DEVICE AND METHOD FOR MICROSCALE CHEMICAL REACTIONS
20200179927 ยท 2020-06-11
Assignee
Inventors
Cpc classification
B01J19/0093
PERFORMING OPERATIONS; TRANSPORTING
B01L3/502707
PERFORMING OPERATIONS; TRANSPORTING
B01J2219/00495
PERFORMING OPERATIONS; TRANSPORTING
B01L2300/165
PERFORMING OPERATIONS; TRANSPORTING
B01J2219/00621
PERFORMING OPERATIONS; TRANSPORTING
B01L2200/16
PERFORMING OPERATIONS; TRANSPORTING
B01L7/52
PERFORMING OPERATIONS; TRANSPORTING
B01L2300/12
PERFORMING OPERATIONS; TRANSPORTING
B01L3/502784
PERFORMING OPERATIONS; TRANSPORTING
B01L2300/089
PERFORMING OPERATIONS; TRANSPORTING
B01F33/30351
PERFORMING OPERATIONS; TRANSPORTING
B01L2300/166
PERFORMING OPERATIONS; TRANSPORTING
B01J2219/00619
PERFORMING OPERATIONS; TRANSPORTING
B01L2300/1805
PERFORMING OPERATIONS; TRANSPORTING
B01L3/502715
PERFORMING OPERATIONS; TRANSPORTING
B01F33/3021
PERFORMING OPERATIONS; TRANSPORTING
International classification
B01L3/00
PERFORMING OPERATIONS; TRANSPORTING
B01J19/00
PERFORMING OPERATIONS; TRANSPORTING
Abstract
A microfluidic synthesis platform includes a microfluidic chip holder that has a computer controlled heating element and cooling element therein. A microfluidic chip is mountable in the microfluidic chip holder. The microfluidic chip is formed by a hydrophobic substrate having patterned thereon a hydrophilic reaction site and a plurality of hydrophilic channels or pathways extending outward from the hydrophilic reaction site and terminating at respective loading sites on the substrate, wherein the hydrophilic channels or pathways are tapered with an increasing width in an inward direction toward the hydrophilic reaction site. A fixture is provided for holding a plurality of non-contact reagent dispensing devices above the microfluidic chip at locations corresponding to the loading sites of the plurality of hydrophilic channels or pathways, the fixture further holding a moveable collection tube disposed above the hydrophilic reaction site of the microfluidic chip for removing droplets containing reaction products.
Claims
1. A passive microfluidic device comprising: a hydrophobic substrate having patterned thereon a hydrophilic reaction site and a plurality of hydrophilic channels or pathways extending outward from the hydrophilic reaction site and terminating at respective loading sites on the substrate, wherein the hydrophilic channels or pathways are tapered with an increasing width in an inward direction from the loading sites to the hydrophilic reaction site.
2. The passive microfluidic device of claim 1, wherein the plurality of hydrophilic channels or pathways have a taper angle of at least 4.
3. The passive microfluidic device of claim 1, further comprising a non-contact reagent dispensing device disposed above the substrate configured to dispense reagent onto the plurality of hydrophilic channels or pathways.
4. The passive microfluidic device of claim 3, wherein the non-contact reagent dispensing device comprises a separate dispenser for each of the plurality of hydrophilic channels or pathways.
5. The passive microfluidic device of claim 1, further comprising a heating and cooling system in thermal contact with the passive microfluidic device.
6. The passive microfluidic device of claim 1, wherein the substrate comprises one of silicon, glass, glassy carbon, metal, polymer-metal blend, or a polymer coated with a hydrophobic coating or layer.
7. The passive microfluidic device of claim 1, wherein the plurality of hydrophilic channels or pathways formed on the substrate are chemically inert with respect to radiochemical species.
8. The passive microfluidic device of claim 1, further comprising a moveable collection tube disposed above the hydrophilic reaction site and moveable between a first position above a droplet located on the hydrophilic reaction site and a second position in contact with the droplet, the collection tube being fluidically coupled to a collection vial or container.
9. A passive microfluidic device comprising: a hydrophobic substrate having patterned thereon a hydrophilic reaction site and one or more hydrophilic channels or pathways extending outward from the hydrophilic reaction site on the substrate, wherein the one or more hydrophilic channels or pathways are tapered along a length thereof and have a taper angle of at least 4.
10. A microfluidic synthesis platform comprising: a microfluidic chip holder comprising a computer-controlled heating element and cooling element; a microfluidic chip mountable in the microfluidic chip holder, the microfluidic chip comprising a hydrophobic substrate having patterned thereon a hydrophilic reaction site and a plurality of hydrophilic channels or pathways extending outward from the hydrophilic reaction site and terminating at respective loading sites on the substrate, wherein the hydrophilic channels or pathways are tapered with an increasing width in an inward direction from the loading sites to the hydrophilic reaction site; and a fixture holding a plurality of non-contact reagent dispensing devices disposed above the microfluidic chip at locations corresponding to the loading sites of the plurality of hydrophilic channels or pathways, the fixture further holding a moveable collection tube disposed above the hydrophilic reaction site of the microfluidic chip.
11. The microfluidic synthesis platform of claim 10, wherein the non-contact reagent dispensing devices comprise solenoid dispensers each coupled to a respective vials or containers containing different reagents.
12. The microfluidic synthesis platform of claim 11, wherein the vials or containers are coupled to a pressurized source of gas.
13. The microfluidic synthesis platform of claim 11, wherein one of the vials or containers contains a radioisotope or prosthetic group.
14. The microfluidic synthesis platform of claim 11, wherein one of the vials or containers contains a precursor solution.
15. A method of using the microfluidic synthesis platform of claim 10, comprising: loading one or more liquid droplets containing reactants onto one or more of the plurality of hydrophilic channels or pathways of the microfluidic chip via one or more of the non-contact reagent dispensing devices, whereby the liquid droplets spontaneously move to the hydrophilic reaction site; and reacting the reactants at the hydrophilic reaction site.
16. The method of claim 15, further comprising contacting the collection tube with a droplet containing a product generated by the reaction of the reactants at the hydrophilic reaction site and withdrawing the droplet from the surface of the microfluidic chip.
17. The method of claim 15, wherein the product is a radiochemical species.
18. The method of claim 15, further comprising heating at least one of the reactants with heating element.
19. The method of claim 18, wherein heating evaporates a droplet at the hydrophilic reaction site to leave a dried reagent.
20. The method of claim 19, further comprising loading a second droplet containing a reactant onto one of the hydrophilic channels or pathways and contacting the second droplet with the dried reagent.
21. A method of synthesizing [.sup.18F]fallypride using the microfluidic synthesis platform of claim 10 comprising: loading one or more droplets containing [.sup.18F]fluoride solution onto of the hydrophilic channels or pathways, wherein the one or more droplets containing [.sup.18F]fluoride solution automatically transports to the hydrophilic reaction site; heating the microfluidic chip with the heating element to evaporate the one or more droplets containing [.sup.18F]fluoride solution; loading one or more droplets containing fallypride precursor solution at another loading site, wherein the droplets containing fallypride precursor solution automatically transports to the hydrophilic reaction site; heating the microfluidic chip with the heating element to form [.sup.18F]fallypride; loading a plurality of droplets of a diluting solution at another loading site, wherein the droplets containing the dilution solution automatically transports to the hydrophilic reaction site containing the [.sup.18F]fallypride; and removing a droplet containing the [.sup.18F]fallypride from the microfluidic chip.
22. A method of synthesizing [.sup.18F]FDG using the microfluidic synthesis platform of claim 10 comprising: loading one or more droplets containing [.sup.18F]fluoride/K222/K.sub.2CO.sub.3 solution onto of the hydrophilic channels or pathways, wherein the one or more droplets containing [.sup.18F]fluoride/K222/K.sub.2CO.sub.3 solution automatically transports to the hydrophilic reaction site; heating the microfluidic chip with the heating element to evaporate the one or more droplets containing [.sup.18F]fluoride/K222/K.sub.2CO.sub.3 solution; loading a plurality of droplets containing mannose triflate solution at another loading site, wherein the droplets containing mannose triflate solution automatically transports to the hydrophilic reaction site; heating the microfluidic chip with the heating element; loading one or more droplets of sodium hydroxide solution at another loading site, wherein the one or more droplets containing sodium hydroxide solution automatically transports to the hydrophilic reaction site whereby a hydrolysis reaction takes place to generate [.sup.18F]FDG; loading a plurality of droplets of a diluting solution at another loading site, wherein the droplets containing the dilution solution automatically transports to the hydrophilic reaction site; and removing a droplet containing the [.sup.18F]FDG from the microfluidic chip.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
[0016]
[0017]
[0018]
[0019]
[0020]
[0021]
[0022]
[0023]
[0024]
[0025]
[0026]
[0027]
[0028]
DETAILED DESCRIPTION OF ILLUSTRATED EMBODIMENTS
[0029]
[0030] Each of the hydrophilic channels or pathways 18 are tapered with an increasing width as one proceeds in an inward direction to the hydrophilic reaction or collection site 16. The hydrophilicity of the exposed silicon features (e.g., reaction or collection site 16 and channels or pathways 18) may be enhanced by exposing the same to a Piranha cleaning solution as explained herein during the manufacturing process. In some embodiments, the hydrophilic reaction or collection site 16 and the hydrophilic channels or pathways 18 may be rendered or made superhydrophilic while the hydrophobic layer 14 may be superhydrophobic.
[0031] In one embodiment, the central hydrophilic reaction or collection site 16 has a diameter of around 2.0-3.0 mm. As seen in
[0032]
[0033] With reference to
[0034] In some embodiments, the surface of the passive microfluidic chip 10 may be open or exposed to the external environment (i.e., there is no top) as is illustrated in the cross-sectional view of
[0035] To fabricate the chip as seen in
TABLE-US-00001 TABLE 1 Treatment Contact angle () (n = 3) Initial Si wafer 41 4 Hydrophobic region before patterning 122 2 Hydrophilic region (after acetone wash) 57 10 Hydrophilic region (after Piranha clean) 7 3
[0036] For automated droplet reactions, a custom-built temperature controlled synthesis platform 60 was used to control the dispensing of reagents and the collection of the final product.
[0037] The chip holder 62 was made as a plastic frame above the Peltier cooling device 66 (and bolted to the heatsink 68 via bolt 63) helped keep the heater 64 in place while also providing two flat vertical edges E for rapidly positioning one corner of the microfluidic chip 10. The signal from a K-type thermocouple embedded in the heater 64 was amplified through a K-type thermocouple amplifier 65 (
[0038] With reference to
[0039] Reagent stock solutions can be pipetted directly into the vial 78. For precursor solution and [.sup.18F]fluoride solution, the smaller volume (30-50 L) was loaded into a 250 l vial insert (5181-1270, Agilent Technologies, Santa Clarita, Calif., USA) installed into the V-vial. The outlet of each dispenser 76 was fitted with a nozzle (ID 0.005, INZA4650935K, Lee Company), which is recommended for generation of droplets with volume in the range of 100s of nL to several L. With reference to
[0040] While the above describes the [.sup.18F]fluoride solution being loaded into a vial or other container that is connected to the dispenser 76 it should be appreciated that the [.sup.18F]fluoride solution may also come directly from the cyclotron, a fluoride dispenser, a fluoride concentrator, or any other source. In such configurations a vial may not be needed for fluoride loading as the [.sup.18F]fluoride solution may come from tubing, nozzle, or other dispenser.
[0041] A fixture 90 was built to hold six (6) dispensers 76 with nozzles 2 mm above the six (6) loading sites of the microfluidic chip 10 (only one such dispenser 76 is illustrated in
[0042] A liquid collection subsystem was implemented in the microfluidic synthesis platform 60 to transfer the final crude reaction product droplet 100 from the microfluidic chip 10 to the collection vial. As seen in
Example: Radiosynthesis of [.SUP.18.F]Fallypride
[0043] Prototype passive microfluidic chips 10 were first used to test the feasibility of multi-step radiochemical reactions. In a first example, the synthesis of [.sup.18F]fallypride, a tracer for brain imaging used in PET and related to neuropsychiatric conditions and aging, was performed on a passive microfluidic chip 10 that was loaded manually. In this first experiment, the prototype passive microfluidic chip 10 included a single hydrophilic reaction or collection site 16 and a single hydrophilic channel or pathway 18 (i.e., one track chip). As explained below, an additional manual experiment was carried out on a passive microfluidic chip 10 that included a plurality of hydrophilic channels or pathways 18. The synthesis scheme of [.sup.18F]fallypride is seen in
[0044] Performance was assessed via measurements of radioactivity (via dose calibrator) at the beginning and ending of each step. Fluorination efficiency of the extracted product was measured via radio thin layer chromatography (radio-TLC, Minigita Star detector, BakerFlex IB-F silica gel plates, mobile phase 60% MeCN in 25 mM ammonium formate aqueous solution with 1% TEA). Crude radiochemical yield (crude RCY) is fluorination efficiency multiplied by extracted radioactivity, divided by starting radioactivity. Distribution of radioactivity on the passive chip after each step was assessed via Cerenkov imaging.
[0045] [.sup.18F]fallypride synthesis on the prototype (one track chip) passive microfluidic chip exhibited 892% fluorination efficiency (n=3) and 603% crude RCY (n=3), which are comparable to the performance on an EWOD chip (crude RCY, 847%, n=6). Activity loss at each step was calculated for future protocol optimization, all details of performance were summarized in Table 2 below.
TABLE-US-00002 TABLE 2 Parameter Value (N = 3) Starting activity (mCi) 0.1~0.2 Evaporation loss (%) 3 1 Fluorination loss (%) 18 0 Extraction loss (%) 11 4 Fluorination efficiency (%) 89 2 Crude product yield (%) 60 3
[0046] The distribution of radioactivity at various stages verified that majority of activity was moved to the reaction site, and minimal residual radioactivity was left in the reaction site after extraction.
[0047] [.sup.18F]fallypride was also synthesized without pipetting using the automated microfluidic synthesis platform 60 illustrated in
[0048] The performance of [.sup.18F]fallypride synthesis for both manual synthesis and automated synthesis is summarized in Table 3 below.
TABLE-US-00003 TABLE 3 Parameter Manual synthesis Automated synthesis Fluorination efficiency (%) 74 8 76 4 Radioactivity recovery (%) 79 4 84 4 Collection efficiency (%) 90 4 Not measured Synthesis time (min) 25 3 20 1 Crude RCY (%) 59 9 64 6 Isolated RCY (%) NA 46 4
[0049] With manual operations, the fluorination efficiency was 748% (n=4), collection efficiency was 904% (n=4), and the crude RCY was 599% (n=4). Analysis of radioactivity measurements during the synthesis on passive chips showed negligible losses (31%, n=4, relative to the starting radioactivity) during drying of [.sup.18F]fluoride, but slightly higher losses of 152% (n=4) during fluorination and 94% (n=4) residual activity on chip and pipette tips after collection. Note that the negative evaporation loss is likely due to measurement error in the dose calibrator. The crude RCY was slightly lower than previously reported for the droplet-based synthesis using EWOD chips, i.e. 847% (n=6). The reported fluorination and collection efficiencies on EWOD were 909% (n=6) and 943% (n=6), respectively, suggesting the current platform and reaction conditions give slightly lower fluorination efficiency. The synthesis time (up to the end of the collection process) for [.sup.18F]fallypride was 25 min.
[0050] Automated loading and collection provided a marginal increase in the crude RCY of [.sup.18F]fallypride to 646% (n=4). The isolated RCY was 464% (n=4). Typically, in macroscale synthesis, about 5-10% of the radioactivity of the crude product can be lost during purification and formulation. Here about 28% of the activity was lost, suggesting that significant improvements can be made, perhaps in injection of the small volume of collected product into the HPLC system. The synthesis time was reduced to 20 minutes (12 minutes for drying and fluorination steps and 8 minutes for collection) due to elimination of manual steps. This time is slightly shorter than reported for EWOD-based synthesis (i.e., 31 minutes for [.sup.18F]fallypride). The synthesis time is also somewhat shorter than macroscale processes (29 minutes for [.sup.18F]fallypride). It should be pointed out that purification and formulation times were omitted for comparison purposes, but it is expected that these processes could be performed more quickly than in the reported macroscale methods due to the smaller crude reaction product volume. This smaller volume can accelerate both the purification and formulation processes. The time for collection can possibly be further condensed by optimizing the speed of the product droplet collection process.
Example: Radiosynthesis of [.SUP.18.F] FDG
[0051] [.sup.18F]FDG is analogue of glucose and is by far the most commonly used PET imaging tracer. In an initial experiment, the fluorination of [.sup.18F]FDG was performed using a microfluidic chip 10 having multiple tracks (e.g., like that illustrated in
[0052] [.sup.18F]FDG was also synthesized using the automated microfluidic synthesis platform 60 illustrated in
[0053]
[0054] [.sup.18F]FDG was further purified with a custom miniaturized cartridge adapted from a commercially available FDG Purification cartridge for the base hydrolysis (Chromabond Set V, ABX). The commercial cartridge was designed for macroscale purification of [.sup.18F]FDG and would result in too much dilution of the purified product when making small amounts of the tracer. Instead, custom cartridges were made by repacking the resin beads (18.4 mg cation exchange resin (PS-H.sup.+), 18.2 mg anion exchange resin (PS-HCO.sub.3), 30.4 mg neutral alumina (ALOX N) and 15.6 mg reversed-phase resin (HR-P)) inside a 0.063 ID perfluoroalkoxy alkane (PFA) tubing (ZEUS, Orangeburg, S.C., USA). The resins were sandwiched and separated with 1.5 mm diameter fits (FRPE1CC, OROCHEM, Naperville, Ill., USA). Before use, the cartridge was pre-conditioned with 0.5 mL EtOH and then 1 mL DI water. During purification, the 100 L diluted crude product was passed through the cartridge, then an additional 300 L DI water were used to collect the pure product.
[0055] The performance of [.sup.18F]FDG synthesis (for both full manual synthesis and automated synthesis) is shown in Table 4 below.
TABLE-US-00004 TABLE 4 Parameter Manual synthesis Automated synthesis Fluorination efficiency (%) 84 4 72 7 Hydrolysis efficiency (%) 100 0 100 0 Radioactivity recovery (%) 49 12 69 5 Collection efficiency (%) 70 15 Not measured Synthesis time (min) 18 1 21 2 Crude RCY (%) 40 8 50 8 Isolated RCY (%) NA 36 6
[0056] With manual handling, the fluorination efficiency, collection efficiency and crude RCY were 844% (n=4), 7015% (n=4) and 408% (n=4), respectively. The intermediate [.sup.18F]FTAG was completely hydrolyzed into [.sup.18F]FDG as determined by radio-TLC with hexane and ethyl acetate (1:1, v:v) mobile phase. Evaporation loss (12%, n=4) was minimal, but some radioactivity losses were observed during fluorination (303%, n=4), and there was significant residual radioactivity on the chip and pipette tips after collection (209%, n=4). These losses were comparable to the losses reported on EWOD platform (483%, n=2). The crude RCY was marginally lower than crude RCY on EWOD platform (4510%, n=2), which was mainly due to lower fluorination efficiency compared to that on EWOD platform (933%, n=2). After fluorination, the radioactivity would ideally be uniformly distributed through the reaction droplet, but in fact is confined to a smaller region corresponding to the location of the [.sup.18F]TBAF residue after the initial [.sup.18F]fluoride drying step. Further optimizations will focus on improving fluorination efficiency by adding external means to facilitate mixing and dissolution processes, and by carefully controlling volume of solution in reaction site.
[0057] As expected, after implementation of automated reagent loading and product collection for [.sup.18F]FDG synthesis, the crude RCY was enhanced to 508% (n=4). Higher radioactivity recovery (695%, n=4) compared to manual synthesis (4912%, n=4) dominated the increase of crude RCY. Isolated RCY was 366% (n=4). Purification efficiency of the custom cartridge was 729% (n=4) and can likely be improved by optimization of the custom purification cartridges and purification process. The synthesis time (up to the end of the collection process) for [.sup.18F]FDG was 21 minutes, which is significantly shorter than reported for EWOD-based synthesis (50 min). Including purification, the synthesis time was 36 minutes, which only slightly longer than the fastest times reported for macroscale synthesis (22 min).
[0058] The starting activity of [.sup.18F]fallypride and [.sup.18F]FDG synthesis was minimized in preliminary experiments for safety reasons to 0.2-0.4 mCi by loading a 2 L droplet (radioactivity concentration 0.1-0.2 mCi/L). Though sufficient radioactivity was recovered for small animal imaging, it will be desirable in the future to scale this up to enable tracer production for multiple animal studies or for clinical doses. One way to scale up activity is by pre-concentrating the [.sup.18F]fluoride solution from the cyclotron using a miniaturized anion exchange cartridges. Another approach is to repeatedly load droplets of [.sup.18F]fluoride solution before drying.
[0059] Preliminary experiments were conducted to test the feasibility of the latter approach with manual loading and collecting. To ensure the same ratio of precursor to TBAHCO.sub.3 in the fluorination reaction, multiple 2 L droplets of [.sup.18F]fluoride/[.sup.18O]H.sub.2O solution (i.e. no TBAHCO.sub.3) were first loaded, followed by a single 2 L, droplet of TBAHCO.sub.3 solution (3.6 mM). The mixture was dried at 105 C. for 1 min. In a preliminary experiment, loading of 2, 4, or 8 L, of [.sup.18F]fluoride/[.sup.18O]H.sub.2O solution resulted in crude RCYs was 58% (n=1), 54% (n=1), and 50% (n=1). Results are shown in Table 5 below.
TABLE-US-00005 TABLE 5 Parameter Trial 1 Trial 2 Trial 3 Trial 4 [.sup.18F]fluoride/[.sup.18O]H.sub.2O solution 2 4 6 8 volume (L) Starting radioactivity (mCi) 0.24 0.42 0.57 0.63 Radioactivity recovery (%) 83 72 76 79 Fluorination efficiency (%) 70 76 57 63 Crude RCY (%) 58 55 43 50
[0060] This apparent reduction in crude RCY as a function of [.sup.18F]fluoride/[.sup.18O]H.sub.2O volume could be a mixing issue as it may become increasingly difficult to dissolve the increasing amount of residue in the precursor solution droplet prior to fluorination. Instead of loading a large volume and drying it once, each droplet of [.sup.18F]fluoride/[.sup.18O]H.sub.2O could be dried after loading, perhaps limiting the lateral extent of the initial residue. For the 8 L case, the starting activity was 2.34 MBq (0.63 mCi).
[0061] Though the volume capacity of the chip used in the experiments was low (e.g., a few microliters), it is likely that the reagent pathways and reaction region could be scaled up or down to accommodate larger or smaller reaction volumes, respectively. Another way to scale-up is to combine with an auxiliary miniature ion-exchange cartridge, which allows large amounts of radioactive isotope to be concentrated into microliter volumes prior to loading onto the microfluidic chip 10. Thus, a concentrated droplet containing reactants can be used in conjunction with the microfluidic chip 10. This would allow production of sufficient quantities of tracers for clinical PET imaging. In addition to the production of radiotracers for PET, the chip could also be used to make agents for Single-Photon Emission Computed Tomography (SPECT) imaging, labeled peptides/proteins, or radiolabeled therapeutic molecules. It could be used to perform small scale chemical reactions in a variety of other applications as well.
[0062] The passive microfluidic device 10 has numerous advantages over EWOD-based devices and other microfluidic approaches. First, microscale radiochemical reactions largely reduce the cost of reagents. Using microliter scale reactions, <1% of the amount of reagents used for macroscale reactions are needed while maintaining similar or higher concentrations. The fabrication of passive chips is much less complicated and much less expensive than EWOD chips or other microfluidic methods for performing chemical reactions. Passive microfluidic chips 10 eliminate the need of extra electronics and pumps to manipulate the fluids on the chip. In addition, the compact size of the passive microfluidic platform requires much less shielding than a traditional macroscale radiosynthesizer. While the latter must be located in a hot cell weighing several tons, the chip can be shielded with the same thickness and potentially be light enough in weight to be used on the benchtop.
[0063] While the microfluidic chip 10 described herein has generally been described as containing a single hydrophilic reaction or collection site 16 it should be appreciated that the microfluidic chip 10 may contain multiple hydrophilic reaction or collection sites 16 and associated delivery channels or pathways 18 on a single substrate 12. For example, the multiple hydrophilic reaction or collection sites 16 may be arranged as an array such that parallel or multiple separate synthesis reactions can take place on a single microfluidic chip 10. Such an embodiment, may require a moveable reagent dispenser and/or moveable microfluidic chip 10 (e.g., using a moveable stage or the like) whereby fluids may be loaded and unloaded from the various locations formed on the microfluidic chip.
[0064] While embodiments of the present invention have been shown and described, various modifications may be made without departing from the scope of the present invention. The invention, therefore, should not be limited, except to the following claims, and their equivalents.