Abstract:
In many miniaturized high-throughput assays, effective stirring is difficult to achieve, and its consequences difficult to predict. Most microtitre plate-based in vitro assays of membrane permeability, such as Caco-2 and PAMPA, of sparingly soluble lipophilic test compounds in pharmaceutical research and development report permeability of water, and not of the intended membrane barrier. This is so because the aqueous boundary layer on both sides of the membrane barrier is rate limiting for these highly permeable molecules. The thickness of this water layer can be 1500-4000 μm in unstirred assays. Under in vivo conditions, however, the aqueous boundary layer is believed to be 30-100 μm thick in the intestine, and &lt;1 μm at the blood-brain barrier. Using plate shakers to stir microtitre plates cannot lower the thickness of the water layer to match that found in vivo. We have discovered a high-throughput method and a simple, “robotics-friendly” device where individual-well stirring at speeds of about 600 rpm can lower the aqueous boundary layer thickness to &lt;15 μm, which had not been previously achieved for plate-based permeability assays.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS  
       [0001]     This application claims the priority of U.S. Provisional Application No. 60/575,883 filed Jun. 1, 2004 and entitled, METHOD AND MINIATURIZED DEVICE TO REDUCE THE AQUEOUS BOUNDARY LAYER THICKNESS, which is hereby incorporated by reference herein. 
     
    
     BACKGROUND OF THE INVENTION  
       [0002]     Commonly, drug absorption and transport across the blood brain barrier (BBB) or gastrointestinal tract (GIT) is studied via in vitro permeability assays. These assays are typically performed in an apparatus featuring solution filled donor and acceptor compartments separated by a porous support such as a microporous material or structure. A molecular entity such as a drug of interest permeates from the donor compartment into the acceptor compartment through the porous support of the apparatus. For example, to model GIT drug absorption and transport, monolayers of living cells are grown on the porous support to form a lipid membrane permeation barrier. These monolayers often can include Caco-2 type cells. Alternatively, a lipid membrane permeation barrier can be formed by depositing biomimetic materials on or into the porous support for an assay that is often referred to as a parallel artificial membrane permeability assay (PAMPA).  
         [0003]     The donor and acceptor compartments of the apparatus are usually incorporated into microtitre plates of various formats to conduct numerous assays simultaneously. The shortcoming with the compartments is that their small volume causes thick aqueous boundary layers of stagnant solution adjacent to the porous support comprising, for example, biological or biomimetic materials. A thick boundary layer along the upper or lower surface of the support can introduce significant errors to permeation measurements. For example, a molecular entity will be physically impeded from passing through the porous support, which comprises a biological or biomimetic material to form a permeation barrier, from the donor to acceptor compartment.  
         [0004]     With a conventional PAMPA, the total thickness of the aqueous boundary layers adjacent to the upper and lower surface of the porous support is from about 1,500 to 4,000 microns (μm). Measurements of, for example, a drug through a permeation barrier in such an assay can be appreciably biased by resistance due to the boundary layers. Indeed, drug studies are replete with lipophilic compounds that have reported permeability values that merely represent that of boundary layers characteristic to a given acceptor or donor compartment.  
         [0005]     In vivo GIT boundary layers are usually considered to be from about 30 to 100 μm thick. Moreover, BBB boundary layers are presumed to be less than 1 μm. With a standard Caco-2 type cell assay or PAMPA, the total thickness of the aqueous boundary layers adjacent to the porous support is commonly more than 1,500 μm thick such that the layers tend to become a limiting factor when measuring the permeability of lipophilic compounds. For such assays, it is well established that solution agitation can diminish aqueous boundary layer thickness. A common approach to achieve agitation of solution in the donor and acceptor compartments is to place the compartments on a vibrational body such as an orbital or linear plate shaker. Other approaches for reducing aqueous boundary layer thicknesses include using a chemical sink in the acceptor compartment or to induce a pH gradient across the porous support comprising, for example, biological or biomimetic materials.  
         [0006]     These approaches are still unable to reduce boundary layer thicknesses below 300 to 500 μm, which is necessary to closely model biological conditions, for example, for drug absorption and transport. Moreover, such approaches become even less attractive for donor and acceptor compartments incorporated into microtitre plates. For example, a standard 96 compartment microtitre plate exhibits a high degree of anisotropy across the plate with compartments along its edges being more effectively agitated than those near the center. This sort of anisotropy is even more pronounced in higher density plates such as those with 384 or 1536 compartments.  
         [0007]     In view of the interest in using high density microtitre plates to conduct numerous permeation assays simultaneously, minimizing aqueous boundary layer thicknesses is increasingly difficult as smaller donor and acceptor compartments require more vigorous agitation to only marginally reduce boundary layer thickness. Such a shortcoming as well as those mentioned above demonstrate the need to have a convenient means by which to reduce aqueous boundary layer thicknesses in permeation assays. The means should also be adaptable to easily modify a standard Caco-2 type cell assay or PAMPA for in vitro studies of drug absorption and transport.  
       SUMMARY OF THE INVENTION  
       [0008]     The present invention provides a permeation device comprising a receiving vessel having an aperture. The aperture of the vessel is adapted to receive an insert well. Both the receiving vessel and insert well can comprise either the donor or acceptor compartment for a permeability assay. In addition, the insert well comprises a porous support, for example, disposed, attached or formed in a lower section of the well. Alternatively, the support may be, for example, disposed, attached or formed in an upper section of the receiving vessel. The porous support can, for example, comprise biological, biomimetic or both materials. The porous support is adapted for a molecular entity to permeate therethrough as the entity passes from the donor into the acceptor compartment. For example, an entity in solution in the donor compartment permeates from solution, through the support and into solution in the acceptor compartment.  
         [0009]     In one embodiment, a stirring member is disposed in the receiving vessel. The stirring member is operable to agitate a solution in, for example, the receiving vessel, insert well or a combination thereof. Solution agitation can reduce the thickness of the boundary layers adjacent to the upper, lower or both surfaces of the porous support. Generally, agitating a solution in the insert well or receiving vessel reduces the thickness of the boundary layer adjacent to, for example, the upper or lower surface, respectively, of the porous support. For example, the boundary layers comprise a portion of solution, which is substantially stagnant. The thickness of the boundary layers can, for example, be reduced such that a molecular entity can permeate the support, which comprises, for example, biological or biomimetic materials, in close approximation to in vivo absorption and transport conditions.  
         [0010]     A device of the invention is well suited for a Caco-2 type cell assay or PAMPA. For a Caco-2 type cell assay, the cells are, for example, grown on the porous support. For a PAMPA, a variety of biomimetic materials can be, for example, deposited or assembled on the support or into its pores. A porous support for a device of the invention can also comprise biological or biomimetic materials disposed or grown on the support or in its pores. The aqueous boundary layer thicknesses that are achievable using a device of the invention can be as thin as, for example, 15 μm. The extent of agitation caused by a stirring member disposed in the donor, acceptor or both compartments can also be controlled to adjustably change a boundary layer thickness. By changing the boundary layer thicknesses, a device of the invention can model in vivo absorption and transport across, for example, the GIT. For example, the invention contemplates a controller device or assembly for a stirring member that is calibrated to produce boundary layer thicknesses from, for example, about 500 to 15 μm.  
         [0011]     A stirring member for a device of the invention can be composed of any suitable material(s). The member can be inert such that it does not interfere with the assay. For example, a stirring member can be a magnetized or magnetizeable coated metal in which the coating is an inert polymer. A member can also be an inert metal such as stainless steel. A magnetized or magnetizeable member can be moved by, for example, a magnet. Alternatively, a member can be a glass or inert plastic bead that is moved using a vibrational body such as an orbital or linear plate shaker.  
         [0012]     In another embodiment, a second stirring member is disposed in the insert well. The second member can also be comprised of such materials as described above. For example, the second stirring member can be inert and moved by a magnet or vibrational body. A device of the invention can also employ both a magnet and vibration body for solution agitation. In one embodiment, a stirring member can also comprise a molecular entity. The invention also contemplates using a plurality of stirring members in either the receiving vessel, insert well or a combination thereof.  
         [0013]     A stirring member can be retained in place in an insert well or receiving vessel so as to not contact biological or biomimetic materials therein. A member can also be held in place so as to not contact the porous support. Any suitable means may be used to retain a stirring member for a device of the invention. For example, a member can be retained by constrictions disposed about the interior of the well or vessel or a strainer positioned therein. Alternatively, a retaining member or structure such as, for example, an inert grid associated with the well or vessel can be used to hold the stirring member in place.  
         [0014]     In one embodiment, a donor and acceptor plate can comprise a plurality of either insert wells or receiving vessels. Preferably, the plates are standard format microtitre plates. For example, such plates can include 6, 12, 24, 48, 96, 384 or 1536 wells or vessels. These plates are typically composed of inert and non-magnetic materials such as polycarbonate or any other thermoplastic. An insert well or receiving vessel can also be composed of such inert and non-magnetic materials. A donor or acceptor plate of the invention can also be adapted to be easily manipulated by robotic equipment as is understood within the art. The invention also contemplates assays using a plurality of stackable donor and acceptor plates or a plurality of receiving vessels and insert wells, which can also be stacked.  
         [0015]     Another embodiment of the invention comprises biological or biomimetic materials disposed on an upper and lower surface of the porous support. For example, cells of the same type can be grown on the upper and lower surface of the porous support. Similarly, cells of a different type can be grown on the upper and lower surface of the support, respectively. Such an arrangement of biological materials is often used in what is referred to as a co-culture assay. A co-culture assay can also be performed by having a first type of biological material disposed or grown on the porous support and a second type of biological material disposed or grown in the insert well or receiving vessel. For a co-culture assay, it can be particularly important to have a means by which to prevent these materials from being contacted by a stirring member, which could potentially damage the materials.  
         [0016]     In another embodiment, a probe is disposed in a receiving vessel. The probe can be based on a variety of principles such as, without limitation, thermal sensing, ion selective electrode technology, spectroscopic methods or a combination thereof. Preferably, the probe is used when the stirring member comprises a molecular entity. For example, the entity can be covered by a biological or biomimetic material disposed about the member such that as the member is moved, the molecular entity permeates therethrough and into the receiving vessel. The permeation can be monitored by the probe.  
         [0017]     The present invention also provides a method for reducing boundary layer thicknesses. The method comprises providing one or more permeation devices of the invention. A stirring member(s) for the device is then moved to agitate a solution that preferably contains a molecular entity. The agitation of the solution can reduce the thickness of the boundary layers adjacent to the upper, lower or both surfaces of the porous support, which may include biological or biomimetic materials disposed thereon or therein. For example, boundary layer thicknesses are reduced by reducing the portion of solution that is substantially stagnant and adjacent to the porous support.  
         [0018]     A reduction in boundary layer thicknesses can allow permeation of a molecular entity through the support, which comprises biological or biomimetic materials, to closely approximate in vivo absorption and transport conditions. The method also contemplates controlling the extent of agitation due to a stirring member(s) so as to adjustably change the boundary layer thicknesses adjacent to the upper, lower or both surfaces of the porous support. A method of the invention can also be carried out with a plurality of vessels or wells incorporated into donor or acceptor plates as described above. 
     
    
     DESCRIPTION OF THE DRAWINGS  
       [0019]     Other features and advantages of the present invention will be apparent from the detailed description of the invention that follows herein, taken in conjunction with the accompanying drawings of which:  
         [0020]      FIG. 1  is a partial representation of a device of the invention having a stirring member disposed in a receiving vessel;  
         [0021]      FIG. 2  is a partial representation of a device of the invention having stirring members disposed in both the insert well and receiving vessel;  
         [0022]      FIG. 3  is a partial representation of a device of the invention having cell cultures disposed or grown in both the insert well and receiving vessel;  
         [0023]      FIG. 4  is a partial representation of a device of the invention having constrictions extending into both the insert well and receiving vessel to retain one or more stirring members;  
         [0024]      FIG. 5  is a partial representation of a device of the invention having retaining members disposed in both the insert well and receiving vessel to retain one or more stirring members;  
         [0025]      FIG. 6  is a partial representation of a device of the invention having retaining members disposed in both the insert well and receiving vessel to retain one or more stirring members;  
         [0026]      FIG. 7  is a partial representation of a device of the invention having cell cultures disposed or grown on an upper and lower surface of the porous structure;  
         [0027]      FIG. 8  is a partial representation of a device of the invention having stirring members that comprise a molecular entity disposed in both the insert well and receiving vessel;  
         [0028]      FIG. 9  is a partial representation of a device of the invention having a probe disposed in a receiving vessel with a stirring member that comprises a molecular entity;  
         [0029]      FIG. 10  is a partial representation of a donor and acceptor plate;  
         [0030]      FIG. 11  shows six logarithm of effective permeability (P e ) versus pH plots of ionizable acid and base molecular entities measured at different stirring speeds;  
         [0031]      FIG. 12  shows plots of the logarithm of boundary layer permeability (P u ) versus the logarithm of molecular weight (MW) at stirring speeds of 0, 186 and 622 revolutions per minute (rpm);  
         [0032]      FIG. 13  is a plot of the logarithm of P u  versus the logarithm of stirring speeds (ν) for 36 different measurements based on 14 molecular entities;  
         [0033]      FIG. 14  shows plots of the logarithm of P u  of four molecular entities versus the logarithm of ν; and  
         [0034]      FIG. 15  shows a plot of the relationship between the thickness of aqueous boundary layers and ν based on both literature studies and a device of the invention. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0035]     The present invention provides a permeation device comprising a receiving vessel having an aperture adapted for receiving an insert well. Both the receiving vessel and insert well can comprise either the donor or acceptor compartment for a permeability assay. The insert well includes a porous support, for example, disposed, attached or formed in a lower section of the well. Alternatively, the support may be, for example, disposed, attached or formed in an upper section of the receiving vessel. A molecular entity in solution in a donor compartment can permeate the porous support and pass into solution in an acceptor compartment. Preferably, the porous support comprises biological, biomimetic materials or a combination thereof such as, for example, a living cell membrane layer or a non-living lipid layer.  
         [0036]     In one embodiment, a solution is agitated by a stirring member disposed in the receiving vessel. By agitating the solution, the aqueous boundary layers adjacent to the upper, lower or both surfaces of the porous support, which comprises, for example, biological or biomimetic materials, can be reduced such that permeation of a molecular entity therethrough closely models in vivo absorption and transport. Generally, agitating a solution in the insert well or receiving vessel reduces the thickness of the boundary layer adjacent to, for example, the upper or lower surface, respectively, of the porous support. For example, boundary layer thicknesses adjacent to the support can be reduced to approximate absorption and transport conditions in the GIT. Boundary layer thicknesses are reduced by, for example, reducing the portion of solution that is substantially stagnant and adjacent to the porous support.  
         [0037]     A device of the invention can reduce the total thickness of the aqueous boundary layers to less than, for example, 15 μm. The extent of agitation due to a stirring member can also be controlled to adjustably change boundary layer thicknesses. By adjustably changing boundary layer thicknesses, a device of the invention can model in vivo absorption and transport across, for example, the GIT. For example, the invention contemplates a controller device or assembly for the stirring member that is calibrated to produce boundary layer thicknesses from, for example, about 500 to 15 μm. A device of the invention can also be used for a conventional Caco-2 type cell assay or PAMPA in which the biological or biomimetic materials are, for example, comprised by the porous support.  
         [0038]      FIG. 1  shows a partial representation of a device of the invention. As shown, a device  2  comprises a receiving vessel  6  having an aperture. An insert well  4  is disposed in the vessel  6  through the aperture. A lower section of the well  4  comprises a porous support  8 . The porous support  8  can be, for example, disposed, attached or formed in the lower section of the insert well  4 . The support can also be adapted to receive a biological or biomimetic material disposed or grown on its upper or lower surface. Such materials can also be disposed or grown on both the upper and lower surfaces of the support  8 . Similarly, these materials can be disposed or grown in the pores of the support. For example, a non-living, biomimetic lipid-based membrane can be assembled on the support or in its pores.  
         [0039]     The receiving vessel  6  can include a stirring member  10 . The member  10  can be inert such that it does not interfere with an assay. For example, a stirring member can be a magnetized or magnetizeable coated metal in which the coating is an inert polymer. A member can also be an inert metal such as stainless steel. A magnetized or magnetizeable member can be moved by, for example, a magnet. The magnet can, for example, be fixed with respect to the receiving vessel such that the magnet is positioned substantially beneath the vessel.  
         [0040]      FIG. 1  shows the member  10  as a thin ferromagnetic or paramagnetic disk attracted to a permanent magnet  14  below the bottom of the vessel  6  so as to keep the magnet away from the support  8 . The magnet is rotated by a motor  16 , which can be controlled using a controller device  18 . Alternatively, a stirring member can be a glass or inert plastic bead that is moved using a vibrational body such as an orbital or linear plate shaker. The vibrational body can also be, for example, fixed with respect to the receiving vessel such that the body is positioned substantially beneath the vessel.  
         [0041]     In  FIG. 1 , as the motor  16  turns, the stirring member  10  also turns or moves. When solution(s) is added to the well  4  and vessel  6  of the permeation device  2 , the thickness of the aqueous boundary layer adjacent to, for example, the upper, lower or both surfaces of the porous support  8  can be controlled by the speed of the motor. In general, a stirring member that is disposed in a receiving vessel predominately reduces the aqueous boundary layer along the lower surface of a porous support disposed between the vessel and an insert well. Similarly, a stirring member that is disposed in an insert well predominately reduces the aqueous boundary layer along the upper surface of the porous support disposed between a receiving vessel and the well. For example, boundary layer thicknesses are reduced by reducing the portion of solution that is substantially stagnant and adjacent to the porous support.  
         [0042]     As described above, a boundary layer comprises a portion of solution that is substantially stagnant. Solutions in both the insert well  4  or receiving vessel  6  comprise such a substantially stagnant portion adjacent to the upper and lower surface, respectively, of the porous support  8 . It is also contemplated that the speed of the motor  16  for a permeation device  2  can be calibrated in terms of the thickness of the aqueous boundary layers adjacent to the upper, lower or both surfaces of the porous support.  
         [0043]     For example,  FIG. 1  shows a scaled potentiometer  20 , which is calibrated to adjustably change the boundary layer thickness adjacent to the lower surface of the porous support via the motor  16  and controller device  18 . Such motor control and calibration can readily be performed using conventional laboratory techniques that may include computer software and hardware. A motor, controller device and potentiometer are also exemplary means by which to adjustably change boundary layer thicknesses, although the invention contemplates that any other suitable means can also be used.  
         [0044]     In one embodiment, the device  2  comprises a receiving vessel  6  that features an upper portion  12  and flange  13 , which are intended to accommodate and support the insert well  4 . The upper portion can have a diameter larger than that of the main body portion of the receiving vessel  6 . The insert well  4  can alternatively be supported by any suitable means such as a supporting element or member positioned substantially along the exterior or interior of the vessel  6 , which may obviate the need for an upper portion  12  having a diameter larger than that of the main body portion of the vessel.  
         [0045]     The receiving vessel  6  and insert well  4  may be formed from any suitable materials. For example, inert or non-magnetic materials such as polycarbonate or any other thermoplastic can be used for the vessel and well. The porous support  8  for a device of the invention can also be made from any suitable material such as, for example, polyvinylidene fluoride (PVDF), polyethylene terephtaleate or polycarbonate. In addition, the support preferably has an exemplary thickness from about 10 to 200 μm and an exemplary porosity from about 5 to 80 percent. The support  8  can be disposed, attached or formed in the insert well  4  by any suitable bonding technique known to produce a secure and leak-free attachment. Exemplary techniques include solvent bonding, heat-sealing, insert molding and ultrasonic welding.  
         [0046]      FIG. 2  shows a partial representation of a device of the invention. In  FIG. 2 , a solution in the insert well  4  is capable of being stirred by a stirring member  24 . The permeation device  22  comprises a receiving vessel  6  and an insert well  4 . As described above, the insert well  4  has a porous support  8  disposed, attached or formed in a lower section of the well. The stirring member  24  is disposed in a strainer  26 , which is disposed inside the insert well. The strainer bottom securely separates the stirring member  24  from the support  8  by, for example, being disposed between an interior of the well and stirring member  24 .  
         [0047]     The stirring member can, for example, be driven by magnetic or electromagnetic fields induced by an assembly such as the assembly  34 , which comprises a magnet, motor and controller device. The components of the assembly  34  can operate as described above and may be incorporated into any one or all of the embodiments described herein. Exemplary types of assemblies are also generally described in U.S. Pat. No. 6,176,609, which is hereby incorporated by reference herein.  
         [0048]     A stirring member  24  can be composed of any suitable material(s). The member can be inert such that it does not interfere with the assay. For example, a stirring member can be a magnetized or magnetizeable coated metal in which the coating is an inert polymer. A member can also be an inert metal such as stainless steel. A magnetized or magnetizeable member can be moved by, for example, a magnet. Alternatively, a member can be a glass or inert plastic bead that is moved using a vibrational body such as an orbital or linear plate shaker.  
         [0049]     The strainer  26  can be provided with, for example, a flange  28  to suspend strainer  26  inside insert well  4  at a defined distance from support  8 . The suspension of the strainer can be achieved by any suitable means such as a ring or other support feature inside or outside the insert well. The assembly  30  in the partial representation on the right in  FIG. 2  shows the strainer  26  with the stirring member  24  disposed therein. The strainer can be fixed with respect to the lid  32  so as to trap the stirring member for ease of manufacture, transportation or use. The strainer can be fixed with respect to the lid by, for example, a constriction over the edge of a rim  36 , although any other suitable approaches for fixing or positioning the strainer may be employed. Such exemplary approaches include bonding, heat-sealing, ultra-sonic welding or adhering the strainer to the lid.  
         [0050]     As described above, the porous support  8  of  FIG. 2  can also be adapted to receive a biological or biomimetic material disposed or grown on its upper or lower surface. Similarly, these materials can be disposed or grown in the pores of the support. For example, a non-living, biomimetic lipid-based membrane can be assembled on the support or in its pores. In one embodiment, a device of the invention comprises biological or biomimetic materials disposed or grown on an upper and lower surface of the porous support. Such an embodiment can be used for a co-culture assay. For co-culture assays, it is also contemplated that two different cell types are disposed or grown on the upper and lower surface, respectively, of the porous support.  
         [0051]     It is also recognized that a similar assay may be carried out by, for example, having a first biological material such as a cell type disposed or grown on the porous support and a second material disposed or grown in the receiving vessel.  FIG. 3  shows a partial representation of a permeation device having a first cell culture  38  deposited or grown on the porous support  8  in the lower section of the insert well  4  as well as a second cell culture  40  deposited or grown along a bottom of the receiving vessel  6 . For such a co-culture assay, it can be particularly important to have a means by which to prevent such biological materials from being contacted by a stirring member, which could potentially damage the materials.  
         [0052]     For example,  FIG. 3  shows a second strainer  42  contained in the receiving vessel  6  to retain the stirring member  10  from contacting the second cell culture  40 . As described above, the strainer can be fixed with respect to the vessel  6  by any suitable means. As also described above, a strainer can be disposed in the insert well  4  to prevent the stirring member therein from contacting the first cell culture  38  disposed or grown along an upper surface of the porous support  8 . Exemplary strainers can be inert to common water-solvent mixtures. Such strainers are commonly formed from a non-magnetic mesh material or by using injection molding. Other typical methods or processes used to form a strainer as shown in  FIGS. 2 and 3  are also applicable for a device of the invention.  
         [0053]      FIG. 4  shows a partial representation of a permeation device of the invention that is similar to those described above. The device in  FIG. 4  can also include any type of constriction such as a ring-shaped constriction  44  in either or both the insert well  4  and receiving vessel  6 . The constrictions  44  may, for example, be disposed about the diameter of the well  4  or vessel  6 . Such constrictions can contain stirring members  10  and  24 , which can feature exterior diameters slightly larger than the diameter of the corresponding constriction.  
         [0054]     Exemplary stirring members  24  and  10  are shown in  FIG. 4  as donut-shaped bits. Other exemplary stirring members include solid discs. The constrictions are intended such that the members will not make physical contact with the support  8  or the bottom of the well or vessel in any orientation. Moreover, constrictions  44  are also easy to incorporate into injection molds for the well or vessel, although any other suitable or conventional means of incorporating such constrictions into a device of the invention are possible.  
         [0055]     As described above, the stirring members  24  and  10  shown in  FIG. 4  can, for example, be donut-shaped to allow access to the porous support  8  or to allow light to be passed through the members into the bottom of the well  4  or vessel  6  for photometric analyses, which preferably occur when the members are not being moved. Such analyses can be performed without any sort of damage to the optical quality of the porous support or bottom of the well or vessel. Exemplary optical analyses can include ultraviolet (UV), infrared (IR), near IR, fluorescence spectroscopy or a combination thereof. In addition, a bottom portion of the receiving vessel  6  can be part of the vessel itself or be a suitable optical membrane  46  disposed, attached or formed in a leak-free manner in the vessel. Such leak-free manners or techniques include, for example, those that are described above.  
         [0056]      FIG. 5  is a partial representation of another device embodiment of the invention. For example, ring members  48 , which have an inside diameter smaller than an outside diameter of stirring members  10  and  24 , in the insert well  4  and receiving vessel  6  prevent the stirring members from making physical contact with support  8  or an optical quality bottom  46  of the vessel  6 . Such an embodiment of the invention can be particularly advantageous when the receiving vessel  6  is molded from an optical quality material that does not allow a constriction, for example, such as shown in  FIG. 4 , to be molded in place.  
         [0057]     The ring members  48  can also prevent the stirring members from contacting any biological or biomimetic materials that are disposed or grown in the insert well or receiving vessel. The ring members in  FIG. 5  are shown as examples of a retaining member or means, which is preferably used to retain the stirring members, although any other suitable or conventional means can be used with a device of the invention. Additional exemplary retaining members or means are also described herein.  
         [0058]      FIG. 6  is a partial representation of a device of the invention featuring retaining members disposed in both the insert well and receiving vessel. For example, retaining members are shown as molded-in or inserted grids  54 , fixed with respect to the insert well  4  and receiving vessel  6 . Exemplary profiles for the grids are shown as structures  56  and  58  in the partial representations on the right in  FIG. 6 . The retaining members are intended to prevent stirring members  10  and  24  from making physical contact with porous support  8 , while allowing a molecular entity to pass through the members and support.  
         [0059]     For example, the retaining members  54  can prevent a stirring member  10 , which may be a steel ball, from making physical contact with the support when the member  10  is raised. The stirring member can be raised and lowered to achieve stirring by using, for example, a magnetic field source located outside the vessel  6 . In one embodiment, another retaining member  50 , which is shown, for example, also as a grid, can be used to allow an additional well or vessel to be partially disposed in the insert well  4 . Such an arrangement can be used for double-permeation assays. The invention also contemplates assays using a plurality of stackable insert wells and receiving vessels.  
         [0060]     As described above, for a non-magnetic stirring member such as a glass bead or a dense inert polymer, movement of the member can be achieved by using a vibrational body such as linear or orbital shaker. The retaining members  50  and  54  shown in  FIG. 6  serve equally well as guards for retaining such non-magnetic members within the insert well  4  or receiving vessel  6 . A device of the invention can also employ several different means for moving a stirring member(s) during an assay. For example, a stirring member can be moved by a magnet and vibrational body simultaneously.  
         [0061]     The partial representation of a permeation device of the invention in  FIG. 7  shows a co-culture assay. In particular,  FIG. 7  shows a permeation device having a first cell culture  38  disposed or grown on the porous support  8  and a second cell culture  40  disposed or grown along a lower surface of the support. The first and second cell culture can be biological materials of the same or a different type. Alternatively, biomimetic materials can be disposed or assembled along an upper or lower surface of the porous support. In one embodiment, a combination of biological and biomimetic materials can be disposed or grown on both surfaces of the support. As described above, the support also allows biological or biomimetic materials to be disposed or grown in its pores.  
         [0062]     As shown in  FIG. 7 , the insert well  4  and receiving vessel  6  are generally arranged as described above.  FIG. 7  also shows the insert well partially disposed in the aperture of the vessel with a top surface  66  of the vessel supporting the well. The insert well  4  can comprise features that allow it to be suspended in the vessel  6  at a defined distance from the bottom of the vessel. For example, such features can be fins  64 . Exemplary fins are shown in the partial representation on the right in  FIG. 7 , although any other suitable arrangement of fins or other features can alternatively be used.  
         [0063]     The stirring member  10  in the vessel  6  can be similar to any of those that are described above. The member  24  in the insert well  4  can also be flexibly attached or coupled to an upper support structure  60  such that the member may move freely in a more or less horizontal plane, while being held securely at a given distance from the support  8 . In one embodiment, the support structure  60  can be fixed with respect to the insert well. When the stirring members are moved, for example, via a rotating magnetic field(s), the member  24  can swing from side to side like, for example, a pendulum to enable solution agitation. Such a stirring member  24  can be coupled to the support structure  60 , for example, by an extension  6 , although any other suitable means may be used. The extension  62  can also be disposed or formed along with a coating for the member  24 . In addition, the extension  62  can be formed as part of or separate from the support structure  60 .  
         [0064]      FIG. 8  shows a partial representation of a permeation device of the invention similar to those described above. For example, the device may be any one of the embodiments described above or may incorporate features from any or all of the embodiments described herein. In one embodiment, the stirring members  68  and  70  disposed in the receiving vessel  6  and insert well  4 , respectively, can have a means for holding an amount of a molecular entity in any form. The entity then permeates from the stirring member into solution. A molecular entity can be comprised by a stirring member in, for example, a powder, crystalline or pressed-pellet form. Preferably, only one of the stirring members comprises a molecular entity in which instance the other stirring member is optionally provided for solution agitation.  
         [0065]     A molecular entity is held, for example, behind a hydrophilic filter membrane of the stirring member. For example, the assemblies  74  and  78  shown in the partial representations on the right in  FIG. 8  exemplify different possible ways for having the entity comprised by a stirring member. In the assembly  74 , a donut-shaped stirring member  71  provides space in its center to accommodate the entity. Filter material such as, for example, a hydrophilic material comprise covers  72  and  76 , which are used to cover each side of the member.  
         [0066]     In the assembly  78 , the stirring member  69  is shaped as a shallow bowl providing space for the entity. In the assembly  78 , a single cover  80  of, for example, filter material can be used to hold an entity. Preferably, the cover  80  is disposed on the member  69  to hold the entity therein. The covers  72 ,  76  and  80  can, for example, be comprised entirely of a filter material or include other materials that may be suitable for a molecular entity to permeate therethrough. Such stirring member assemblies allow for simultaneous or independent study of dissolution, solubility and permeation properties for a molecular entity.  
         [0067]     Attaching or sealing one or more filter material covers to the stirring members can be performed by any suitable means such as, for example, solvent bonding, heat-sealing and ultrasonic welding. While  FIG. 8  shows the stirring member  68  in the receiving vessel  6 , it is understood that it could also be introduced in the insert well  4 . Alternatively, the member  70  can be introduced into the vessel  6 . Similarly, stirring members  69  and  71  can be disposed in either the insert well or receiving vessel. During, for example, dissolution or solubility based studies, the insert well  4  may not be necessary such as shown in  FIG. 9 .  
         [0068]      FIG. 9  is a partial representation of a permeation device having a receiving vessel  84  with a sample-containing stirring member  73 . The member  73  is intended to initially hold a molecular entity behind, for example, a filter such as a hydrophilic filter. The entity then permeates from the stirring member into solution. The filter can be a cover attached or sealed to the stirring member. Alternatively, the cover can include other materials with the filter material that may be suitable for a molecular entity to permeate therethrough. As described above, assemblies  74  and  78 , shown in the partial representations on the right in  FIG. 9 , exemplify different ways to include a molecular entity in a stirring member.  
         [0069]      FIG. 9  also shows a probe  82  inserted in the solution of the vessel  84  to permit measurement of, for example, the concentration of a molecular entity during dissolution of the entity. The probe may be based on a variety of principles such as, without limitation, thermal sensing, ion selective electrode technology, spectroscopic methods or a combination thereof. The latter may also be accomplished by using, for example, an optical quality receiving vessel to measure entity concentrations based on transmitted or transflected light during dissolution, which may not require the probe to come into direct contact with the device.  
         [0070]     A partial representation of exemplary donor and acceptor microtitre plates is shown in  FIG. 10 . The microtitre plates are shown as a donor plate  86  and an acceptor plate  88 . The donor plate comprises a plurality of insert wells  4 . Moreover, the plate  88  comprises a plurality of receiving vessels  6 . In another embodiment, a plurality of insert wells are comprised by an acceptor plate, while the donor plate comprises a plurality of receiving vessels. The donor and acceptor plates can be placed together to form a conventional permeation assay sandwich.  FIG. 10  shows a stirring member  10  disposed in each of the receiving vessels  6 .  FIG. 10  also shows the stirring members in the vessels in different orientations.  
         [0071]     An exemplary stirring member  10  can be a magnetized flipper. Such magnetized flippers can be simultaneously moved using any suitable means such as a magnet, motor and controller device or assembly as described above. The device or assembly may also have a speed dial setting calibrated so as to adjustably control the thicknesses of the individual aqueous boundary layers for each of the wells and vessels. The wells and vessels of the microtitre plates in  FIG. 10  can also include or incorporate the variations of any or all other embodiments of the invention.  
         [0072]     For example, an insert well or receiving vessel can include any type of stirring member that has been described above or any of those known in the art that are suitable for solution agitation. Similarly, for example, constrictions, retaining members, retaining means or a combination thereof can be included with any one of the embodiments described herein. Preferably, such plates as shown in  FIG. 10  are microtitre plates of various formats that are adapted to be manipulated by an individual or a robotic device(s).  
         [0073]     As described above, the invention also contemplates biological or biomimetic materials that are disposed in both the insert wells and the receiving vessels of the plates. In such a device of the invention, it may be particularly important to have a means by which to prevent these materials from being contacted by a stirring member, which could potentially damage the materials. Such means can include, for example, the constrictions, retaining members or retaining means described herein.  
         [0074]     The present invention also provides a method for reducing boundary layer thicknesses. The method comprises providing one or more permeation devices of the invention. A stirring member(s) for the device is then moved to agitate a solution that preferably contains a molecular entity. The agitation of the solution can reduce the thickness of the boundary layers adjacent to the upper, lower or both surfaces of the porous support, which may include biological or biomimetic materials disposed thereon or therein. For example, boundary layer thicknesses are reduced by reducing the portion of solution that is substantially stagnant and adjacent to the porous support.  
         [0075]     A reduction in boundary layer thicknesses can allow permeation of a molecular entity through the support, which comprises biological or biomimetic materials, to closely approximate in vivo absorption and transport conditions. The method also contemplates controlling the extent of agitation due to a stirring member(s) so as to adjustably change the boundary layer thicknesses adjacent to the upper, lower or both surfaces of the porous support. A method of the invention can also be carried out with a plurality of vessels or wells incorporated into donor or acceptor plates as described above.  
         [0076]     The example herein is provided to illustrate advantages of the present invention that have not been previously described and to further assist a person of ordinary skill in the art with using a permeation device according to the invention. The example can include or incorporate any of the variations or embodiments of the invention described above. The embodiments described above may also further each include or incorporate the variations of any or all other embodiments of the invention.  
         [0077]     For example, an insert well or receiving vessel can include any type of stirring member that has been described above or any of those known in the art that are suitable for solution agitation. Similarly, for example, constrictions, retaining members or retaining means or a combination thereof can be included with any one of the embodiments described herein. The following example is not intended in any way to otherwise limit the scope of the disclosure as provided herein.  
       EXAMPLE  
       [0078]     Fifty five different molecular entities were used for the present example. These entities included 2-naphthoic acid, 4′N-Et-3′-Me-ciprofloxacin, 4′N-Et-3′-Et-ciprofloxacin, astemizole, 4′N—Pr-3′-Me-ciprofloxacin, acebutolol, amlodipine-maleate, antipyrine, 3-hydroxyphenylacetic acid, ergonovine, benzoic acid, diltiazem-hydrochloric acid (HCl), desipramine-HCl, phenazopyridine-HCl, diclofenac-sodium (Na), flurbiprofen, fluvoxamine, ibuprofen, imipramine-HCl, ketoprofen, lansoprazole, protriptyline-HCl, naproxen, nortriptyline-HCl, warfarin, nalidixic acid, naringenin, nicardipine, ondansetron, oxprenolol, phenytoin-Na, pindolol, propranolol-HCl, piroxicam, prazosin-HCl, probenecid, progesterone, quinine-HCl, salicylic acid, tiamdipine, timolol-maleate, zimelidine, tamoxifen 1 , terfenadine 1 , amiodarone-HCl 1 , miconazole-nitrate 1 , itraconazole 1 , alprenolol-HCl 2 , chlorpromazine-HCl 2 , gemfibrozil 2 , indomethacin 2 , primaquine-diphosphate 2 , verapamil-HCl 2 , metoprolol-tartrate 2  and promethazine-HCl 2 .  
         [0079]     The above entities footnoted as “1” were insoluble in an aqueous buffer such that permeability measurements were conducted with the addition of 20 percent acetonitrile to the buffer. Additionally, those molecular entities that are footnoted as “2” had permeability measurements obtained in an aqueous buffer and a buffer having 20 percent acetonitrile added thereto. For this example, a PAMPA Evolution instrument from pION INC of Woburn, Mass. 01801 was used. A DOUBLE-SINK (pION INC of Woburn, Mass. 01801) GIT-0 lipid was also used as the material for the porous support, described below, to form a permeation barrier. A GUT-BOX (pION INC of Woburn, Mass. 01801) was also employed to provide stirring and for environmental control.  
         [0080]     Solution pH was adjusted using a universal buffer as well as a buffer solution having a pH of 7.4 and containing a chemical scavenger to simulate serum proteins, which can be obtained from pION INC of Woburn, Mass. 01801. Donor and acceptor microtitre plates with 96 compartments were also employed for this example. The acceptor plate was obtained from Millipore Corporation of Billerica, Mass. 01821. The porous supports between the plate compartments had thicknesses of 125 μm and a pore size of 0.45 μm.  
         [0081]     The P e  of each entity was determined in a range of pH from about 3 to 10, using approximately equally spaced pH values to ensure obtaining results both above and below the effective ionization constant (pK a   FLUX ) value for the entities as generally described by Avdeef, “Absorption and Drug Development,” Wiley Interscience, pp. 116-246 (2003). This approach for determining P e  is often referred to as the pK a   FLUX  method.  
         [0082]     pK a   FLUX  refers to the pH value where the resistance to transport across a permeation barrier is 50 percent due to the aqueous boundary layers and 50 percent due to the barrier. The donor solution samples, with each sample being about 50 micromolar (μM), were varied in pH, while the acceptor solutions had a consistent pH of about 7.4. As indicated above, the acceptor solutions contained a surfactant in order to mimic some of the function of serum proteins.  
         [0083]     When not being stirred, a PAMPA sandwich was formed and permitted to incubate in the GUT-BOX at about 23° C. for up to several hours in an atmosphere saturated in humidity and scrubbed free of oxygen and carbon dioxide. Preferably, incubation was performed for up to about four hours. As described above,  FIG. 10  shows a partial representation of exemplary donor and acceptor plates for a PAMPA sandwich. For example, the stirring members in  FIG. 10  can be magnetized flippers that are controlled by a magnetic stirrer in the GUT-BOX, which causes the members to rotate about a horizontal axis. A speed dial for the magnetic stirrer, as described above, can be calibrated in units of thickness of the expected boundary layer rather than as standard units such as rpm. For example, such a calibration was based on 36 P u  values of 14 different molecular entities at rotational speeds from about 49 to 622 rpm.  
         [0084]     After a permeation time in the GUT-BOX was reached, the PAMPA sandwich could then be separated and the donor and acceptor compartments studied for the amount of entity present. The amount of entity present was determined from UV measurements compared to UV spectra obtained from reference standards. The reference UV spectra were performed in a range from about 230 to 500 nanometers (nm). Moreover, mass balance was used to determine the amount of material retained by the porous support and DOUBLE-SINK GIT-0 lipid as generally described by Avdeef et al., Eur. J. Pharm. Sci., 14, pp. 271-280 (2001).  
         [0085]     Donor to acceptor compartment P e  was also determined as described above for a range of pH from 3 to 10 using approximately equally spaced pH values for the pK a   FLUX  method. The determination of P e  also accounted for the porous support area and its porosity. In particular, the support area of 0.3 centimeters squared (cm 2 ) was multiplied by the apparent porosity (ε a ) of the support, which was about 0.76, such as generally described by Nielsen et al., Eur. J. Pharm. Sci., 22, pp. 33-41 (2004). Accounting for support area and its apparent porosity ensures that the aqueous boundary layer thicknesses determined from the PAMPA would be comparable to assays using different supports of various sizes and porosities.  
         [0086]     Tables 1 to 5 includes the P u  values of 53 ionizable entities determined by the pK a   FLUX  method described above. These entities were each sufficiently lipophilic such that their intrinsic permeability coefficients (P o ) were nearly equal to or greater than P u , which is a requirement of the pK a   FLUX  method. The majority of the data in Tables 1 through 5 is from unstirred assays and those stirred at about 186 rpm. The P u  values of propranolol, desipramine, imipramine and verapamil were determined at five different speeds of 0, 49, 118, 186 and 622 rpm. Moreover, metoprolol and naproxen were characterized at four different speeds. Tamoxifen, chlorpromazine, indomethacin, itraconazole, ketoprofen, miconazole, probenecid and nifedipine were also studied in stirred solutions. The maximum speed used for these entities was 622 rpm.  
         [0087]     Again, several entities were studied in a buffer comprising about 20 percent acetonitrile. These entities are footnoted as “1” in Tables 1 through 5. Given the known fractional −⅙ power dependence of P u  on solution viscosity, the use of an acetonitrile cosolvent did not substantially affect the assays such as shown by chlorpromazine at 622 rpm, which was studied both with and without the cosolvent. Tables 1 through 5 are provided below with Table 1 at 0 rpm, Table 2 stirred at 49 rpm, Table 3 stirred at 118 rpm, Table 4 stirred at 186 rpm and Table 5 stirred at 622 rpm. Tables 1 through 5 also include the standard deviation (SD) of determined P u  values.  
                                                             TABLE 1                       Molecular       Daq           h       Entity   MW   (cm 2  s −1 )   P u     SD   (μm)                                4′N-Bu-3′-Me-ciprofloxacin   401.5   4.9 × 10 −6     23   3   2133       4′N-Et-3′-Me-ciprofloxacin   373.4   5.0 × 10 −6     53   28   945       4′N-Pr-3′-Me-ciprofloxacin   387.4   4.9 × 10 −6     40   24   1236       3-hydroxyphenylacetic acid   152.1   7.6 × 10 −6     50   12   1524       Acebutolol   336.4   5.3 × 10 −6     63   26   837       Aiprenolol   249.4   6.0 × 10 −6     32   6   889       Benzoic   122.1   8.4 × 10 −6     86   8   983       Chlorpromazine   318.9   5.4 × 10 −6     32   3   1713       Desipramine   266.4   5.9 × 10 −6     48   3   1227       Diclofenac   296.2   5.6 × 10 −6     41   5   1362       Diltiazem   378.1   5.0 × 10 −6     40   6   1244       Ergonovine   325.4   5.3 × 10 −6     25   4   2113       Flurbiprofen   244.3   6.1 × 10 −6     70   6   878       Gemfibrozil   250.0   6.0 × 10 −6     53   12   1135       Ibuprofen   206.3   6.6 × 10 −6     40   5   1666       Imipramine   280.4   5.7 × 10 −6     44   4   1293       Indomethacin   357.8   5.1 × 10 −6     32   1   1604       Ketoprofen   254.3   6.0 × 10 −6     37   3   1637       Lansoprazole   369.0   5.0 × 10 −6     35   17   1462       Metoprolol   267.4   5.9 × 10 −6     61   6   953       Nalidixic acid   232.2   6.2 × 10 −6     44   5   1429       Naproxen   230.3   6.3 × 10 −6     64   6   983       Naringenin   272.3   5.8 × 10 −6     39   6   1496       Nortriptyline   263.4   5.9 × 10 −6     60   11   991       Ondansetron   293.4   5.6 × 10 −6     59   10   949       Oxprenolol   265.4   5.9 × 10 −6     67   9   882       Phenazopyridine   213.2   6.5 × 10 −6     29   3   2264       Phenytoin   252.3   6.0 × 10 −6     26   4   2277       Pindolol   248.3   6.1 × 10 −6     28   11   2194       Piroxicam   331.4   5.3 × 10 −6     31   3   1688       Prazosin   383.4   5.0 × 10 −6     38   7   1305       Primaquine   259.4   5.9 × 10 −6     30   7   1992       Probenecid   285.4   5.7 × 10 −6     43   8   1336       Promethazine   284.4   5.7 × 10 −6     50   4   1147       Propranolol   259.3   5.9 × 10 −6     41   3   1455       Quinine   324.4   5.4 × 10 −6     24   2   2231       Salicylic acid   138.1   7.9 × 10 −6     37   7   2151       Timolol   316.2   5.4 × 10 −6     67   28   809       Verapamil   454.6   4.6 × 10 −6     46   3   994       Warfarin   308.3   5.5 × 10 −6     70   12   789                  
 
         [0088]    
       
         
               
               
               
               
               
               
               
             
           
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                   
               
               
                   
                 Molecular 
                   
                 Daq 
                   
                   
                 h 
               
               
                   
                 Entity 
                 MW 
                 (cm 2  s −1 ) 
                 P u   
                 SD 
                 (μm) 
               
               
                   
                   
               
             
             
               
                   
                 Desipramine 
                 266.4 
                 5.9 × 10 −6   
                 367 
                 27 
                 159 
               
               
                   
                 Imipramine 
                 280.4 
                 5.7 × 10 −6   
                 337 
                 33 
                 146 
               
               
                   
                 Metoprolol 
                 267.4 
                 5.9 × 10 −6   
                 177 
                 80 
                 335 
               
               
                   
                 Propranolol 
                 259.3 
                 5.9 × 10 −6   
                 369 
                 38 
                 160 
               
               
                   
                 Verapamil 
                 454.6 
                 4.6 × 10 −6   
                 383 
                 80 
                 130 
               
               
                   
                   
               
             
          
         
       
     
         [0089]    
       
         
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                   
                 TABLE 3 
               
               
                   
                   
               
               
                   
                   
               
               
                   
                 Molecular 
                   
                 Daq 
                   
                   
                 h 
               
               
                   
                 Entity 
                 MW 
                 (cm 2  s −1 ) 
                 P u   
                 SD 
                 (μm) 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Desipramine 
                 266.4 
                 5.9 × 10 −6   
                 747 
                 39 
                 78 
               
               
                   
                 Imipramine 
                 280.4 
                 5.7 × 10 −6   
                 786 
                 93 
                 69 
               
               
                   
                 Metoprolol 
                 267.4 
                 5.9 × 10 −6   
                 490 
                 237 
                 121 
               
               
                   
                 Naproxen 
                 230.3 
                 6.3 × 10 −6   
                 493 
                 65 
                 129 
               
               
                   
                 Propranolol 
                 259.3 
                 5.9 × 10 −6   
                 601 
                 80 
                 101 
               
               
                   
                 Verapamil 
                 454.6 
                 4.6 × 10 −6   
                 681 
                 31 
                 69 
               
               
                   
                   
               
             
          
         
       
     
         [0090]    
       
         
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 3 
               
               
                   
               
               
                   
               
               
                 Molecular 
                   
                 Daq 
                   
                   
                 h 
               
               
                 Entity 
                 MW 
                 (cm 2  s −1 ) 
                 P u   
                 SD 
                 (μm) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 2-naphthoic acid 
                 172.2 
                 7.2 × 10 −6   
                 595 
                 22 
                 121 
               
               
                 Alprenolol 
                 249.4 
                 6.0 × 10 −6   
                 1310 
                 104 
                 46 
               
               
                 Alprenolol 1   
                 249.4 
                 6.0 × 10 −6   
                 2530 
                 240 
                 24 
               
               
                 Amlodipine 
                 403.9 
                 4.8 × 10 −6   
                 1380 
                 25 
                 35 
               
               
                 Astemizole 
                 458.6 
                 4.6 × 10 −6   
                 746 
                 104 
                 61 
               
               
                 Chlorpromazine 
                 318.9 
                 5.4 × 10 −6   
                 1430 
                 88 
                 38 
               
               
                 Desipramine 
                 266.4 
                 5.9 × 10 −6   
                 801 
                 85 
                 73 
               
               
                 Diclofenac 
                 296.2 
                 5.6 × 10 −6   
                 1390 
                 353 
                 40 
               
               
                 Diltiazem 
                 378.1 
                 5.0 × 10 −6   
                 904 
                 168 
                 55 
               
               
                 Flurbiprofen 
                 244.3 
                 6.1 × 10 −6   
                 2260 
                 301 
                 27 
               
               
                 Gemfibrozil 
                 250.0 
                 6.0 × 10 −6   
                 1370 
                 69 
                 44 
               
               
                 Imipramine 
                 280.4 
                 5.7 × 10 −6   
                 1240 
                 94 
                 46 
               
               
                 Indomethacin 
                 357.8 
                 5.1 × 10 −6   
                 1040 
                 180 
                 49 
               
               
                 Indomethacin 1   
                 357.8 
                 5.1 × 10 −6   
                 926 
                 22 
                 55 
               
               
                 Itraconazole 1   
                 705.6 
                 3.7 × 10 −6   
                 1360 
                 184 
                 28 
               
               
                 Ketoprofen 
                 254.3 
                 6.0 × 10 −6   
                 1750 
                 539 
                 34 
               
               
                 Metoprolol 
                 267.4 
                 5.9 × 10 −6   
                 693 
                 64 
                 84 
               
               
                 Miconazole 1   
                 416.1 
                 4.8 × 10 −6   
                 1690 
                 243 
                 28 
               
               
                 Naproxen 
                 230.3 
                 6.3 × 10 −6   
                 1320 
                 375 
                 48 
               
               
                 Nicardipine 
                 479.5 
                 4.5 × 10 −6   
                 1250 
                 109 
                 36 
               
               
                 Ondansetron 
                 293.4 
                 5.6 × 10 −6   
                 6949 
                 396 
                 59 
               
               
                 Phenazopyridine 
                 213.2 
                 6.5 × 10 −6   
                 1340 
                 690 
                 48 
               
               
                 Pindolol 
                 248.3 
                 6.1 × 10 −6   
                 1440 
                 660 
                 42 
               
               
                 Primaquine 1   
                 259.4 
                 5.9 × 10 −6   
                 2470 
                 522 
                 24 
               
               
                 Probenecid 
                 285.4 
                 5.7 × 10 −6   
                 1030 
                 187 
                 55 
               
               
                 Promethazine 
                 284.4 
                 5.7 × 10 −6   
                 1240 
                 244 
                 46 
               
               
                 Promethazine 1   
                 284.4 
                 5.7 × 10 −6   
                 1440 
                 543 
                 40 
               
               
                 Propranolol 
                 259.3 
                 5.9 × 10 −6   
                 951 
                 154 
                 62 
               
               
                 Quinine 
                 324.4 
                 5.4 × 10 −6   
                 905 
                 58 
                 59 
               
               
                 Tamoxifen 1   
                 371.5 
                 5.0 × 10 −6   
                 1120 
                 234 
                 45 
               
               
                 Tiamdipine 
                 435.5 
                 4.7 × 10 −6   
                 951 
                 38 
                 49 
               
               
                 Timolol 
                 316.2 
                 5.4 × 10 −6   
                 1640 
                 206 
                 33 
               
               
                 Verapamil 
                 454.6 
                 4.6 × 10 −6   
                 697 
                 65 
                 66 
               
               
                 Verapamil 1   
                 454.6 
                 4.6 × 10 −6   
                 691 
                 91 
                 66 
               
               
                   
               
             
          
         
       
     
         [0091]    
       
         
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 3 
               
               
                   
               
               
                   
               
               
                 Molecular 
                   
                 Daq 
                   
                   
                 h 
               
               
                 Entity 
                 MW 
                 (cm 2  s −1 ) 
                 P u   
                 SD 
                 (μm) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Amiodarone 1   
                 172.2 
                 7.2 × 10 −6   
                 595 
                 22 
                 121 
               
               
                 Chlorpromazine 
                 318.9 
                 5.4 × 10 −6   
                 2940 
                 349 
                 18 
               
               
                 Chlorpromazine 1   
                 318.9 
                 5.4 × 10 −6   
                 2570 
                 742 
                 21 
               
               
                 Desipramine 
                 266.4 
                 5.9 × 10 −6   
                 1980 
                 314 
                 30 
               
               
                 Fluvoxamine 
                 318.3 
                 5.4 × 10 −6   
                 1520 
                 380 
                 36 
               
               
                 Gemfibrozil 1   
                 250.0 
                 6.0 × 10 −6   
                 1350 
                 197 
                 45 
               
               
                 Imipramine 
                 280.4 
                 5.7 × 10 −6   
                 2720 
                 220 
                 21 
               
               
                 Indomethacin 
                 357.8 
                 5.1 × 10 −6   
                 2910 
                 609 
                 18 
               
               
                 Itraconazole 1   
                 705.6 
                 3.7 × 10 −6   
                 2210 
                 254 
                 17 
               
               
                 Ketoprofen 
                 254.3 
                 6.0 × 10 −6   
                 1110 
                 122 
                 54 
               
               
                 Metoprolol 1   
                 267.4 
                 5.9 × 10 −6   
                 1520 
                 316 
                 39 
               
               
                 Miconazole 1   
                 416.1 
                 4.8 × 10 −6   
                 1520 
                 316 
                 31 
               
               
                 Naproxen 
                 230.3 
                 6.3 × 10 −6   
                 2040 
                 209 
                 31 
               
               
                 Probenecid 
                 285.4 
                 5.7 × 10 −6   
                 1280 
                 211 
                 44 
               
               
                 Propranolol 
                 259.3 
                 5.9 × 10 −6   
                 3110 
                 313 
                 19 
               
               
                 Protriptyline 
                 263.4 
                 5.9 × 10 −6   
                 2150 
                 518 
                 27 
               
               
                 Tamoxifen 1   
                 371.5 
                 5.0 × 10 −6   
                 980 
                 235 
                 51 
               
               
                 Terfenadine 1   
                 471.7 
                 4.5 × 10 −6   
                 2440 
                 85 
                 18 
               
               
                 Verapamil 
                 454.6 
                 4.6 × 10 −6   
                 3540 
                 523 
                 13 
               
               
                 Zimelidine 
                 317.2 
                 5.4 × 10 −6   
                 1670 
                 516 
                 32 
               
               
                   
               
             
          
         
       
     
         [0092]     Also listed in Tables 1 through 5 are aqueous diffusivity (D aq ) values at about 25° C., which can be approximated from the empirical formula of 
 
log  D   aq =−4.113−0.4609 (log  MW ) 
 
 This formula was generally described by Avdeef, “Absorption and Drug Development,” Wiley Interscience, pp. 116-246 (2003). The boundary layer thickness (h) in Tables 1 through 5 can be determined by Fick&#39;s second law of diffusion, which is  
       h   =       D   aq       P   u           
 
         [0093]      FIG. 11  shows six logarithm of P e  versus pH plots of ionizable acid and base molecular entities measured at different stirring speeds. Solid line curves were fitted to the measured points according to the equation 
 log  P   e =log P e   MAX −log(10 +(pH−pK     a       FLUX     )+ 1)  
 for monoprotic acids and the equation 
 log  P   e =log  P   e   MAX −log(10 −(pH−pK     a       FLUX     ) +1)  
 for monoprotic bases such as generally described by Avdeef et al., Eur. J. Pharm. Sci., 22, pp. 365-374 (2004) in which P e   MAX  relates to a value less than P e  given that boundary layer thicknesses cannot be entirely eliminated by stirring. 
 
         [0094]     The dotted horizontal lines on top of the solid line curves in  FIG. 11  indicate the actual values of P u . The dashed curves were calculated from knowledge of a true aqueous pK a  and a refined P o , which was based on a curve-fit according to an equation (s) similar to those above for monoprotic acids and bases. The tops of the dashed curves correspond to values of the logarithm of P o . The points in the horizontal solid line domains indicate transport that is almost entirely boundary layer limited. The points along the horizontal solid line domains also show sensitivity to the selected stirring speed.  
         [0095]     Furthermore,  FIG. 12  shows plots of the logarithm of P u  versus the logarithm of MW at 0, 186 and 622 rpm. For each of the stirring speeds, the data were fitted to the empirical equation 
 
log  P   u =log  D   aq −log  h   MEAN  
 
 from which the empirical formula describe above can be substituted in order to yield 
 
log  P   u =−4.113−0.4609 (log  MW )−log  h   MEAN  
 
 Thus, average boundary layer thicknesses (h MEAN ) can be determined based on a weighted regression analysis such that average thickness values of 1462 μm, 177 μm, 91 μm, 47 μm and 28 μm are based on stir speeds of 0 rpm, 49 rpm, 118 rpm, 186 rpm and 622 rpm, respectively. 
 
         [0096]     P u  values derived at various stirring speeds by using the pK a   FLUX  method, as described above, were also subjected to a hydrodynamic analysis using the equation 
 
P u =Kν α 
 
 in a logarithmic form. For example,  FIG. 13  provides a plot of the logarithm of P u  versus the logarithm of ν comprising 36 measurements based on 14 molecular entities studied at several different stirring speeds. The intercept in such a plot is the logarithm of the stirring efficiency factor (K) with the slope being the hydrodynamic factor (α). A regression analysis then describes the average hydrodynamic character of a stirred PAMPA sandwich. 
 
         [0097]     K was determined by the regression analysis in  FIG. 13  to be 23×10 −6  cm s −1  and α was determined to be 0.71. The value of α is close to the value 0.8 reported by Adson et al., J. Pharm. Sci., 84, pp. 1197-1204 (1995), although the PAMPA K factor is about 6 times higher than the previous maximum reported value. This result is significant as it means that for a given stirring speed, the thicknesses of the boundary layers in a PAMPA are dramatically less than in the most efficiently stirred Caco-2 type cell assay.  
         [0098]     In addition,  FIG. 14  shows the individual behavior of four different molecular entities that were studied at various stirring speeds. Due to the limited number of measured points for each of the molecular entities and the narrow range of values of the logarithm of ν, the shown fitting constrained a to an average value of about 0.71. For example, as shown in  FIG. 14 , the individual K values ranged from about 22×10 −6  cm s −1  for the entity desipramine to about 27×10 −6  cm s −1  for imipramine.  
         [0099]      FIG. 15  shows the relationship between h and ν, comparing the results from literature to those of this example using a device of the invention. As shown, the solid circles are based on testosterone data at 22° C. from Adson et al., J. Pharm. Sci., 84, pp. 1197-1204 (1995). The dashed line was calculated from the equation  
       h   =       (       D   aq     K     )     ⁢     v   α             
 using D aq  at a value of 5.0×10 −6  cm s −1 , K being 4.1×10 −6  cm s −1  and α at 0.8. The open circles represent testosterone at 37° C. from data taken by Karlsson et al., Int. J. Pharm., 7, pp. 55-64 (1991). The dotted curve in  FIG. 15  is based on D aq  at a value of 7.84×10 −6  cm s −1 , K equal to 0.57×10 −6  cm s −1  and α at 1. In view of the higher K value in the work of Adson et al., J. Pharm. Sci., 84, pp. 1197-1204 (1995), it appears that permeation from the donor plate with support comprising Caco-2 type cells to new and fresh acceptor plates every five minutes, which is generally referred to as the “break” sandwich procedure, yields a more efficient mixing model. 
 
         [0100]     The efficiency of break sandwich procedures can often produce an efficient mixing model as a rigorous sink state can be readily maintained so that the back flux of the molecular entity may be substantially eliminated. In addition, only the resistance of the boundary layer along the donor side of the permeation barrier can contribute to the kinetics related to mass transport. As a result, the solid circle boundary layer thicknesses are less than half of those of the open circles for any given stirring speed. The data for desipramine based on a PAMPA using a device of the invention are indicated by the square points fitted to a solid line curve with D aq  having a value of 5.9×10 −6  cm s −1 , K being 23×10 −6  cm s −1  and α at 0.71. As is evident from  FIG. 15 , the stirring efficiency using a device of the invention is significantly better than that reported in the literature.  
         [0101]     While the present invention has been described herein in conjunction with a preferred embodiment, a person of ordinary skill in the art, after reading the foregoing specification, will be able to effect changes, substitutions of equivalents and other alterations to the devices and methods that are set forth herein. Each embodiment described above can also have included or incorporated therewith such variations as disclosed with regard to any or all of the other embodiments. For example, an insert well or receiving vessel can include any type of stirring member that has been described above or any of those known in the art that are suitable for solution agitation. Similarly, for example, constrictions, retaining members or retaining means or a combination thereof can be included with any one of the embodiments described herein. It is therefore intended that protection granted by Letter Patent hereon be limited in breadth only by the definitions that are contained in the appended claims and any equivalents thereof.