Acoustic wave based particle agglomeration

Articles of manufacture, including an apparatus for acoustic wave based agglomeration, are provided. The apparatus may include a well and an acoustic wave device. The well may be configured to hold a suspension that includes a plurality of particles. The acoustic wave device may be configured to generate a plurality of acoustic waves. The plurality of acoustic waves inducing acoustic streaming within the suspension. The acoustic streaming agitating the suspension to form an agglomerate comprising at least a portion of the plurality of particles. Methods for acoustic wave based agglomeration are also provided.

TECHNICAL FIELD

The subject matter described herein relates generally to tissue engineering and more specifically to techniques for forming cell agglomerates.

BACKGROUND

A cell agglomerate may refer to a three-dimensional cell formation such as, for example, a spheroid of cells. Cell agglomerates may provide a more realistic representation of an in vivo environment than two-dimensional cell formations such as, for example, a monolayer of cells. As such, cell agglomerates may have a variety of clinical and research applications. For example, cancerous cell agglomerates that replicate tumors may be used in the development of treatments such as, for instance, chemotherapy, radiation therapy, and/or the like. In doing so, these cell agglomerates may provide an exemplary in vitro supplement and/or alternative to animal testing.

SUMMARY

Articles of manufacture, including apparatuses, and methods for acoustic wave based agglomeration are provided. An apparatus for acoustic wave based agglomeration may include a well and an acoustic wave device. The well may hold a suspension that includes a plurality of particles. The acoustic wave device may be configured to generate a plurality of acoustic waves. The plurality of acoustic waves may induce acoustic streaming within the suspension. The acoustic streaming may agitate the suspension to form an agglomerate comprising at least a portion of the plurality of particles.

In some variations, one or more features disclosed herein including the following features can optionally be included in any feasible combination. The agglomerate may be a 3-dimensional formation that includes at least the portion of the plurality of particles. The plurality of particles may be cells. The suspension may be a mixture of the plurality of particles and one or more fluids.

In some variations, the acoustic wave device may include a piezoelectric material configured to convert electric energy into the plurality of acoustic waves. The piezoelectric material may include a monocrystalline and/or a polycrystalline. In order to cause the acoustic wave device to generate the plurality of acoustic waves, between 50 milliwatts to 5.0 watts of electric power may be applied to the acoustic wave device.

In some variations, the acoustic wave device may be configured to generate the plurality of acoustic waves in one or more intermittent bursts. A length of the one or more intermittent bursts of acoustic waves may be between 1 second and 100 seconds. Each of the one or more intermittent bursts of acoustic waves may trigger a corresponding cycle of the acoustic streaming. The acoustic wave device may be configured to expose the suspension to between 1 cycle and 1000 cycles of the acoustic streaming. Each cycle of the acoustic streaming may be between 0.1 seconds per minute to 15 seconds per minute

In some variations, the acoustic wave device may be configured to operate in accordance with a duty ratio. The duty ratio may correspond to a proportion of total elapsed time during which the acoustic wave device is generating the plurality of acoustic waves. The duty ratio may be between 10% and 50%.

In some variations, the apparatus may further include a couplant material configured to transmit the plurality of acoustic waves from the acoustic wave device to the well. The acoustic wave device may be oriented such that the plurality of acoustic waves enters a bottom of the well at between an 5° angle of incidence and an 55° angle of incidence. The acoustic wave device may be oriented such that the acoustic streaming is induced at between ½ to ¾ of a distance between from a center of the well and an edge of the well.

A method for acoustic wave based agglomeration includes generating, by an acoustic wave device, a plurality of acoustic waves. The plurality of acoustic waves may induce acoustic streaming within a suspension comprising a plurality of particles. The suspension may be held in a well. The acoustic streaming may agitate the suspension to form an agglomerate that includes at least a portion of the plurality of particles

In some variations, one or more features disclosed herein including the following features can optionally be included in any feasible combination. The agglomerate may be a 3-dimensional formation that includes at least the portion of the plurality of particles. The plurality of particles may be cells. The suspension may be a mixture of the plurality of particles and one or more fluids.

In some variations, a piezoelectric material included in the acoustic wave device may convert electric energy into the plurality of acoustic waves. In order to cause the acoustic wave device to generate the plurality of acoustic waves, between 50 milliwatts and 3.0 watts of power may be applied to the piezoelectric material.

In some variations, the acoustic wave device may generate the plurality of acoustic waves in one or more intermittent bursts. A length of the one or more intermittent bursts of acoustic waves is between 1 second and 100 seconds. Each of the one or more intermittent bursts of acoustic waves may trigger a corresponding cycle of acoustic streaming. The acoustic wave device may expose the suspension to between 1 cycle and 1000 cycles of the acoustic streaming. Each cycle of the acoustic streaming may be between 0.1 seconds per minute to 15 seconds per minute.

In some variations, the acoustic wave device may be operated in accordance with a duty ratio corresponding to a proportion of total elapsed time during which the acoustic wave device is generating the plurality of acoustic waves. The duty ratio may be between 10% and 50%.

In some variations, the plurality of acoustic waves may be transmitted from the acoustic wave device to the well via a couplant material. The acoustic wave device may be oriented such that the plurality of acoustic waves enters a bottom of the well at between an 5° angle of incidence and an 55° angle of incidence. The acoustic wave device may be oriented such that the acoustic streaming is induced at between ½ to ¾ of a distance between a center of the well and an edge of the well.

DETAILED DESCRIPTION

Despite the many clinical and research applications for cell agglomerates, conventional techniques for forming cell agglomerates may not be viable for high volume production of quality cell agglomerates. For instance, cell agglomerates may be formed by stirring a cell culture with a spinner flask, but the resulting cell agglomerates may be inconsistent in size. Other techniques for forming cell agglomerates such as, for example, micromolding and hanging-drop, may yield cell agglomerates that are uniform in size. However, these agglomeration techniques may be cost prohibitive due to technical complexities such as, for example, the requirement for agarose gels cast from three-dimensional printed micromolds, microarrays made via photopolymerization, and/or micropatterns generated on an inverted polydimethyl-siloxane substrate. As such, in some example embodiments, cell agglomerates may be formed by at least exposing cells to ultrasonic energy such as, for example, acoustic waves and/or the like.

In some example embodiments, an apparatus for acoustic wave based agglomeration may include one or more wells for holding a suspension, which may be a heterogeneous mixture that includes a fluid and a plurality of solid particles such as cells. The apparatus for acoustic wave based agglomeration may further include an acoustic wave device configured to generate a plurality of acoustic waves. The acoustic wave device may include a piezoelectric material such as, for example, a monocrystalline (e.g., lithium niobate, quartz, lithium tantalate, langasite, and/or the like), a polycrystalline (e.g., ceramic and/or the like), and/or the like. As such, the acoustic wave device may generate the plurality of acoustic waves as a response to being subject to an electric field. The plurality of acoustic waves generated by the acoustic wave device may be delivered to the one or more wells via a couplant material configured to enable the transmission of ultrasonic energy such as, for example, acoustic waves and/or the like. The plurality of acoustic waves may generate, within each of the one or more wells, a vortex that causes the suspended particles (e.g., cells) to form agglomerations such as, for example, spheroids and/or the like. It should be appreciated that the use of acoustic waves may produce uniformly sized cell agglomerations that are substantially (e.g., 15 times) larger than cell agglomerations formed using conventional agglomeration techniques. These larger cell agglomerations may be more viable test specimen than the smaller cell agglomerations generated using conventional agglomeration techniques.

FIGS.1A-Cdepict an apparatus100for acoustic wave based agglomeration, in accordance with some example embodiments. Referring toFIGS.1A-C, the apparatus100may include an acoustic wave device120. The apparatus100may further include one or more wells including, for example, a well115. The well115may be configured to hold a suspension150, which may be a heterogeneous mixture that includes a plurality of solid particles. For instance, the solid particles may be a biological material such as cells and/or a nonbiological material. It should be appreciated that the well115may be any type of receptacle, container, and/or reservoir. Furthermore, as shown inFIG.1A, the well115may be part of a well plate110that includes a plurality of individual wells. Here, it should be appreciated that the well plate110may include any number of wells including, for example, 24 wells, 48 wells, and/or the like. The well plate110including the well115may be coupled with a couplant material140. For instance, the well plate110including the well115may be in contact with the couplant material140and/or at least partially submerged within the couplant material140.

In some example embodiments, the acoustic wave device120may include a piezoelectric material such as, for example, a monocrystalline (e.g., lithium niobate, quartz, lithium tantalate, langasite, and/or the like), a polycrystalline (e.g., ceramic and/or the like). For instance, as shown inFIGS.1A-C, the acoustic wave device120may include one or more monocrystalline and/or polycrystalline plates. The acoustic wave device120may be configured to operate at 2.134 megahertz (or a different frequency) in order to optimize the formation of an agglomerate155within the well115. As shown inFIGS.1A-C, the acoustic wave device120may include wiring125, which may supply an electric current to the piezoelectric material included in the acoustic wave device120. The acoustic wave device120may generate a plurality of acoustic waves160when the piezoelectric material included in the acoustic wave device120converts electric energy into mechanical energy in the form of acoustic waves such as, for example, surface acoustic waves, Lamb waves, flexural waves, thickness mode vibrations, mixed-mode waves, longitudinal waves, shear mode vibrations, bulk wave vibrations, and/or the like.

According to some example embodiments, the acoustic waves160may be burst waves generated using pulse width modulation (PWM). As such, the suspension150in the well115may be subject to intermittent acoustic waves instead of constant acoustic waves. In order to generate burst waves, the power that is input into the acoustic wave device110(e.g., via the wiring125) may alternate between zero and a constant amplitude level. The use of burst waves may reduce overall power and the concomitant risk of overheating the suspension150. For instance, when the suspension150is subject to intermittent acoustic waves over a period of 10 minutes, the temperature of the suspension150remained between 23° C. and 26° C. As the agglomerate155may be formed from living cells, maintaining the temperature of the suspension150may be critical for preserving the viability of the agglomerate155. High temperatures (e.g., in excess of 40° C.) may cause cellular death.

The acoustic waves160may be delivered to the well150via the couplant material140. As noted, the couplant material140may be configured to enable the transmission of ultrasonic energy such as, for example, the acoustic waves160generated by the acoustic wave device110. According to some example embodiments, the couplant material140may include water and glycerol, although the couplant material140may have a different composition.

The acoustic waves160generated by the acoustic device110may induce acoustic streaming162in the suspension150. The acoustic streaming162may be the non-laminar and/or turbulent fluid flow that result from variations in a density of the suspension150and variations in a velocity of the suspension150due to agitation from the acoustic waves160generated by the acoustic wave device110. As shown inFIG.1C, the acoustic streaming162may cause the formation of a vortex164within the suspension150. It should be appreciated that the vortex164may be a region in the suspension150in which the suspension150revolves around a straight axis and/or a curved axis. The vortex164may cause the particles (e.g., cells) in the suspension150to agglomerate, thereby forming the agglomerate155. For instance, the vortex164may cause a shear-induced migration of the solid particles in the suspension150, which may concentrate at least a portion of these solid particles toward a center of the well115. The agglomerate155may be a three-dimensional formation of the solid particles included in the suspension150. For example, the agglomerate155may be a spheroid of cells and/or the like.

In some example embodiments, the apparatus100may include one or more mechanisms for orienting the acoustic wave device120relative to the well115. As shown inFIG.1A, the acoustic wave device120may be deposed on a base plate130configured to maintain the orientation of the acoustic wave device120relative to a base of the well115. The base plate130may be formed from any suitable material including metals such as, for example, aluminum (Al) and/or the like. Moreover, the base plate130may be fabricated to include and/or support one or more staggered ramps including, for example, a ramp160. The one or more ramps (e.g., the ramp160) may be formed from any suitable material including, for example, glass and/or the like.

The orientation of the acoustic device120relative to the well115may determine the angle of incidence θ at which the acoustic waves160enters the well115and into the suspension150. For instance, as shown inFIG.1C, the one or more staggered ramps (e.g., the ramp160) may position the acoustic wave device120(e.g., the monocrystalline and/or polycrystalline plates) at an angle θ (e.g., θ=20°) with respect to the base of the well115. The angle θ may correspond to the angle of incidence θ at which the acoustic waves160enters the well115and into the suspension150. Alternatively and/or additionally, the orientation of the acoustic device120relative to the well115may also determine the radial location x of the acoustic streaming162. As shown inFIG.1C, the radial location x may corresponding a distance between the acoustic streaming162in the suspension150and a center of the well115.

In some example embodiments, the formation of the agglomerate155may depend on a number of parameters including, for example, the angle of incidence θ and/or the radial location x. Alternatively and/or additionally, the formation of the agglomerate155may also depend on an input power E applied to the acoustic wave device110, a duty ratio D of the acoustic waves160, a total exposure time Tdto the acoustic waves160, a length of a burst period Tbof the acoustic waves160, a concentration Npof the solid particles within the suspension150, and/or a length of each exposure cycle Tito the acoustic streaming162. Table 1 below summarizes these parameters. It should be appreciated that these parameters may affect the formation of the agglomerate155including, for example, a size of the agglomerate155, a location of the agglomerate155within the well115, and/or a location of unagglomerated solid particles within the well115.

FIGS.2A-Edepicts a relationship between the angle of incidence θ and the formation of the agglomerate155, in accordance with some example embodiments. Referring toFIGS.1A-Cand2A-E, the formation of the agglomerate155may be affected by varying the angle of incidence θ, for example, over a range between 0° and 45° (e.g., 0°<θ<45°). As shown inFIGS.2A-E, the formation of agglomerate155may vary at different angles of incidence including, for example, 20°, 25°, and 30°, while the other parameters are held constant. For example, the radial location x may be fixed at 5.0 millimeters, the input power E may be fixed at 3.0 watts, the duty ratio D may be fixed at 100%, the total exposure time Tdmay be fixed to 30 seconds, and the concentration Npmay be fixed to 1.0×104particles per milliliter.

To further illustrate,FIGS.2A-Bdepict graphs illustrating the formation of the agglomerate155at different angles of incidence θ, in accordance with some example embodiments. Referring toFIGS.2A-B, the formation of the agglomerate155may be quantified based on a ratio

ApAw,
wherein Apmay correspond to a cross-sectional area occupied by the agglomerate155and Awmay correspond to a cross-sectional area of the well115.FIG.2Adepicts a graph200illustrating a change in the ratio

ApAw
at different angles of incidence θ (e.g., 20°, 25°, and 30°) over the duration of the total exposure time Td.

ApAw
Meanwhile,FIG.2Bdepicts a graph250illustrating the relationship between me ratio and the angle of incidence θ.FIGS.2C-Edepict images of the agglomerate155formed at different angles of incidence θ including, for example, 20°, 25°, and 30°. For example,FIG.2Cdepicts an image of the agglomerate155formed at an 20° angle of incidence,FIG.2Ddepicts an image of the agglomerate155formed at an 25° angle of incidence, andFIG.2Edepicts an image of the agglomerate155formed at an 30° angle of incidence.

The formation of the agglomerate155may be optimized when the angle of incidence θ maximizes a portion of the acoustic waves160entering the well115and/or minimizes a portion of the acoustic waves160that fails to enter the well115. As shown inFIGS.2A-E, the formation of the agglomerate155may be optimized when the angle of incidence θ is between 20° and 30° (e.g., 20°≤θ≤30°). For example, the size of the agglomerate155that is formed when the angle of incidence θ is between 20° and 30° may be larger because the magnitude of the acoustic streaming162may be maximized when the angle of incidence θ is between 20° and 30°. If the angle of incidence θ is too small (e.g., θ<15°), the incoming acoustic waves160may be nearly perpendicular to the surface of the suspension150within the well115. This may give rise to sufficient acoustic pressure against the surface of the suspension150to cause the suspension150to atomize. When the angle of incidence θ is too large (e.g., θ>35°), the acoustic waves160may merely graze and/or even bypass the well115such that the resulting acoustic streaming162may be too weak to generate the vortex164.

FIGS.3A-Cdepicts a relationship between the radial location x and the formation of the agglomerate155, in accordance with some example embodiments. As noted, the radial location x may correspond to a distance between the acoustic streaming162in the suspension150and a center of the well115. Referring toFIGS.1A-Cand3A-F, the formation of the agglomerate155may be affected by varying the radial location x. As shown inFIGS.3A-F, the formation of agglomerate155may vary at different radial locations x including, for example, 0 millimeter, 2 millimeters, 5.0 millimeters, and 7.5 millimeters, while the other parameters are held constant. For example, the angle of incidence θ may be fixed at 20°, the input power E may be fixed at 3.0 watts, the duty ratio D may be fixed at 100%, the total exposure time Tdmay be fixed at 30 seconds, and the concentration Npmay be fixed at 1.0×104particles per milliliter.

To further illustrate,FIGS.3A-Bdepict graphs illustrating the formation of the agglomerate155at different radial locations x, in accordance with some example embodiments. Referring toFIGS.3A-B, the formation of the agglomerate155may be quantified based on a ratio

ApAw,
wherein Apmay correspond to a cross-sectional area occupied by the agglomerate155and Awmay correspond to a cross-sectional area of the well115.FIG.3Adepicts a graph300illustrating a change in the ratio

ApAw
at different radial locations x (e.g., 0 millimeter, 2.5 millimeters, 5.0 millimeters, and 7.5 millimeters) over the duration of the total exposure time Td. Meanwhile,FIG.3Bdepicts a graph350illustrating the relationship between the ratio

ApAw
and the radial location x.FIGS.3C-Fdepict images of the agglomerate155formed at different radial locations x including, for example, 0 millimeter, 2.5 millimeters, 5.0 millimeters, and 7.5 millimeters. For example,FIG.3Cdepicts an image of the agglomerate155that is formed when the radial location x is 0 millimeter,FIG.3Ddepicts an image of the agglomerate155that is formed when the radial location x is 2.5 millimeters,FIG.3Edepicts an image of the agglomerate155that is formed when the radial location x is 5.0 millimeters, andFIG.3Fdepicts an image of the agglomerate155that is formed when the radial location x is 7.5 millimeters.

As shown inFIGS.3A-F, the formation of the agglomerate155may be optimized when the radial location x is between ½ and ¾ of the distance between a center of the well115and an edge of the well115, which may correspond to being between 2.5 millimeters and 5.0 millimeters (e.g., 2.5 millimeters≤x≤5.0 millimeters). Notably, the particles forming the agglomerate155may be bound more loosely when the radial location x is 2.5 millimeters whereas the particles forming the agglomerate155may be bound more tightly when the radial location x is 5.0 millimeters. For instance, the agglomerate155shown inFIG.3Emay be better defined than the agglomerate155shown inFIG.3D, indicating an increase in the stability of the agglomerate155when the acoustic streaming162is located farther away from the center of the well115then when the acoustic streaming162is located closer towards the center of the well115. It should be appreciated acoustic streaming near the center of the well115may induce an upwelling of the suspension150that tends to destabilize the agglomerated155and cause the formation of the less defined agglomerate155shown inFIG.3D.

FIGS.4A-Edepicts a relationship between the duty ratio D, the length of the burst period Tb, the input power E, and the formation of the agglomerate155, in accordance with some example embodiments. As used herein, the duty ratio D may correspond to a proportion (e.g., percentage) of total elapsed time during which the acoustic wave device110may be generating the acoustic waves160and subjecting the suspension150to the acoustic streaming162. For instance, when the duty ratio D is 75%, the acoustic wave device110may be generating the acoustic waves160and subjecting the suspension150to the acoustic streaming162during 75% of the total elapsed time. Alternatively and/or additionally, the acoustic wave device110may be generating the acoustic waves160continuously and constantly subjecting the suspension150to the acoustic streaming162, when the duty ration D is 100%.

As noted, the acoustic waves160may be burst waves generated using pulse width modulation. Burst waves may reduce power and the concomitant risk of overheating the suspension150. In some example embodiments, the length of the burst period Tbmay correspond to a duration of each burst of the acoustic waves160. The length of the burst period Tbmay determine whether the acoustic waves160generated by the acoustic device110is sufficient to induce the acoustic streaming162within the well115and cause the formation of the agglomerate155.

Referring toFIGS.1A-Cand4A-E, the formation of agglomerate155may vary at different duty ratios D including, for example, 25%, 50%, and 75%. The formation of the agglomerate155may also vary at different burst periods Tbincluding, for example, 2 milliseconds, 20 milliseconds, and 200 milliseconds. Alternatively and/or additionally, the formation of the agglomerate1155may also vary at different input power E including, for example, 0.75 watts and 1.5 watts. It should be appreciated that other parameters that may affect the formation of the agglomerate155may be held constant. For example, the angle of incidence θ may be fixed at 20°, the radial location x may be fixed at 5.0 millimeters, and the concentration Npmay be fixed to 1.0×104particles per milliliter.

To further illustrate,FIGS.4A-Cdepict graphs illustrating the formation of the agglomerate155at different duty ratios D, lengths of burst period Tb, and/or input powers E, in accordance with some example embodiments.FIG.4Adepicts a graph400illustrating the formation of the agglomerate155over the duration of the total exposure time Tdwhen the suspension150is subject to different combinations of duty ratios D and input powers E. For example, the formation of the agglomerate155may be quantified based on a ratio

ApAw,
wherein Apmay correspond to a cross-sectional area occupied by the agglomerate155and Awmay correspond to a cross-sectional area of the well115. The graph400plots the different values of the ratio

ApAw
that are observed when the input power E is 0.75 watts and the duty ratio D is 25%, when the input power E is 1.5 watts and the duty ratio D is 25%, and when the input power E is 1.5 watts and the duty ratio D is 50%.

FIG.4Bdepicts a graph410illustrating the formation of the agglomerate155at various combinations of duty ratios D and lengths of burst period Tbwhile the input power E is held constant at 0.75 watts. Meanwhile,FIG.4Cdepicts a graph420illustrating the formation of the agglomerate155at various combinations of duty ratios D and lengths of burst period Tbwhile the input power E is held constant at 1.5 watts.FIGS.4D-Fdepicts images of the agglomerate155formed at different combinations of input power E and duty ratios D. For example,FIG.4Ddepicts the agglomerate155that is formed when the input power E is 0.75 watts and the duty ratio D is 25%,FIG.4Edepicts the agglomerate155that is formed when the input power E is 1.5 watts and the duty ratio D is 25%, andFIG.4Fdepicts the agglomerate155that is formed when the input power E is 1.5 watts and the duty ratio D is 50%.

Referring toFIGS.4B-F, the agglomerate155may form at select combinations of the duty ratio D, the length of the burst period Tb, and the input power E. For instance, when the input power E is 0.75 watts, a duty ratio D of 25% and a burst period Tbof 20 milliseconds may be required to form the agglomerate155. Alternatively and/or additionally, when the input power E is 1.5 watts, a burst period Tbof 20 milliseconds and a duty ratio D of either 25% or 50% may be required to form the agglomerate155. Other combinations of duty ratios D, burst periods Tb, and input powers E may not produce the agglomerate155. For instance, a too short burst period Tb(e.g., 2 milliseconds) may not induce the acoustic streaming162, which may be necessary to form the agglomerate155. A lengthy burst period Tb(e.g., 200 milliseconds) may also prevent the formation of the agglomerate155by causing an excessive dispersion of the solid particles within the suspension150and/or even portions of the suspension155to be jetted from the well115.

FIGS.5A-Edepicts the relationship between the length of the burst period Tband the formation of the agglomerate155, in accordance with some example embodiments. As noted, the formation of the agglomerate155may be affected by varying the length of the burst period Tb. Here,FIGS.5A-Eillustrates the formation of the agglomerate155at different burst periods Tbincluding, for example, 12 milliseconds, 16 milliseconds, 20 milliseconds, and 24 milliseconds while other parameters are held constant. For example, the angle of incidence θ may be fixed at 20°, the radial location x may be fixed at 5.0 millimeters, the input power E may be fixed at 1.5 watts, the duty ratio D may be fixed at 50%, the total exposure time Tdmay be fixed to 30 seconds, and the concentration Npmay be fixed to 1.0×104particles per milliliter.

To further illustrate,FIGS.5A-Bdepict graphs illustrating the formation of the agglomerate155with different burst periods Tb, in accordance with some example embodiments. Referring toFIGS.5A-B, the formation of the agglomerate155may be quantified based on a ratio

ApAw,
wherein Apmay correspond to a cross-sectional area occupied by the agglomerate155and Awmay correspond to a cross-sectional area of the well115.FIG.5Adepicts a graph500illustrating a change in the ratio

ApAw
at different length burst periods Tb(e.g., 16 milliseconds, 20 milliseconds, and 24 milliseconds) over the duration of the total exposure time Td. Meanwhile,FIG.2Bdepicts a graph550illustrating the relationship between the ratio ratio

ApAw
and the length of the burst period Tb.FIGS.5C-Edepict images of the agglomerate155formed at different length burst periods Tbincluding, for example, 16 milliseconds, 20 milliseconds, and 24 milliseconds. For example,FIG.5Cdepicts an image of the agglomerate155formed with a 16-millisecond long burst period Tb,FIG.5Ddepicts an image of the agglomerate155formed with a 20-millisecond long burst period Tb, andFIG.5Edepicts an image of the agglomerate155formed with a 24-millisecond long burst period Tb.

As shown inFIGS.5A-E, the formation of the agglomerate155may be optimized when the length of the burst period Tbis 16 milliseconds. That is, subjecting the suspension150to 16-millisecond long bursts of the acoustic waves160may yield a larger, more cohesive agglomerate155. By contrast, the agglomerate155may fail to form when the length of the burst period Tbis too short (e.g., 12 milliseconds) because a too short burst period Tbmay not induce the acoustic streaming162required to form the agglomerate155. The agglomerate155may also fail to form when the length of the burst period Tbis too long (e.g., 24 milliseconds) because a too long burst period Tbmay over agitate the suspension150, thereby causing an excessive dispersion of the solid particles within the suspension150and/or even portions of the suspension155to be jetted from the well115.

FIG.6A-Gdepicts the relationship between the concentration Npand the formation of the agglomerate155, in accordance with some example embodiments. As used herein, the concentration Npmay correspond to a proportion of solid particles (e.g., cells) in the suspension150. Referring toFIGS.1A-Cand6A-E, the formation of agglomerate155may vary at different concentration Npincluding, for example, 1.0×103particles per milliliter, 5.0×103particles per milliliter, 1.0×104particles per milliliter, 5.0×104particles per milliliter, and 1.0×10′ particles per milliliter while the other parameters are held constant. For example, the radial location x may be fixed at 5.0 millimeters, the input power E may be fixed at 3.0 watts, the duty ratio D may be fixed at 50%, the total exposure time Tdmay be fixed to 30 seconds, and the length of the burst period Tbmay be fixed to 16 milliseconds.

To further illustrate,FIGS.6A-Bdepict graphs illustrating the formation of the agglomerate155at different concentrations Np, in accordance with some example embodiments. Referring toFIGS.6A-B, the formation of the agglomerate155may be quantified based on a ratio

ApAw,
wherein Apmay correspond to a cross-sectional area occupied by the agglomerate155and Awmay correspond to a cross-sectional area of the well115.FIG.6Adepicts a graph600illustrating a change in the ratio

ApAw
at different concentrations Np(e.g., 5.0×103particles per milliliter, 1.0×104particles per milliliter, and 5.0×104particles per milliliter) over the duration of the total exposure time Td. Meanwhile,FIG.6Bdepicts a graph650illustrating the relationship between the ratio ratio

ApAw
and the concentration Np.FIGS.6C-Gdepict images of the agglomerate155formed at different concentration Npincluding, for example, 1.0×103particles per milliliter, 5.0×103particles per milliliter, 1.0×104particles per milliliter, 5.0×104particles per milliliter, and 1.0×105particles per milliliter. For example,FIG.6Cdepicts an image of the agglomerate155that is formed when the concentration Npis 1.0×103particles per milliliter,FIG.6Ddepicts an image of the agglomerate155that is formed when the concentration Npis 5.0×103particles per milliliter,FIG.6Edepicts an image of the agglomerate155that is formed when the concentration Npis 1.0×104particles per milliliter,FIG.6Fdepicts an image of the agglomerate155that is formed when the concentration Npis 5.0×104particles per milliliter, andFIG.6Gdepicts an image of the agglomerate155that is formed when the concentration Npis 1.0×105particles per milliliter.

As shown inFIGS.6A-G, higher concentrations Npdid not necessarily yield a larger and/or more cohesive agglomerate155. For instance, as shown inFIG.6G, a loosely bound agglomerate155may be formed when the concentration Npis high (e.g., Np=1.0×105particles per milliliter). Meanwhile, the formation of the agglomerate155may be optimized at intermediate concentrations Npincluding, for example, 5.0×103particles per milliliter and 1.0×104particles per milliliter. Notably, the agglomerate155that is formed when the concentration Npis 1.0×104particles per milliliter may be the most cohesive and well-defined.

FIGS.7A-Cdepicts a relationship between the length of the exposure cycles Tiand the formation of the agglomerate155, in accordance with some example embodiments. As noted, the suspension150may be subject to intermittent bursts of acoustic waves160. Meanwhile, the acoustic waves160may induce the acoustic streaming162in the suspension150. Accordingly, the length of the exposure cycle Timay correspond to the duration of the period of time during which the suspension150is exposed to the acoustic streaming162.

Referring toFIGS.1A-Cand7A-E, the formation of the agglomerate155may be affected by varying the length of the exposure cycles Ti, for example, between 3 seconds per minute and 10 seconds per minute, while the other parameters are held constant. For example, the angle of incidence θ may be fixed at 20°, the radial location x may be fixed at 5.0 millimeters, the input power E may be fixed at 3.0 watts, the duty ratio D may be fixed at 50%, the total exposure time Tdmay be fixed to 10 minutes, the length of the burst period Tbmay be fixed to 16 milliseconds, and the concentration Npmay be fixed to 1.0×104particles per milliliter.

To further illustrate,FIG.7Adepicts a graph700illustrating the formation of the agglomerate155with different lengths exposure cycles Ti, in accordance with some example embodiments. As shown inFIG.7A, the formation of the agglomerate155may be quantified based on a ratio

ApAw,
wherein Apmay correspond to a cross-sectional area occupied by the agglomerate155and Awmay correspond to a cross-sectional area of the well115. The graph700plots the different values of the ratio

ApAw
that are observed over the course of the total exposure time Tdwhen the suspension150is subject to different lengths exposure cycles Tiincluding, for example, 3 seconds per minute and 10 seconds per minute.FIGS.7B-Cdepicts images of the agglomerate155formed at different lengths exposure cycles Ti. For example,FIG.7Bdepicts the agglomerate155that is formed when the suspension150is exposed to the acoustic streaming162for 3 seconds every minute whileFIG.7Cdepicts the agglomerate150that is formed when the suspension150is exposed to the acoustic streaming162for 10 seconds per minute. As shown inFIGS.7A-C, the formation of the agglomerate155may be optimized when the suspension150is subject to shorter exposure cycles Ti(e.g., Ti=3 seconds per minute).

FIG.8depicts a flowchart illustrating a process800for acoustic wave based agglomeration, in accordance with some example embodiments. Referring toFIGS.1-8, the process700may be performed by the apparatus100.

At802, one or more parameters for acoustic wave based agglomeration may be determined. In some example embodiments, the apparatus100may be configured to generate the acoustic waves160, which may induce the acoustic streaming162within the suspension150and cause the formation of the agglomerate155. As noted, the agglomerate155may be a three-dimensional formation of living cells. The parameters for generating the agglomerate155may include the angle of incidence θ of the acoustic waves160, the radial location x of the acoustic streaming162, the input power E applied to the acoustic wave device110, the duty ratio D of the acoustic waves160, the total exposure time Tdto the acoustic waves160, the length of a burst period Tbof the acoustic waves160, and/or the concentration Npof the solid particles within the suspension150.

According to some example embodiments, the formation of the agglomerate155may be optimized when the angle of incident θ is between 5° and 55° from a bottom of the well115, the radial location x is ½ to ¾ of the distance between a center of the well115and an edge of the well115, the input power E is intermittent at 50 milliwatts to 5.0 watts, the duty ratio D is between 10% and 50%, the length of the burst period Tbis between 1 second to 100 seconds, the length of the burst cycle Tiis between 0.1 seconds per minute to 15 seconds per minute, and the total exposure time Tdis 1 cycle to 1000 cycles.

At804, the apparatus100may form the agglomerate155by at least generating and delivering, in accordance with the one or more parameters, a plurality of acoustic waves to a well including a suspension containing a plurality of solid particles. For example, the acoustic wave device110may generate the plurality of acoustic waves160, which may be delivered to the well115via the couplant material140. The acoustic waves160may induce, within the suspension150held in the well115, the acoustic streaming162. The acoustic streaming162may generate the vortex164, which may a shear-induced migration of the solid particles in the suspension150. The agglomerate155may be formed when the vortex164cause at least a portion of the solid particles to concentrate toward a center of the well115.