FINAL YEAR PROJECT

Design, Development and Testing of a Device for AcousticTrapping of Live Cells and Micrometre-Scale Particles

Author: Frederick A. O. White

Project Code: NPSM1012

Date Submitted: April 27, 2015

Supervisors: Dr Adrian Barnes &Dr Monica Berry

Assessor: Dr Terence McMaster

Number of Words: 7405

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Declaration

This report is solely my own work and was written and compiled using LATEX. Some sections of the introduction and theory aremodified from my own literature review on acoustic trapping. The device design was inspired by the work of Scholz et al. butmy lab partner and I introduced significant modifications for this work. During construction, my lab partner and I operated thelaser cutter and 3D printers to produce device bodies and cases. The final construction of the device was also a joint effort. Allexperimental work and results were produced jointly. I wrote the code used to analyse particle distributions while the ellipse

eccentricity fitting was completed by my lab partner. All results were cross checked between us. All plots, analysis andinterpretation of the data presented in this report are my work. My lab partner and I were not qualified to handle live cell

cultures directly; therefore Dr Berry assisted with work involving live cells. Throughout the project, day-to-day practical helpand advice was provided by Tom Kennedy.

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Contents

Declaration i

Abstract iii

I. Introduction and Background 1

II. Theory 1A. Acoustic Trapping 1B. Piezoelectric Transducers and Acoustic Power 1C. Cell Viability 2

III. Experimental 2A. Design and Setup 2B. Polymer Bead and Fixed Cell Studies 4C. Image Analysis 5D. Temperature Variation 6E. Live Cell Experiments 6

IV. Results 6A. Observations of Alignment of Fixed Cells and Polymer Beads 6B. Computational Image Analysis 8C. Temperature Variation 9D. Cell Viability 9

V. Discussion 10A. Device Design 10B. Directional Distribution Analysis 10C. Alignment of Polymer Beads and Fixed Cells 10D. Cell Viability 11E. Future Work 11

VI. Conclusions 11

VII. Acknowledgements 12

VIII. Appendices 12A. Cell Culturing Technique 12

1. Live Cell Culturing 122. Cell Fixation 12

B. Angular Distribution Calculator 121. Theta Calculator Code 12

C. Certificate of Ownership 13

References 14

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Abstract

A simple non-resonant, centimetre-scale acoustic trap was designed and constructed. The device used Lead Zirconate Titanatetransducers to produce a standing wave acoustic field at 6.7 MHz. It successfully aligned human cells and 8 µm polystyrene

beads in aqueous suspensions at separations of 115 µm. The quality and rate of alignment was studied via analysis ofdirectional distribution of particle positions. The device also demonstrated the ability to maintain viability of greater than 50%

compared to controls for Araki-Sasaki and IOBA cells when aligned for up to two hours.

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I. INTRODUCTION AND BACKGROUND

Acoustic trapping was first observed in 1868 by Kundt. Inhis work, cork dust aligned with a standing wave in a resonantair-filled cylinder[1]. Since its discovery the technique hasbeen used in the manipulation of inert particles, filtering andcell–cell interaction studies[2–5].

Acoustic manipulation provides a non-contact, non-invasive method for trapping particles and cells without re-moving them from culture[6]. Trapping is achieved using thepressure gradient produced in a non-uniform acoustic field.The technique produces forces on the order of pN to nN whenworking with µm-scale particles. This makes it ideal for han-dling cells[2, 7, 8]. It is also cheap and simple to integrate withother equipment for observations and cell culturing[9]. Theonly requirement to acoustically trap a particle is a density andcompressibility contrast to the suspending medium[10, 11].This makes the approach applicable to a broad range of parti-cles and cells without any modification to the technique used.Significant work with a variety of cells has been carried out inthe last decade and there are several demonstrations that cellviability can be maintained during manipulation in a varietyof devices[12–15]. Recent work with non-adherent cells hasdemonstrated the usefulness of acoustic trapping to manipu-late cells that do not naturally cluster during culturing[4].

Acoustic manipulation is one of several techniques that ex-ist for non-contact particle handling. For the manipulationof live cells it has several advantages over the alternatives.Magnetic trapping and electrophoresis use non-uniform mag-netic and electric fields respectively. Magnetic trapping re-quires either naturally magnetic cells or doped cells, limit-ing its applicability. Electrophoresis risks cell damage dueto Joule heating of the fluid medium and has a limited rangeas the electrodes must be closely spaced[16]. Optical tweez-ers utilise the radiation force due to a focused laser beamto manipulate particles with nanometre precision. However,the laser can rapidly induce heat-related cell-death and theequipment required is difficult to integrate with cell culturecontainers[3, 9].

The aim of this project was to construct a centimetre-scaledevice capable of aligning living cells using ultrasound whilemaintaining their viability, allowing optical observations andsimple sterilisation between uses. The device also had to beas cheap and simple to manufacture as reasonably possible.Overall robustness and simplicity were two primary goals ofthe design. Having constructed a device, the aim was to studyits effect on living cells. However, due to loss of access tocell-containment facilities, the bulk of work in this paper wasundertaken with inert polystyrene microbeads and fixed cells,to analyse the rate and quality of trapping and alignment pro-vided by the device.

II. THEORY

A. Acoustic Trapping

In an acoustic trap, particles are manipulated using the pri-mary radiation force (PRF). This arises when an ultrasonicstanding wave scatters off a particle or cell with an acousticcontrast to the fluid medium.

The first theoretical description of the PRF for incom-pressible spheres was produced in 1934 by King[17]. Thiswas extended to compressible particles in 1955 by Yosiokaand Kawasima[18] and finally generalised for viscid fluids in1962 by Gor’kov, whose derivation is most commonly usedtoday[19]. Bruus provides a full derivation which results in adescription of the primary radiation force, acting on a spher-ical object, F rad, as the negative gradient of an acoustic po-tential, Urad[20]:

F rad = −∇Urad (1a)

Urad =4π

3a3

[f1

1

2κ0〈p2

1〉 − f23

4ρ0〈v2

1〉]

(1b)

The quantities f1 and f2 are dimensionless scattering coeffi-cients defined by the compressibility and density of the parti-cle compared to that of the surrounding fluid:

f1(κ) = 1− κ with κ =κpκ0

(2a)

f2(ρ) =2(ρ− 1)

2ρ+ 1with ρ =

ρpρ0

(2b)

In Eq. 1b, 〈p21〉 and 〈v2

1〉 are the time-averaged incoming pres-sure and velocity fields squared, κ0 and ρ0 are the compress-ibility and density of the fluid and subscripts p in Eq. 2 denotethe same quantities for the spherical particle with radius a.The form of the coefficients f1 and f2 means that most cellswill move to the minima in the potential since their densitytends to be higher and their compressibility lower than the sur-rounding medium[6]. These minima are coincident with thepositions of the pressure nodes of the acoustic field and so areseparated by a distance of half an acoustic wavelength. In one-dimensional trapping, these pressure nodes form in lines par-allel to the driving transducer. With multiple transducers, orthe use of reflectors, more complex nodal patterns can be pro-duced by interference of multiple standing waves. This givesthe ability to trap particles in multiple dimensions. Once thefirst cells are entrapped, secondary forces gather nearby cellsinto a cluster centred on the nodal point or line.

B. Piezoelectric Transducers and Acoustic Power

A piezoelectric crystal produces electric charge whenplaced under mechanical stress[21]. In the inverse piezo-electric effect, an applied voltage across a crystal causes it

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to expand or contract. Applying an alternating voltage sig-nal across a piezoelectric material will cause it to expand andcontract at the same frequency as the applied signal with anamplitude proportional to the applied electric field. This os-cillation in the size of the crystal can be used to produce apropagating longitudinal wave. If one face of a piezoelectriccrystal is placed firmly against a material, the wave can bemade to propagate through the material in order to produce anultrasonic acoustic field.

In order to achieve efficient trapping, it is desirable to con-vert as much electrical power as possible to acoustic power,via the transducer, producing the strongest acoustic field withminimum heating. Conversion is governed by the impedanceand phase of the transducer. Maximum power is convertedwhen the transducer acts as a pure resistor. This occurs whenthe phase difference, φ, between current and voltage is equalto zero. The resistance can be calculated from the impedanceusing:

R = Z|cos(φ)| (3)

where R is the resistance and Z the impedance. In a range offrequencies near resonance, the impedance has a characteristicdip followed by a peak as the transducer passes through res-onance and anti-resonance. Using a resonant frequency max-imises the transfer of electrical power to acoustic power. Theimpedance and phase can both be measured in order to findthe ideal frequency at which to drive the transducers. Havingcalculated the resistance of the transducer using Eq. 3, thepower input to the transducers can be estimated using:

P =V 2rms

R(4)

where P is the power, Vrms the root-mean-square of the alter-nating voltage and R the resistance.

It is desirable to use pairs of transducers with closelymatched resonant frequencies, ideally with as little as 10 kHzdifference, to ensure that both have similar responses whenloaded[2].

When choosing materials from which to construct an acous-tic device, the acoustic impedance of materials is an importantconsideration. Acoustic impedance is a measure of a mate-rial’s resistance to longitudinal waves propagating through it.If acoustic impedance is not matched between materials, en-ergy is reflected. This causes losses in the system and in turnrequires more power to be supplied to the transducers in orderto produce the same trapping force. The reflection coefficient,R, for a wave propagating from material 1 (with characteris-tic acoustic impedance Z1) to material 2 (with characteristicacoustic impedance Z2) is given by[22]:

R =

(Z1 − Z2

Z1 + Z2

)(5)

Since all the input energy is either reflected or transmitted, thefraction of energy transmitted can be calculated as T = 1−R.

C. Cell Viability

In order to maintain cell viability, the effects of ultrasoundon living tissue must be considered. There is a large body ofevidence that low-intensity ultrasound has no significant im-pact on bulk human tissue[23, 24]. The effects of ultrasoundare generally considered as either thermal or non-thermal.Thermal effects arise due to heating of the cell medium push-ing the temperature outside the narrow ideal range[24]. Hu-man cells have best viability at 37 ± 1 C, correspondingto body temperature. Bulk tissue can tolerate a temperaturerange of 33–39 C and in vitro cells can tolerate an even widerrange than this[24]. In the range 1–10MHz, absorption ofacoustic energy by water is low, so acoustic heating shouldbe minimal. For small volumes of liquid, as used here, directheating by the transducers can become significant. For heat-ing to rapidly affect cell viability the temperature of the cellmedium would have to exceed 40 C[24].

Non-thermal effects include streaming, cavitation andstress due to the PRF. Eckart streaming is the dominant pro-cess in systems with scales greater than λ/2. It is caused byenergy absorption by the fluid leading to bulk motion[25].The amplitude of streaming scales with the depth of fluid,so can be limited by reducing the depth[26]. If the stream-ing is too large, particles can be pulled out of the acoustictrap[12, 27]. At the frequencies and depth of fluid used in thiswork, streaming should not affect trapping[26]. Cavitation isalso a consideration as the formation of bubbles inside cellscan cause them to rupture. Fortunately, cavitation is limitedwith acoustic frequencies greater than 1 MHz. In additionto this, bubbles formed in a water based medium are lowerdensity than the medium, while cells are higher density. Bub-bles are attracted to the pressure antinodes of the acoustic fieldwhile cells travel to the pressure nodes, physically separatingthe cells and damaging bubbles[24].

III. EXPERIMENTAL

A. Design and Setup

In order to achieve acoustic trapping, an ultrasonic stand-ing wave field must be produced. While the ultrasonic waveis almost always provided by piezoelectric ceramic transduc-ers, the arrangement of these transducers and the structure ofthe device can take several forms[10]. The most commonapproach is multi-layer resonant systems. Each layer mustbe precisely the right thickness, requiring precision engineer-ing. Resonant systems also limit the potential for manipula-tion as the trapping positions are defined by their geometry.Two other alternatives, which have been proved experimen-tally, are the use of focused ultrasound beams[28] or lineararrays of transducers parallel to a reflector[29]. The approachused in this work is to use two opposing transducers. Thestanding wave for trapping is set up by interference of the twocounter-propagating travelling waves produced. This methodgives a standing wave which is independent of the resonantfrequency of the chamber through which it propagates, reduc-

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FIG. 1: The original device showing the circular mount holding thetransducers. This is then inserted into a petri-dish containing the cell

culture.

ing the effects of high particle densities[8]. It also producesa system which is robust to partial misalignment of the trans-ducers. Any misalignment merely introduces a phase shiftbetween the two travelling waves, moving the nodes of thestanding wave rather than interrupting it. This reduces theneed for high precision manufacturing. Deliberate introduc-tion of a phase difference between the two input waves, canbe used to arbitrarily position the nodes[30].

The basis of the design was a previous device developedin the UoB Biosciences group, which used two pairs of op-posed piezoelectric transducers glued into a 3D printed frame,shown in Fig. 1. This frame was then submerged in thecell culture medium. The transducers used in the original de-vice and in all subsequent work were Noliac group NCE51,2 × 15 × 0.975 mm Lead Zirconate Titanate (PZT) piezo-electric elements[31]. The device successfully aligned cellsbut did not maintain viability. Placing the transducers inthe fluid medium had the advantage of maximising acousticpower transfer to the fluid, since there were no additional ma-terial boundaries to cause reflections. However, It was diffi-cult to maintain sterility with the design due to the porosityof the printed plastic. In addition, all heat output from thetransducers was deposited directly into the fluid, potentiallyrisking cell viability. Construction of the power supplies wasalso complicated by the need to feed them under the petri-dishcover.

Due to the difficulties with the original device, it was de-cided that separating the transducers and fluid medium wouldmake sterilisation easier. However, the opposing transducerapproach to trapping was retained due to its simplicity andresilience when handling large particle concentrations. Onepair of transducers was used, allowing only one-dimensionaltrapping but minimising the complexity of the design. The de-vice developed and used in this work is based on the work ofScholz et al.[8].

As shown in Figs. 2 and 3, the device was designed arounda standard optical microscope slide, to ensure that it wouldbe compatible with standard microscopes. The design usedthree chambers – a central one to contain the sample fluid andtwo smaller chambers to hold the transducers providing theacoustic field. The body of the device was laser cut in 3 mmPolyMethylMethacrylate (PMMA) acrylic, avoiding the useof porous plastic in the fluid chamber. Acrylic was chosen asit is cheap enough that the body of the device could be dispos-able and can be laser cut easily, in a matter of minutes, making

FIG. 2: Top and side cut-through schematics of the new device. A –PMMA, B – air gap, C – fluid chamber, D – PZT transducer crystal,E – microscope slide. When in operation a second transducer was

placed opposite the first, on the far side of the fluid chamber.

FIG. 3: Completed two transducer device in the 3D printed case.

for rapid construction. Glass was considered as an option butrequired water-cutting, which would have added significantlyto construction time as this can only be carried out by work-shop technicians. Laser cutting required digital models of thedevice to be made in order to produce two-dimensional out-lines for cutting. The body was then glued to the slide usingcommercially available silicone sealant.

The transmission of acoustic energy into the fluid cham-ber is vital for trapping. The acoustic impedance of PMMAis 3.4 MPasm−1s[32] while that of the PZT crystals is 35.1MPasm−1[33]. This means that ∼ 70% of the applied acous-tic energy is reflected at the PZT–PMMA boundary. How-ever, water has an impedance of just 1.5 MPasm−1[33] lead-ing to the reflection of only ∼ 15% of the remaining energyat the PMMA–water boundary. Overall this gives a transmis-sion of ∼ 25% of the input energy assuming minimal absorp-tion. Glass has an impedance of 14.1 MPas−s, leading to an

FIG. 4: Autocad model of the device case prepared for 3D printing.

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FIG. 5: Completed four transducer device with two transducers andaluminium reflector mounted.

overall transmission to a water-based sample of ∼ 28%. Thismarginal improvement in transmitted energy did not warrantthe increased difficulty involved in the use of glass.

A 3D printed case, shown in Fig. 4, was designed and man-ufactured to hold the device and the transducers’ electricalconnectors. Transducers were held in place on opposite sidesof the fluid chamber using 3D printed x-shapes, allowing thetransducers to be separated from the body of the device whilestill attached to the power supplies. Having removed the trans-ducers, the acrylic and glass body of the device could be sub-merged in ethanol for sterilisation without risk to the transduc-ers or power cables. Alternatively, the whole body of the de-vice could be replaced, retaining only the transducers and thecase. It was found that a coupling medium was required be-tween the transducers and the PMMA body to fill any air gapand transmit acoustic power effectively to the fluid chamber.Medical ultrasound gel was used here as it is a close acous-tic impedance match to water-based media so should transmitacoustic energy efficiently. A thin layer of this gel was appliedto the front face of the transducers, before they were mounted,every time the device was used. This device was used for allexperimental work using cells in this paper.

A second device, shown in Fig. 5, was constructed with ad-ditional spaces for a second pair of transducers. This was con-structed on three microscope slides, and an enlarged case wasalso manufactured. However, by this stage in the project, onlytwo transducers were available, so a 2 mm thick aluminiumreflector was introduced at 45 to two orthogonal transducers,in order to produce a two-dimensional grid pattern of nodes inthe half of the fluid chamber with the transducers.

For efficient conversion of electrical power to acousticpower, the transducers had to be driven at their resonant fre-quencies. Since both were driven from a single signal gener-ator, it was necessary to identify pairs with closely matchedresonances to achieve the highest acoustic field strength. Theresonant frequency of the transducers was identified by mea-suring their impedance and phase using a Wayne Kerr 6500BImpedance Analyser[34]. The resonance of each transducerwas identified in air. The two transducers were then mountedin the device, with water acting as the fluid medium, and testedagain to find the combined minimum impedance. This fre-

quency was then used to drive the transducers for trapping.Fig. 6 shows a sample graph of impedance and phase mea-surements. The plotted resistance was calculated using Eq.3. For work with cells of ∼ 10 µm in diameter, the short-est wavelength of sound possible was used to produce maxi-mum acoustic forces as predicted by Eq. 1. The highest res-onant frequency varied between transducers in the range 6.7–6.9MHz, corresponding to wavelengths of 215–220 µm in awater-based medium. It was noted that when the transducerswere operated while mounted in the device, rather than in air,the peaks in the phase corresponding to resonance broadenedbut did not change in frequency. This broadening reducedthe requirement for extreme close matching of resonant fre-quencies between transducers, as it increased the range of fre-quencies at which energy conversion would be improved overnon-resonant conditions. The driving voltage for trapping wasprovided by a Tektronix AFG2021 arbitrary function genera-tor producing a sinusoidal alternating current with a voltagerange of 0 − 10V and an output impedance of 50 Ω[35]. Theimpedance was approximately 15 Ω for all transducers at res-onance. This presents a considerable mismatch to the outputimpedance of the function generator. However, extracting themaximum power was not the goal of this design, so improve-ments on impedance matching were not carried out.

B. Polymer Bead and Fixed Cell Studies

Initial tests to study the performance of the device werecarried out with Sigma-Aldrich 8 µm polystyrene microbeadssuspended in Phosphate buffered saline (PBS). A suspensionwith a concentration of ∼ 107 beads ml−1 was produced bymixing 1 × 10−4 g of beads with 10ml PBS. 0.5% v/v Tri-ton TX-100 surfactant was added to prevent clumping. Thissuspension was then diluted at 1% v/v in PBS for experimen-tal work. Beads were aligned using both the one-dimensionaland two-dimensional devices.

Live cell cultures and fixed cells were provided by DrBerry; the process for their production is recorded in Ap-pendix A. Araki-Sasaki (AS) human corneal epithelial andIOBA human conjunctival epithelial cells were used in thisproject. Visibility of lines formed under application of theacoustic field was found to be best when 1.5% v/v fixed cellconcentrate was added to PBS. This produced suspensions of∼ 5 × 105 cells ml−1. The central sample chamber of thedevice has a volume of 650µl, but since the transducers are2mm high only 450 µl of this is exposed to ultrasound, there-fore 400 µl of the fluid under inspection were used.

Alignment was studied over 90 s exposures to an acous-tic field at driving voltages of 4, 6 and 8 Vpp using bothpolystyrene microbeads and fixed AS cells. The effect of volt-age on quality of alignment was also studied by recording themovement of fixed AS cells over 90 s exposure to fields atvoltages between 4 and 10 Vpp in 0.5 V increments. For eachtest, 400 µl of suspension were placed in the central cham-ber of the device while the field was inactive. The field wasthen activated and snapshots were taken at 0.5 s intervals us-ing an Olympus SZX16 microscope[36] coupled to a Lumen-

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FIG. 6: Plots of the measured impedance and phase for one transducer. The upper red line is resistance and the black impedance. There areseveral peaks in the lower frequency range corresponding to various resonances of the piezoelectric crystal; the rightmost peak is the highest

frequency resonance and the one used for trapping.

era InfityX-21C[37] camera and a KL1500 LCD co-axial lightsource[38].

The two-dimensional trap using an aluminium reflector wasbriefly tested using the polystyrene beads. The transducerswere driven at 6.7 MHz and 8 Vpp for 90 s before imaging, aswith the one-dimensional device.

C. Image Analysis

The quality of alignment was investigated via analysis ofthe directional distribution of particles. The angle, θ, fromthe horizontal of the line between pairs of particles was cal-culated for all particles within a given radius from a “home”particle. This process was repeated with each particle in animage acting as the “home” particle in turn. For each image,the values of θ were then plotted as histograms with 5 bins.For a random distribution, there should be no preferred val-ues of θ, as there is no preferred relative position of particles.Where alignment is present, there will be two preferred val-ues of θ – in opposite directions along the lines of particles.This is because where lines form, higher densities of parti-cles exist in the line than away from it. By analysing circularareas with a radius just less than the expected separation oflines, the histograms produced should start as circular distri-butions at t = 0, when cells are randomly distributed. Theyshould tend towards straight lines along the axis of alignmentas time progresses. In the case of partial alignment, ellipticaldistributions were expected to form. Therefore ellipses werefitted to these histograms and the eccentricity calculated as√

(1− (b/a)2) where a and b are the semi-major and semi-minor axis lengths. The value of the eccentricity of the fittedellipse for each frame gives a single value ranging from 0 fornon-aligned particles to 1 for perfectly aligned particles.

For each video, frames 1, 10, 20, 40, 90, 120 and 180 were

FIG. 7: Schematic of the parallax problem. The blue grid representsthe pixels, the green point represents the “home” pixel and redpoints represent pixel centres as recorded by (x,y) coordinates.

Overlaid are 36 radial bins with the apparent pixel count for eacharound the edge. The pattern of counts repeats every 90.

processed using the ImageJ analysis package and the approachdescribed by Costa and Yang to enhance contrast and removebackground noise[39]. Images were converted to binary witha threshold of 5%. Cell counts and (x,y) coordinate data wereextracted in ImageJ using the inbuilt analyse particles option.

The coordinates of the cells were then processed using thecode presented in Appendix B. The code took the (x,y) coor-dinates of each particle in turn and calculated the distances∆x and ∆y to every other particle in the data set. Fromthese, the radial distance was calculated. For all particles in-side a 45 pixel radius from the “home” particle, the angle θfrom the horizontal was calculated as tan−1( ∆y

∆x ) using theinbuilt atan2 function available in C. This pixel distance cor-

6

responded to a half-wavelength of the acoustic wave appliedto the particles and correspondingly the line separation in ourimages. The values of θ were then written to a new file forproducing histograms.

One challenge in this technique was that ImageJ produced(x,y) coordinate data from pixel counts leading to discrete val-ues. This in turn produced discrete values of θ which in-troduced a parallax effect when producing histograms. Thisoccurred because, despite the fact that all bins occupied thesame total area, each bin was sensitive to cells in a differentnumber of pixels. This is demonstrated in Fig. 7. To cor-rect for this effect, the program was run with a “full-field”where every (x,y) coordinate contained a “cell”. The resul-tant values of θ were then placed in 5 bins. The histogramcounts produced by this “full-field” are in effect a responsefunction for the binning process when applied to discrete (x,y)values. Subsequent results were scaled by the average countof this response function for all bins divided by the count in agiven bin to remove the parallax effect. Ellipse fitting was car-ried out using an open source Python conversion of a Matlabscript[40]. This code used a linear least squares method basedon the method of Gander et al. to produce values for the semi-major and semi-minor axes of an ellipse fitted to a given dataset[41]. The code and process were tested using two pseudo-random distributions. The first was a uniform distribution of3000 points and the second a set of 3000 points distributedrandomly along straight lines separated by 50 pixels with agradient of 0.1. Both were distributed over the same pixelrange as experimental images.

D. Temperature Variation

The temperature variation of a cell sample was investigatedto ensure that direct heating of the cell culture would notpresent a risk to viability during live cell tests. The tem-perature was recorded during a 90 minute exposure to an 8Vpp acoustic field. This was the highest voltage and there-fore the highest power supplied to the transducers during livecell work, so represents an upper limit on the rate of heating.A 400µl sample of fixed IOBA cells in PBS at a concentra-tion of ∼ 5× 105 cells ml−1 was placed in the fluid chamberin place of a live cell sample. The room temperature, cul-ture temperature and temperature of both transducers at threepoints across their length were recorded at 10 minute inter-vals over a 90 minute exposure. Ideally the temperature inthe acoustic field would have been measured via RhodamineB fluorescence to avoid interrupting the acoustic field. How-ever, a real-time fluorescence microscope was unavailable soan RS206–3750 Digital Thermometer was used instead[42].This did not present significant issues as it was not necessaryto measure temperature while maintaining trapping.

E. Live Cell Experiments

The viability of IOBA and AS cells after exposure of upto two hours to the acoustic field of the device was studied.

Prior to live cell studies, the device was submerged in 50%ethanol for 10 minutes to sterilise it. It was then rinsed ex-haustively with PBS before the sample chamber was filld withcell medium. Sterilisation was repeated between every test.

The process for exposures was to place a 400 µl sample ofPBS in the sample chamber, activate the signal generator andthen add the appropriate cell sample. This allowed more ac-curate timing of exposures. In order to culture the cells forviability studies, it was necessary to remove them from thedevice. This was achieved by placing a fibronectin-soaked13 mm cover-slip in the device before adding cells. The fi-bronectin improved binding of cells to the cover-slip whenthey settled. The cover-slip could then be removed, with thecells, for overnight culturing. After the allotted exposure, theacoustic field was switched off and the cells left to settle ontothe fibronectin plate for 30 minutes. The test sample was thenplaced in a 24 well plate with 400 µl of fresh medium. Asecond, unexposed 400 µl sample of cells was placed on afibronectin-soaked cover-slip to act as a control. All sampleswere then incubated at 37 C, 4.5% CO2 and 90% humidityovernight. The cultures were incubated for a further hour withCalcein AM dye before inspection with a Spectra Max M2spectrometer. The relative fluorescence of the test and controlcultures gives a measure of the number of living cells in eachsample. Since the samples initially contained the same num-ber of cells, the relative fluorescence gives a measure of therelative viability of the cells exposed to the acoustic field. Thepresence of viable cells was visually double-checked usingTrypan Blue dye, which only permeates the ruptured mem-branes of dead cells.

Viability was measured for exposures of 2 minutes and 60minutes at 4, 6 and 8 Vpp for IOBA cells and 2, 15, 30, 60 and120 minutes at 8 Vpp for the AS cells. Finally AS cells weretested after a 60 minute exposure using a pulsed signal alter-nating 100 ms on and 100 ms off at 8 Vpp. Cell viability wasquantified using relative fluorescence counts between controlcultures and cultures after exposure to ultrasonic fields. Thefluorescence count of the test cultures was then converted to apercentage of the control count.

IV. RESULTS

A. Observations of Alignment of Fixed Cells and PolymerBeads

The initial goal of aligning cells using the acoustic forcewas successful. Despite the significant acoustic impedancemismatch between the transducers and the PMMA body ofthe device, alignment of both 8 µm polystyrene beads and 12µm fixed AS cells was reliably achieved in under a minute.The output voltage of the signal generator and the resistanceof the transducer were used to estimate the power supplied toeach transducer using Eq. 4. The power supplied at 10 Vpp

was calculated to be 0.83 W, while at 4 Vpp the power was0.13 W, per transducer. These values are only an estimate ofthe true quantities as the impedance mismatch between thesource and load is not taken into account. As visible in Fig.

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FIG. 8: Microscope image of AS cells aligned after 90s exposure toa 10Vpp acoustic field.

FIG. 9: Microscope image of AS cells aligned after 90 s exposure toa 4 Vpp acoustic field.

8, fixed AS cells suspended in PBS were clearly aligned after90s with the transducers excited at 10 Vpp. The separationof lines was ∼ 110 µm, corresponding to λ/2 of the acousticwave, as expected theoretically. The visual quality of align-ment did not significantly reduce as the voltage was lowered,as shown by Fig. 9. Polystyrene microbeads aligned morerapidly than AS cells, with alignment apparent from as littleas 10s exposure. Despite this, visual quality of alignment wasnot significantly different after 90s at any voltage. The high-est voltage applied to the beads was 8 Vpp, which produceddistinct lines, as shown in Fig. 10. The minimum voltage at

FIG. 10: Microscope image of 8 µm polystyrene beads aligned after90 s exposure to an 8 Vpp acoustic field.

FIG. 11: Polymer beads trapped using the device equipped with analuminium reflector and orthogonal transducers.

FIG. 12: Histogram using 5 bins of θ counts for a pseudo-randomuniform test distribution. The radial axis is counts and the angular

axis θ bin centre.

which reliable alignment was achieved was found to be 4 Vpp.The second device, using an aluminium reflector, was

tested using the same polymer bead suspension as the one-dimensional trap. Only preliminary tests were carried out withthis device. The reflector partially worked, producing partialalignment to a grid and broken lines of particles as seen in Fig.11.

FIG. 13: Histogram using 5 bins of θ counts for a pseudo-randomtest distribution with lines separated by 50 pixels. The radial axis is

counts and the angular axis θ bin centre.

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FIG. 14: Images at 0, 20 and 90 s from video footage of AS cell alignment under a 9.5 Vpp applied field. The images have been processed toremove background noise and converted to binary images; this is the format from which cell counts were taken.

FIG. 15: Histograms using 5 bins of θ counts corresponding, from left to right, to the images in Fig. 14. The eccentricity of fitted ellipseswas, from left to right: 0.33, 0.37 and 0.82. The radial axis is counts and the angular axis θ bin centre.

B. Computational Image Analysis

The process for analysing directional distribution was con-firmed by running a pseudo-random and linear test distribu-tion through it. All histograms are normalised to a total countof 1000. The pseudo-random distribution produced an almostcircular distribution in θ, shown in Fig. 12, with a fitted eccen-tricity of 0.18. The straight-line test distribution produced Fig.13. The lines of the test distribution had a gradient of 0.1, cor-responding to an angle of 5.74 from the horizontal. Almostall values of θ lay in the 5–10 degree bin. However, a smallnumber fell in the 0–5 bin. This demonstrated the ability ofthe method to detect structure not visible to the naked eye –the “straight” lines of the test distribution were pixelated andso contained groups of pixels on the same row. This produceda fitted eccentricity of 0.99.

Having confirmed the ability of θ histograms to discernstructure in an image, the process was applied to videos ofpolymer bead alignment and AS cell alignment under variousfield strengths. Figs. 14 and 15 show the resultant histogramscompared to the images they result from. The final distribu-tion in Fig. 15 is not, as originally expected, a true ellipse butis instead a highly eccentric ellipse overlaid on a small circu-lar distribution. This is due to cells floating on the surface ofthe medium which did not align but were still detected by theparticle analysis. This introduced a random background dis-tribution to the data. While there were sufficiently few floatingparticles that the alignment was not obscured, if this technique

FIG. 16: Eccentricities of fitted ellipses for histograms of θdistributions of AS cells under 8, 6 and 4 Vpp applied fields.

was used for further work, removal of particles away from theplane of alignment would be ideal.

While alignment of fixed AS cells was successful, the back-ground random distribution did produce relatively small val-ues for the eccentricity of fitted ellipses. For fields of 8, 6and 4 Vpp, as used for the cell viability study, the eccentricitynever exceeded 0.6, as shown in Fig.16. For fields at 9.5 and8.5Vpp the eccentricity peaked at 0.87 and 0.82 respectivelywhereas for fields at 7.5 and 4.5 Vpp it did not exceed 0.6, asshown in Fig. 17. As Fig. 16 and Fig. 17 show, the eccen-tricity generally increases after 10 s. Lines are added to these

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FIG. 17: Eccentricities of fitted ellipses for histograms of θdistributions of AS cells under 9.5, 8.5, 7.5 and 4.5 Vpp applied

fields.

FIG. 18: Eccentricity of ellipse fits to histograms of θ for polymerbead alignment under 8, 6 and 4 Vpp applied acoustic fields.

plots for clarity. It is thought that for t < 10 s particle motionis dominated by the initial motions, whereas for t > 10 s theapplied acoustic field dominates.

Polymer bead alignment was more rapid and reliable thanthat for the fixed AS cells. Fig. 18 shows that the eccentricityfor the polymer bead tests rose rapidly under 6 and 8 Vpp toa peak of ∼0.95, corresponding to strong alignment with al-most no random background distribution. Under a 4 Vpp fieldalignment progressed more slowly and was never as strong asthat under the more powerful fields. This matches the resultsof the AS cell observations in Fig. 17 that the stronger acous-tic force produced by the higher applied voltages led to moreeffective alignment of particles.

C. Temperature Variation

The average temperature of a 400 µl PBS sample increasedby 1.6 C within 10 minutes of an 8 Vpp field being ap-plied, as shown in Fig. 19. The average temperature ofthe transducers also rose sharply in the first 10 minutes, by2.8 C. Subsequently the temperature of the sample rose by0.010 ± 0.002 C min−1 and the temperature of the trans-ducers by 0.018 ± 0.002 C min−1 during the remaining 80

FIG. 19: Average temperature of both transducers and a 400 µl PBSsample over a 90 minute exposure to a 10 Vpp acoustic field.

Triangles are the fluid temperature, the square points are the averagetransducer temperature.

minutes. Temperature measurements were taken at 3 pointsalong the length of each transducer. Errors were then calcu-lated as the standard deviation of the values. The error on thetemperature of the fluid was taken to be twice the precision ofthe digital thermometer, 0.1 C.

D. Cell Viability

TABLE I: Relative cell viability of IOBA cells after exposure toacoustic fields.

Voltage/V Time/min Relative viability/%8 2 89.96 2 149.74 2 136.48 60 62.86 60 51.04 60 136.8

TABLE II: Relative cell viability of AS cells after exposure toacoustic fields.

Voltage/V Time/min Relative viability/%8 15 111.78 30 172.28 60 86.78 120 87.78 (Pulsed) 60 94.8

The study of cell viability was limited by available lab time.However, it was possible to test both IOBA and AS cells withthe device. For all exposures of up to two hours between 4 and8 Vpp it was found that cell viability was greater than 50% inboth IOBA and AS cell lines. Full results are presented in Ta-ble I and Table II. For exposures at 4 Vpp the relative viabilitywas greater than 100%, indicating better cell reproduction in

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the exposed culture than in the control. The pulsed signal pro-duced marginally better viability than the continuous exposurefor 60 minutes in AS cells.

V. DISCUSSION

A. Device Design

The device designed and constructed in this work success-fully achieved its primary goals of enabling acoustic trappingof both inert particles and cells while allowing optical obser-vations. Using opposing transducers to produce the standingwave field for trapping produced a non-resonant device whichcould handle high concentrations of particles, in the range of106 ml−1. The non-resonant design also removed the needfor any high-precision manufacturing or tuning of the device,unlike resonant systems. This made the device robust to re-peated dismantling and general handling during experimentalwork as partial misalignment of the transducers merely relo-cated the position of nodes rather than destroying the trap-ping effect. It was also simple to manufacture and operate.Once the design was finalised, it was possible to produce anew body for the device within 15 minutes, although up to24 hours was required to cure the silicone sealant. No cus-tomised electronics were required and an off-the-shelf MHzrange function generator was used. Furthermore all of the ma-terials required for construction are cheap and readily avail-able. The use of acrylic and microscope slides would allowsimple and rapid manufacture of custom sized devices for fur-ther research, making this device versatile. For live cell work,the device was simple to sterilise using ethanol.

B. Directional Distribution Analysis

The method for analysing the directional distribution of par-ticles from video images of the alignment process, developedfor this paper, proved successful. It was independent of theparticle shape, requiring only (x,y) coordinate data for eachparticle. This process gave a systematic measurement of thealignment of particles within the device. The value of eccen-tricities in the theoretical limit of an infinite, perfectly randomdistribution is 0, from an absolutely circular histogram, andthat in the case of a set of lines is 1, corresponding to a his-togram with equal counts 180 apart. However, experimentalresults fall far short of an infinite sample, with only a fewthousand cells visible in any frame. The results produced by apseudo-random test distribution with 3000 points reflect this,producing an eccentricity of 0.18. This gives a reasonablelower bound for the eccentricity of an experimental unaligneddistribution. The upper bound, provided by the straight-lineartificial distribution was 0.99. The result was not 1 due to thepixelation of the lines introducing horizontal sections. Thistest had no background noise at all, so it is unsurprising thatexperimental data did not reach eccentricity values this high.The experimental range of values was 0.13–0.95, with the ex-treme values recorded at 0 s and 90 s exposure respectively.

C. Alignment of Polymer Beads and Fixed Cells

Alignment was observed in both polystyrene micro-beadsand fixed AS cells for power inputs of 0.13 W to 0.83 W.During all alignment tests, a layer of unaligned particles wasvisible above the plane of alignment throughout exposure toan acoustic field. This implies that the depth at which acous-tic forces were produced was limited to a layer close to thebase of the device. This suggests that some component of theforce may have been produced by a surface wave propagatingthrough the glass slide forming the base of the device, ratherthan the plane wave propagating through the fluid medium.To fully investigate this effect, it would be necessary to eitheranalyse alignment footage taken at multiple focal depths orto produce computational models of the device and comparetheoretical and experimental rates of alignment.

Micro-bead alignment was faster and more consistent thanthat of the fixed cells, reaching a maximum eccentricity injust 20s. The alignment of micro-beads progressed at an al-most identical rate at both 8 and 6 Vpp, reaching a maximumeccentricity of ε = 0.95 in both cases; this corresponds to ap-proximately 10 times as many particles being found along theaxis of alignment as perpendicular to it. At 4 Vpp the align-ment progressed more slowly, reaching a maximum after 45s. However, the quality of the alignment never matched thatat higher voltages, peaking at ε = 0.8 and not increasing overthe subsequent 45s, as seen in Fig. 17. This corresponds toapproximately 4 times as many particles being found alongthe axis of alignment as perpendicular to it. These results sug-gest that other forces acting on the beads, such as streaming,did not reduce in magnitude as quickly as the PRF, limitingalignment. The effect of streaming could be studied by re-ducing the depth of the chamber, using cover slips, as Eckartstreaming scales with depth.

The fixed cell alignment did not reach a maximum valuewithin the 90s exposure time. The lower values of the fixedcell results are in part due to the layer of unaligned parti-cles. Due to the darker colour of the cells relative to thebeads, the randomly aligned cells out of the plane of align-ment were more visible in images and therefore more likelyto be picked up in the cell counting process. However, sincethe unaligned cells were approximately uniformly distributed,their presence should reduce the peak value of eccentricitybut should not change the trend of variation over time of thevalue. Lower voltages tend to produce less effective align-ment overall, however in the fixed cell tests in Fig. 15 the ec-centricity was highest for the 4 Vpp field. This is surprising asthe acoustic force is approximately proportional to the squareof the voltage, so is significantly weaker at lower voltages.However, for the 0.5 V increments higher voltages did pro-duce higher eccentricities, as expected. For all exposures withfixed cells, the alignment did improve. However, it was notas pronounced nor as smooth as that of the polystyrene beads,reaching a peak value of just 0.85. The generally poorer align-ment produced using fixed cells suggests that the PRF actingon the cells was lower than that on the beads. The fixed cellswere larger in diameter than the polystyrene beads, at an av-erage of 12 µm compared to 8 µm. This increased radius

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should increase the force produced by a given acoustic field,which scales with volume for particles of the same material.Both particles are similarly close in density to the water-basedmedium they were suspended in, giving similar values for thedensity-dependent constant in the acoustic potential. Any re-duction in force on the cells is therefore likely due to a lowercompressibility contrast between the cells and the water, dueto their structure, than the beads and the water, reducing themagnitude of the acoustic potential in Eq. 1b. Further studywould be required to confirm this, with the force applied mea-sured externally, either via particle image velocimetry or theuse of optical tweezers.

Only rudimentary two-dimensional alignment wasachieved. Fig. 11 demonstrates that simple modifications tothe device used here could be used to produce more complexpatterning of molecules.

D. Cell Viability

Cell viability was successfully maintained while alignmenttook place. The limited quantity of data available on cell via-bility in the device limits the definition of trends. Ideally, sev-eral cultures would have been produced for every voltage, andover a broader range of exposure times, in order to producefirmer bounds on the impact of acoustic exposure. However,higher voltages generally reduced viability in the tests carriedout here, suggesting that the higher forces and energy densi-ties produced reduced cell viability. Longer exposures at thesame voltage did not seem to have as much effect on viabil-ity as increasing the voltage. The pulsed signal delivered onlyhalf the energy to the cell culture of the continuous signal andproduced a marginally better viability, as shown in Table II.This suggests that pulsed signals could be used to maintainviability during longer exposures. For all these results moredata is required to make statistically significant conclusions.

For cell studies the device was operated at room tempera-ture of approximately 21 C. Even with the temperature in-crease induced by the active transducers this left the mediumtemperature at only ∼ 24 C, considerably below the idealculture temperature of 37.5 C. Lower than ideal temperaturesare only expected to lead to slow cell death due to reducedmetabolic function. If cultures were produced in the device,with it running in an incubator, the temperature rise inducedwould push the culture to ∼ 40 C or higher, which wouldlikely produce rapid cell death as with the previous genera-tion device. It is thought that the stabilisation of the fluid tem-perature at a lower temperature than the transducers may bein part due to evaporation of the fluid. In long term culturesthis would present a problem. One option would be to mod-ify the device so that the central chamber was covered duringoperation to minimise evaporation.

E. Future Work

There is great potential for further development of the de-vice and processes used in this project. Future work could

include development of the ability to manipulate trap posi-tions, further live cell studies or computational analysis of thedevice functionality. The introduction of a second signal gen-erator or an electronic phase shifter would allow manipula-tion of the acoustic trap positions in one dimension. Prelimi-nary work on two-dimensional trapping has been successfullydemonstrated. A multi-dimensional trap combined with con-trol over trap positioning could allow patterning of trap sites.This ability could be used to arrange cells for controlled cul-turing or organise inert particles to produce scaffolds for cellgrowth.

With respect to live cell work, additional studies are nec-essary to confirm the ability of the device developed here tomaintain viability during longer term exposure to the acous-tic field. Ideally, these tests would include culturing cellsin the device while an acoustic field was active and expo-sures greater than 24 hours. The success of these tests woulddemonstrate that the device has potential for structured tis-sue culturing. If temperature variation in the culture chamberproved to be a problem for cell viability a Peltier cell attachedto the base of the device could be used to provide in-devicetemperature control.

For an accurate knowledge of the forces acting on parti-cles trapped in the device finite element modelling and thecreation of 1D transmission-line models would be necessary.These could be used to produce more accurate estimates forthe sound energy density in the cell medium and guide modi-fications to the design. Modelling would also make it possibleto calculate the pressure amplitude of the acoustic field pro-duced in the device, making it possible to directly calculate theexpected force. This could then be compared to experimen-tally measured values. In addition it would allow for bettercomparison of cell-viability results with previous literature.

VI. CONCLUSIONS

A simple non-resonant device for one-dimensional acous-tic trapping of µm particles and cells has been designed andconstructed. Using this device, polymer beads, fixed humancorneal epithelial cells and live corneal epithelial and conjunc-tival cells have been aligned. Preliminary evidence suggeststhat cell viability greater than 50% compared to control cul-tures can be maintained during trapping for up to two hourswith power inputs of up to 0.83 W. Significant further work isdesirable to confirm these results.

It has also been shown that 8 µm polystyrene spheres andfixed AS cells can be aligned at separations of λ/2 of the ap-plied acoustic field, as expected from theoretical descriptionsof the PRF. Additionally, a computational process was devel-oped for analysing structure in images of acoustically manip-ulated particles. It was used here to show that polystyrenebeads reached maximum alignment after 20 s in a field of 8Vpp while the alignment of fixed cells continued to improveover the full 90 s exposure at the same voltage.

Overall the device achieved its initial goals. However, thereis significant potential for future development in a variety ofdirections.

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VII. ACKNOWLEDGEMENTS

I would like to thank both Dr Barnes and Dr Berry for theirsupport and supervision and Mr Tom Kennedy for his invalu-able practical advice during the construction of the device. Fi-nally, I would like to thank my lab partner, Clara Hughes, forher hard work and patience throughout the project.

VIII. APPENDICES

A. Cell Culturing Technique

The cells used in this project were Araki-Sasaki humancorneal epithelial and IOBA human conjunctival epithelialcells.

Throughout experiments the medium used was RPMI 1640with L-glutamine and a pH indicator supplemented with 10%(v/v) foetal bovine serum and antibiotics from Invitrogen, LifeSciences warmed to 37C.

1. Live Cell Culturing

To culture the cells they were removed from cryostoragein liquid N2 and rapidly warmed to 37C. Dimethylsulfox-

ide (DMSO) cryopreservative was used during storage; thisis rapidly toxic above 4C. To avoid cell damage, excessmedium at 37C was added to dilute the DMSO. The suspen-sion was then centrifuged at 100g for 5 minutes at room tem-perature before the removal of the supernatant. 1ml of freshmedium was then added. Cells were differentially countedand the average diameter measured by an automated Life Sci-ences Countess cell counter. Trypan Blue dye was used toidentify dead cells.

2. Cell Fixation

Fixed cells were produced by incubating live cells with 4%glutaraldehyde at 4C overnight. They were subsequently ex-haustively rinsed with 0.1M PBS before storage in 1ml PBS.

B. Angular Distribution Calculator

The following code was written in C and compiled usingGNU GCC compiler in Codeblocks.

1. Theta Calculator Code

#include <stdio.h>#include <stdlib .h>#include <string .h>#include <math.h>#define M PI 3.14159265358979323846

double x y array [12000][2]; // Array to contain x and y data

double theta calc ( int ex, double x, double y, int k)/∗ex is the current ”home” cell row number, x and y are the current x and y’s , k is row number of the current particle under consideration ∗/

long double delt x , delt y , r , theta 2 ; // doubles for the value of delta x, delta y and r for each cellif (k!=ex) // excludes the ”home particle ” from caculations

delt x = x y array [k][0]−x;delt y = x y array [k][1]−y; // calculate delta x and delta yr = sqrt (( delt x ∗delt x )+( delt y ∗delt y ) ) ; // calculate radius from the initial value of x and y.

if ( r<45) // enter the true value ( in pixels ) of lambda/2theta 2 = atan2( delt y , delt x ) ; // calculates arctan of y/x

else

theta 2 = 380; // if a cell is outside the sample radius , set value to extremereturn theta 2 ;

else

return 380;

int fileopen (void) // function to read a tab delimited text file into a two−column array of values , x and yint i ;double a ,b;FILE ∗myfile;

13

myfile = fopen(”xy180. txt ” , ”r”) ; // open fileif ( myfile!=NULL) // tests for file opening

printf (”File found and opened\n”);// for ( i=0;i<1000;i++)for ( i=0; ! feof ( myfile ) ; i++)

fscanf ( myfile ,”%lf%lf”,&a,&b); // read the values inx y array [ i ][0]=a;x y array [ i ][1]=b;

fclose ( myfile ) ;

else

printf (”File opening failed , file not found\n”);i=0; // returns 0 to readout .

return i ;

int main()int d; // Counts number of x−y coords put inint i , j ;double x,y, theta ;theta = 0;d=0; // set d to zero for error checkingFILE ∗ Decay file ;Decay file = fopen(”Theta. txt ” ,”a”) ; // file for readout appending each new result to the existing file

if ( Decay file != NULL)d=fileopen () ; // call the function to open the fileprintf (”The number of data sets read in is %i\n”,d); // count the number of coordinate pairs read in to act as iteratorif (d!=0)

printf (”\nmy array[0][0] is %lf. If this is not 0, the read in has worked\n\n”,x y array [0][0]) ; // checks array read−in hasworkedelse // error check

printf (”The file did not contain any scanable item or was not found, calculation not possible .\nPlease try again .\n”) ;

for ( i=0;i<d;i++)x = x y array [ i ][0];y = x y array [ i ][1]; // set variables with a given value of x and y// Then calculate theta and write to filefor ( j=0;j<d;j++)

theta = theta calc ( i , x, y, j ) ;if ( theta<8) // ignore the values outside r , set to extreme in function ” theta calc ”

fprintf ( Decay file ,”%2.15f\n”, theta ) ;

fclose ( Decay file ) ;return 0;

C. Certificate of Ownership

Project Report presented as part of, and in accordance with, the requirements for the Final Degree of MSci at the Universityof Bristol, Faculty of Science.I hereby assert that I own exclusive copyright in the item named below. I give permission to the University of Bristol Library toadd this item to its stock and to make it available for consultation in the library, and for inter-library lending for use in anotherlibrary. It may be copied in full or in part for any bona fide library or research worked, on the understanding that users are madeaware of their obligations under copyright legislation, i.e. that no quotation and no information derived from it may be publishedwithout the author’s prior consent.

Signed: Frederick WhiteFull name: Frederick Alan Orlando WhiteDate: April 27, 2015

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Author Frederick A. O. WhiteTitle Design, Development and Testing of a Device for Acoustic Trapping of Live Cells and Micrometre-Scale ParticlesDate of Submission April 27, 2015

This project is the property of the University of Bristol Library and may only be used with due regard to the rights of theauthor. Bibliographical references may be noted, but no part may be copied for use or quotation in any published work withoutthe prior permission of the author. In addition, due acknowledgement for any use must be made.

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