G. D.
Skotis‡
a,
D. R. S.
Cumming‡
a,
J. N.
Roberts‡
b,
M. O.
Riehle‡
b and
A. L.
Bernassau‡
*a
aSchool of Engineering, University of Glasgow, Glasgow, G12 8LT, UK. E-mail: Anne.Bernassau@glasgow.ac.uk
bCentre for Cell Engineering, Institute for Molecular, Cell and Systems Biology, CMVLS, University of Glasgow, Glasgow G12 8QQ, UK
First published on 4th December 2014
Advances in diagnostics, cell and stem cell technologies drive the development of application-specific tools for cell and particle separation. Acoustic micro-particle separation offers a promising avenue for high-throughput, label-free, high recovery, cell and particle separation and isolation in regenerative medicine. Here, we demonstrate a novel approach utilizing a dynamic acoustic field that is capable of separating an arbitrary size range of cells. We first demonstrate the method for the separation of particles with different diameters between 6 and 45 μm and secondly particles of different densities in a heterogeneous medium. The dynamic acoustic field is then used to separate dorsal root ganglion cells. The shearless, label-free and low damage characteristics make this method of manipulation particularly suited for biological applications. Advantages of using a dynamic acoustic field for the separation of cells include its inherent safety and biocompatibility, the possibility to operate over large distances (centimetres), high purity (ratio of particle population, up to 100%), and high efficiency (ratio of separated particles over total number of particles to separate, up to 100%).
Ultrasonic forces are non-invasive and can effectively manipulate cells for applications such as medium exchange,16 sample concentration,17–19 sorting,15,20 enhanced bio-detection and immuno-assays. Achieving cell separation21 utilizing ultrasonic manipulation by frequency sweeping11,22 has been previously demonstrated; however, this method has several critical disadvantages. Firstly, unstable forces are generated which leads to differences in the movement of individual trapped particles of the same size or property.23,24 Secondly, this method exclusively allows small particle displacement, which in turn limits sorting efficiency. Thirdly, frequency sweep sorting inherently lacks flexibility because the frequencies that can be used are limited by the types and dimensions of the transducers. Finally, the dimensional properties of the whole resonator may pose some constraints on the frequency regime.
An alternative to manipulating acoustic frequency is to control the signal phase; it has been demonstrated that shifting the phase of acoustic travelling waves can be used to control the position of micro-particles suspended in an aqueous medium.25 When two opposing transducers are excited, a linear interference pattern of nodes and antinodes is formed in the interstitial media. The micro-particles are trapped at the minima of the potential acoustic energy density.26 Electronically shifting the excitation phase of one of the transducers, with respect to the other, proportionally translates the linear interference pattern in the direction of the added phase delay. The shift of the node position translates to a change in the position of the trapped micro-particles.27,28
The new technique devised utilizes a dynamic acoustic field (DAF) with a time-varying phase delay between two opposing travelling waves that results in the separation of particles or cells over large distances (of the order of centimetres). The method shows a high degree of separation selectivity and throughput, making it suitable for applications such as cell sorting. The forces generated by this method are very stable,23 allowing better spatial separation (improved control and manipulation) of particles and cells to be achieved and maintained compared to results realized using frequency sweeping. This ultimately results in separation of sub-populations in the sample volume with much higher purity.
In this paper, we demonstrate that the flow-less DAF method can be used to separate particles within a sample volume depending on their size or density. We also study the discriminative ability of the method for particles of different sizes or densities. The application of DAF to primary pig dorsal root ganglion neurons as a contact-less means of separating these neurons from debris and smaller cells, which results from tissue digestion, is demonstrated.
The technique relies on a repeated cycling pattern of the phase difference between two excited transducers from 0° to 360°. Within each cycle, the phase is swept completely through 360° over a time tramp and then allowed to rest for a period trest before commencing the next cycle. The interplay between the rate at which the phase is swept and the length of the rest time is at the core of the separation technique. During tramp, under the correct conditions, the particles of interest experience a strong acoustic force compared to the viscous force.
For a system with particles trapped in one of many nodes, N, the particles of interest closely follow the node that traps them and travel from the initial position of the node Ni to the initial position of the next node Ni+1 (Fig. 2 and 3). This controlled manipulation occurs since a phase shift of 360° moves each node exactly one integer node position, a distance Λ (Fig. 1). If at the end of the tramp period, the smaller particles have not travelled more than halfway (Fig. 2 and 3) from their initial position of Ni to the next node position Ni+1, they will relax to their starting position during trest, whereas the particles of interest, which have travelled past the midpoint Ni and Ni+1, will relax towards the next node position Ni+1.
The interplay between acoustic force and viscous drag force is at the heart of the discriminating ability of the DAF method with trest serving as an equilibrating interval, during which particles settle at their nearest nodes before the next cycle begins. Assuming the length of tramp has been selected correctly, the best choice of trest to achieve cell or particle discrimination depends on the balance between the acoustic force, Fa, eqn (4), and the viscous force, Fv, eqn (6). trest and tramp were measured for different sizes of particles, by applying a step change of 180° in phase to one of the transducers.25 In water, polystyrene particles of 6, 10 and 45 μm diameters, respectively, require a time delay of 5, 2 and 0.5 s, respectively, to reach their equilibrium positions. This serves as the basis to establish the timescale for trest and tramp required to discriminate between particles during the experiments. The DAF method can then be optimized to achieve the optimum separation performance in specific applications. These optimum values of tramp and trest are dependent on the viscosity of the medium, as well as the density and size of the particles.
The equation of motion of a particle labelled by its position r(t) is given by:
![]() | (1) |
F tot is the sum of Fa and Fv, m is the mass of the particle, and a is the acceleration as a function of particle position r and the relative particle velocity v at time t.
These equations of motion are integrated step by step using the Verlet algorithm,30,31eqn (2) and (3), to produce the movement of the particles.
r(t + Δt) = 2r(t) − r(t − Δt) + a(t)Δt2 | (2) |
![]() | (3) |
The computer program can simulate the movement of P particles among several types of particles differing in their radius and density. Fig. 2 denotes the predicted particle separation of two classes of particles differing in size. The ratio between tramp and trest is 1, with a tramp = trest = 5 s. As predicted, large and small particles are separated.
The transducers were excited at a frequency of 4.00 MHz with an amplitude of 8 Vpp. At this frequency, the wavelength of the sound waves in water is λ = 370 μm (the velocity of sound velocity in water is 1480 m s−1).32 A schematic of the experimental setup is shown in Fig. 3. The particles agglomerate at the nodes with a separation of λ/2 = Λ = 185 μm.33,34 To estimate the order of magnitude of the acoustic pressure experienced by the particles of different diameters (6, 10, and 45 μm), we recorded the time taken for the particles to agglomerate at the nodes starting from a randomly distributed motion state. These experiments were repeated 5 times at 5 different locations within the device using time-lapse microscopy. The viscous force, Fv, derived from the dimensions and densities of the particles as well as the viscosity of the medium (eqn (6)), allows the acoustic pressure amplitude acting on the particles to be calculated. The acoustic pressure was found to be 91 ± 7 kPa, 62 ± 4 kPa and 48 ± 2 kPa for 6, 10 and 45 μm diameter particles, respectively.
The separation experiments were conducted using two mixtures of particles, each at a particle density of 4.99 × 105 particles mL−1. Mixture A contained 10 and 45 μm diameter particles at a ratio of 1:
100. Mixture B contained 6 and 10 μm diameter particles at a ratio of 1
:
100. At these concentrations, no aggregation of particles was observed. As predicted, the time variant acoustic field was able to manipulate and, at the same time, separate particles according to their size (Fig. 4). Fig. 4a shows the expected behaviour of the large and small particles over time (black = t0, purple = t1, red = t2, yellow = t3) in relation to the initial position of the nodes (indicated by Ni and Ni+1) and antinodes (indicated by Ni+1/2) of the acoustic landscape. During tramp, the large particles, experiencing larger acoustic force, follow the moving node and thus can be moved from Ni to Ni+1. At the same time, smaller particles, experiencing a smaller acoustic force, cannot follow the moving node and thus move over a smaller distance. During trest, the smaller particles return to their initial position Ni, while the larger particles settle at the next node Ni+1. Fig. 4b shows particle traces as a function of time (71 frames covering 36 s). In this case, the 45 μm diameter particles follow the shifted acoustic field (moving towards the right-hand side), while the 10 μm diameter particles stay close to the position of the original node. The time between frames was 0.5 s. The average movement of small and large particles was 3 ± 1 μm s−1 and 30 ± 1 μm s−1, respectively, during tramp.
![]() | ||
Fig. 4 Position of the particles as a function of time (represented by colour). (a) A schematic illustration that shows 4 positions of large and small particles. Larger particles, experiencing larger acoustic force, are transported to the next node Ni+1 at x2, whereas smaller particles, experiencing smaller acoustic force, return to Ni at x0. (b) Experimental data of the 45–10 μm particle mixtures under the dynamic acoustic field (71 frames covering 36 s). The longer trails show the distance traversed by 45 μm diameter particles, whereas the short trails illustrate how 10 μm diameter particles do not traverse the space (see video in the ESI†). |
A series of time-lapse images were recorded at regular intervals during separation to produce particle traces. The image stack was then analysed using FIJI35 and the particle positions were extracted. The resulting data (x, y, particle area) was used to calculate the efficiency (eqn (7)) and purity (eqn (8)) of separation for each experiment by computing the particle density projected along the node lines and analysing the time variation of this density. Fig. 5a shows the initial position for 10 and 45 μm diameter particles for seven consecutive nodes. Fig. 5b shows the average displacement of the particles for five cycles of continuous phase shift including the rest period. It can be seen that the large particles successively travel during tramp and stabilise during trest at the next node resulting in an overall displacement over time. Simultaneously, the small particles move only slightly, therefore not crossing the midpoint of the nodes, and then return to their initial node position during trest.
Separation efficiency was simulated using the DAF model outlined above with the same parameters as the experiments. Table 1(a) shows the simulation results. The regions coloured red represent the parameters that did not show particle separation, whereas the particles were successfully separated in the blue region. Table 1(b) shows the experimental results conducted replicating the simulation parameters. The blue regions represent those parameters where >91% separation was achieved and the red regions represent the parameters where <80% separation was achieved. The yellow regions show those parameters where the separation was 80–90% successful. Comparing computational and experimental results, it can be seen that there is a good match between the simulation and the experimental data.
It can be observed that separation performance improves with tramp and trest until it reaches a maximum. This indicates that the acoustic forces that the shifting nodes exert on the particles of interest need a minimum time to overcome inertia and viscous force in order to move the particles from the node Ni to the next node Ni+1. tramp is the critical parameter, since it has the greatest effect on the separation result. The value of trest is less influential on the separation of the entities.
When suitable parameters are selected, the separation process reaches its best experimental performance: with the separation ratio achieving ~100% purity and efficiency when trest = 4 s and tramp = 8 s.
The simulation and experiment were replicated using 6 and 10 μm diameter particles. For these particles, it was found that ~97% of particles separate, with an efficiency and a purity of ~97%. These results were achieved with a value of tramp = 15 s and trest = 15 s. Fig. 6 shows the particle traces as a function of time for 6 and 10 μm diameter particle mixtures (71 frames covering 142 s) under these conditions. The 10 μm diameter particles move from node to node (moving towards the right-hand side), while the smaller particles (6 μm in diameter) remain close to their initial position of the original node. The average movement of the 6 and 10 μm diameter particles was calculated as 2 ± 1 μm s−1 and 10 ± 1 μm s−1, respectively, during tramp.
These above experiments were performed using the smallest gap in size of commercially available particles (10 ± 1 μm and 6 ± 0.6 μm; Polysciences Europe, Germany). Therefore, an experimentally accessible discrimination capability of the acoustic separation device is ±2 μm difference of particle diameter.
As for previous experiments, Fig. 7 shows particle traces as a function of time for 10 μm diameter iron-oxide filled and polystyrene particle mixtures using DAF (140 frames covering 140 s). It can be seen that the denser particles (iron-oxide filled) are significantly affected by the DAF and continuously travel from left to right, whilst the less dense particles (polystyrene) have a more restricted range of movement close to their starting positions. With these particles, a separation performance of ~99% has been recorded, with an efficiency of ~100% and a purity of ~98% for tramp = 14 s and trest = 14 s. The average movement of the polystyrene and iron-oxide filled particles was calculated as 3 ± 1 μm s−1 and 15 ± 1 μm s−1, respectively, during tramp.
The less dense particles (polystyrene) experience smaller acoustic force (eqn (4) and (5)) and thus cannot follow the DAF, while the denser particles (iron-oxide filled) track the movement of the dynamic acoustic field. Thus, particles of the same diameter but different densities can be sorted with the DAF method.
To assess a potential practical application, we applied the dynamic acoustic field to separate porcine dorsal root ganglion (DRG) neurons from a freshly isolated mixture containing myelin debris and other non-neuronal cells. The neurons would normally be separated based on their hydrodynamic state using centrifugation across a Ficoll gradient.40 The DRG neurons have an average size from 17 to 145 μm, while the myelin debris has a size of approximately from 10 to 15 μm.
Fig. 8 shows debris (~26 μm) and a single DRG neuron (~85 μm) in the presence of an acoustic standing wave. These entities aligned themselves in vertical lines, agglomerating at the nodes of the acoustic field.41 A dynamic acoustic field was then applied (using a tramp and trest of 5 s), and the resulting time-lapse overlay is represented in Fig. 9a. The static material does not produce a trace, whereas the material that has been displaced shows a trace that moves from left to right. The DRG cell follows the shifted acoustic field (moving towards the right-hand side), while the debris exhibits minimal displacement of the original node. The time between frames was 0.5 s. The average movement of the DRG cell was calculated to be 18.5 ± 1 μm s−1 during tramp. Fig. 9b shows the displacement of the DRG over time.
In these experiments, the DRG cells exhibit similar behaviour to the particles in the previous experiments. Only the large DRG neurons are differentially shifted to the right, while smaller cells and debris remain in their original node.
![]() | (4) |
![]() | (5) |
Fv = −6πηRv | (6) |
The acoustic contrast factor, eqn (5), represented by ϕ in eqn (4), depends on both the particle density (ρc) and its compressibility (βc) in relation to the corresponding properties of the surrounding medium (ρw, βw). The equation of the primary radiation force, Fa, eqn (4), states that the acoustic force applied on the particles is proportional to the acoustic pressure amplitude (ρ0) squared and to the volume of the particles (Vc). The acoustic dynamic field takes advantage of the size dependency of the mechano-physical properties of the micro-entities being sorting, that scales with particle volume, inducing a primary force which is strongly dependent on particle size (r3) and medium viscosity.
Furthermore, an agar layer was introduced into the device to minimize the streaming42 and maximize the precision in control of the particle movement.
![]() | (7) |
![]() | (8) |
The demonstrated results in Table 1 were calculated using the following formula which is the average of purity and efficiency as described above:
![]() | (9) |
Footnotes |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/c4lc01153h |
‡ G.D.S. did the experiments and analysis of the data. Acoustic technologies were devised by A.L.B. with input from D.R.S.C. M.O.R. and J.N.R. conceived the idea of applying the dynamic acoustic field to dorsal root ganglion cells and extracted the cells from pig tissue. D.R.S.C., M.O.R. and A.L.B. drafted the paper. All authors commented on the final manuscript. |
This journal is © The Royal Society of Chemistry 2015 |