comprising the following steps: In particular, generating (55) droplets (70) at the intersection point (13), introducing (59) the droplets (70) into the at least one trapping structure (41), and collecting (61) the droplets (70) in the depression (42) of the at least one trapping structure (41).

10. Method according to claim 9, wherein prior to introducing (59) the droplets (70) into the at least one trapping structure (41) an analysis (57) of the droplets (70) is carried out and droplets (70) that do not meet at least one predetermined criterion are directed (58) into an outlet area (25) of the microfluidic device.

11. Method according to claim 9 or 10, wherein after collecting (61) the droplets (70) an cultivation (62) of organoids takes place in the droplets (70) while these are stored in the depression (42) of the at least one trapping structure (41). R. 412692 - 17 - 12. Method according to claim 11, wherein during cultivation (62) at least one cultivation liquid is supplied to the droplets (70) through the main line (10) and / or wherein during or after cultivation (62) at least one analysis liquid is supplied to the droplets (70) through the main line (10).

13. Method according to one of claims 11 or 12, wherein after cultivation (70) the droplets (70) are removed from the depression (42) of the at least one trapping structure (41) by passing at least one rinsing liquid through the main line (10) against the flow direction (81).

14. Method according to claim 13, wherein the droplets (70) are flushed with the rinsing fluid into an outlet area (25) of the microfluidic device.

15. Method according to claim 14, wherein the organoids are extracted from the droplets (70) and subsequently split into cells and / or cell clusters (69), wherein the cells and / or cell clusters are subsequently reintroduced into the device and introduced into new droplets (70) at the intersection point (13).

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