Absence of enhanced uptake of fluorescent magnetic particles into human liver cells in a strong magnetic field gradient
AAbsence of enhanced uptake of fluorescent magnetic particlesinto human liver cells in a strong magnetic field gradient
Leon Abelmann , , , Eunheui Gwag , and Baeckkyoung Sung KIST Europe, Saarbr¨ucken, Germany University of Twente, The Netherlands Saarland University, Saarbr¨ucken,Germany [email protected] (Dated: January 11, 2021)We investigated whether we can detect enhanced magnetic nanoparticle uptake under applicationof a large magnetic force by tagging the particles with a fluorescent dye. Human liver cells were cul-tured in a micro-channel slide and exposed to two types of magnetic nanoparticles with a diameterof 100 nm at a concentration of 10 000 particles / cell for 24 hours. Even though we achieved a mag-netic force that exceeded the gravitational force by a factor of 25, we did not observe a statisticallysignificant increase of immobilised particles per cell. Keywords:
I. INTRODUCTION
The interaction of micro- and nanoparticles withcells is a challenging research area of major im-portance. Micro- and nanoparticles, which may betoxic [1], can enter our body by accident, or theycan be administered intentionally in biomedical pro-cedures such as drug delivery [2, 3] and in vivo imag-ing [4, 5].Interaction studies between nanoparticles and cellsare mainly performed using in vitro cell cultures inmulti-well plates [6]. In the case of small molecules,diffusion ensures that the molecule concentration isreasonably constant over the volume of the well.However, micro- and nanoparticles are subject to sed-imentation. This has two implications. First, sedi-mentation gradually increases particle concentrationat the cell membrane, the rate of which dependsstrongly on the particle diameter. Secondly, the par-ticles exert a force on the cell membrane, which mayaffect particle incorporation [7].Magnetic micro- and nanoparticles have the ad-vantage that they can be manipulated by externalmagnetic fields, which is exploited in targeted drugdelivery [8, 9], mechano-stimulation [10] and hyper-thermia treatment [11]. The magnetic forces that onecan apply are orders of magnitude greater than gravi-tational forces. Therefore, by magnetically attractingnano-particles towards the bottom of the well, we canaccelerate sedimentation and increase particle incor-poration.There have been a few reports on the increase ofparticle uptake. For example, Prijic and colleagues el-egantly demonstrated the increased uptake of super-paramagnetic particles [12]. They found that thetotal iron content in the cell, measured by induc-tively coupled plasma atomic emission spectroscopy,increased by a factor of 3–8. Unfortunately, thismethod requires one million or more cells. Moreover, one cannot discriminate between the uptake of parti-cles or iron ions in the solution. The same researchersalso observed particle uptake by transmission electronmicroscopy. This method requires fewer cells, but isvery labour-intensive. It is also difficult to discernbetween particles on the cell membrane and those in-corporated in the cell.Rather than observing the particles themselves, onecan observe their effect on the cell. One elegant op-tion is to use magnetic particles to transinfect cells,a process called magnetofection [13, 14]. Pickard andChari [15] demonstrated this by attaching green flu-orescent protein (GFP) plasmids to Neuromag SPI-ONs. When the particles entered the cell, the plas-mids were reproduced. The subsequent generation ofGFP determined whether cells are transfected. Theapplication of force by means of magnetic field gra-dients enhanced the uptake by a factor of 5. A slowoscillation seemed to have a positive effect.Particles in a cell can be identified with optical mi-croscopy by means of fluorescence, for which Dejardinand colleagues used ScreenMag-Amine magnetic par-ticles tagged with fluorescein [16]. The particles weretreated with activated penetratin to increase their up-take. By integrating the intensity of the emitted lightover the sample area, an increase in uptake of about30 % was observed. The magnet used in this experi-ment was only 13 mm in diameter, leading to particleaccumulation in the center of the observation areaand subsequent loss of information on particle con-centration. A similar approach was taken by Venu-gopal and colleagues [17] as well as by Park and col-leagues [18], who additionally showed by flow cytom-etry an increase in uptake ranging from a factor of0.5 (Venugopal) to 7 (Park).Encouraged by these fluorescence experiments, weinvestigated whether one can use optical microscopyto observe individual fluorescent magnetic nanoparti-cles in in vitro cell cultures to detect an increase in a r X i v : . [ phy s i c s . b i o - ph ] J a n magnetslide holder FIG. 1: Holder to investigate the effect of a high magneticfield gradient on the incorporation of magnetic nanopar-ticles into cells. magnetic particle uptake under application of a mag-netic force. For this experiment, we designed a sys-tem with a large magnet of 70 mm diameter, on top ofwhich Ibidi µ -Slide channel slides could be mounted(Figure 1). Using such a big magnet ensured that theforces are strong and uniform. Human liver cells froma HepG2 cell line in the channel slides were exposed tofluorescent magnetic nanoparticles of 100 nm diame-ter. The number of particles per area served as a met-ric to study the influence of the magnetic force. Weconclude that our experimental configuration showedno significant effect of the magnetic field. II. THEORY
The force on a magnetic object that is small com-pared to the spatial variation of the externally appliedfield B [T] can be approximated from its total mag-netic moment m [A/m] F = − ∇ ( mB ). (1)The magnetic moment of a magnetic object in a fluidis generally a function of strength, direction and his-tory of the applied field. The applied field is a com-bination of the external field and the field of all othermagnetic particles in the fluid. Moreover, very smallparticles will be subject to Brownian motion. There-fore, in principle, the calculation of forces on magneticparticles in a magnetic field gradient is complex. Toobtain first approximations, we consider a single par-ticle that is either a permanent magnetic dipole or asoft magnetic sphere.In the case of the permanent magnetic dipole ap-proximation, we assume a particle with a permanentmagnet moment µ m r = I r V p , where I r [T] is the re-manent magnetisation of the particle with volume V p [m ]. We further assume that field changes are slowsuch that particles can rotate against viscous draginto the direction of the field. In this case, equa-tion (1) reduces to F = m r ∇ B , B = | B | . (2)For the second approximation, we assume a softmagnetic sphere with a susceptibility of χ , which isthe ratio between the magnetisation I [T] in the par-ticle and the internal field B in [T]. As a sphere has ademagnetisation factor of 1/3, the internal magneticfield is B in = − B + 13 I = − B + 13 χB in where I = 3 χ (3 + χ ) B and all fields are (anti-)parallel. In this approxima-tion, the energy and resulting force are U = − V p χµ (3 + χ ) B F = 12 V p χµ (3 + χ ) ∇ B = V p χµ (3 + χ ) ( B ∇ ) B . (3)The factor 1/2 originates from integrating from −∞ ,where the energy is 0, and we used the vector identity ∇ B = 2( B ∇ ) B . III. EXPERIMENTAL
To maximise uniformity, we based the magneticfield system on the largest NdFeB magnet we couldreadily obtain (Supermagnete.de). This magnet has adiameter of 70 mm, a height of 35 mm, and is made ofN45, which is specified to have a remanent magneti-sation of 1 . µ -Slide channel andthe magnet were accurately fixed using a 3D-printednylon plastic top holder (see Figure 1). The sourcefiles for the 3D-printed holder are available as addi-tional material.To calculate the magnetic field and forces gen-erated by the magnet, we integrated the magneticcharge densities. In contrast to finite-element meth-ods, the field is calculated only at the points of in-terest, which is much faster at high precision. Theresulting equations are generated automatically bythe MagMMEMS package, which is a preprocessorfor Cades [19]. The input files are available in thesupplementary material.The magnetic field above the magnet is measuredwith a MetroLab THM1176 three-axis Hall sensor at-tached to a microscope glass slide to obtain the fieldcomponents at the same height as the µ -Slide chan-nel. To visualise the particle density, we used Ibidi µ -Slide I Luer channels (Ibidi 80176) filled with bareiron-oxide nanoparticles of 5 nm diameter (EMG304by FerroTec).For cell studies, human hepatoma HepG2 cells(ATCC, HB-8065) were cultured in Eagle’s mini-mum essential medium supplemented with 10 % fetalbovine serum and 1 % penicillin-streptomycin in anincubator at 37 ° C and 5 % CO atmosphere. The cellconcentration was determined by means of a hemo-cytometer and diluted to 5 × cells / mL. Of thissolution, 30 µ L was introduced into Ibidi µ -Slide VI0.4 channels with an Ibitreat surface coating to pro-mote cell adhesion (Ibidi 80606). The dimension ofthe channels is 0 . × . ×
17 mm, hence themaximum cell density is 23 cells / mm .The Ibidi channels were left inside the incubatorfor 24 hours on top of the holder with and withouta magnet before analysis. To assess cell viability,we used a live/dead double-staining assay (Sigma-Aldrich, 04511). Analysis was performed on 10 im-ages chosen randomly over the channel area. Averageand standard deviations were calculated from threeindependent experiments (30 images in total).We studied the interaction between cells and mag-netic nanoparticles with an average diameter of100 nm. For this we used red fluorescent cross-linked dextran iron-oxide cluster-type particles (94-00-102 from Micromod) with a specified iron concen-tration of 6 mg / mL and a particle concentration of6 × particles / mL. In addition, we used green flu-orescent (510 nm) iron oxide incorporated conjugatedpolymer particles (905038 from Sigma-Aldrich) witha specified iron concentration of 100(10) µ g / mL. Thecomposition of the polymer and the particle concen-tration are not specified by the manufacturer.Both suspensions were first diluted by a factorof 235 and added to the cell culture medium at avolume ratio of 1:51. The final particle concentra-tion for the MicroMod particles in the cell culture istherefore 5 × particles / mL with an iron concen-tration of 0 . µ g / mL. Hence, there is an average of1 × particles per cell in the medium. The finaliron concentration for the cell culture with Sigma-Aldrich particles is 8 ng / mL.Images were taken with a Leica DMi8 fluorescencemicroscope at a size of 2048 pixel × × and a 40 × lens were used, calibrated at 324and 162 nm / pixel, respectively.Particles were counted using ImageJ software(Wayne Rasband, NIH, USA). The image taken witha red (Micromod particles) or green (Sigma-Aldrichparticles) filter was converted into 8-bit greyscale. Anintensity threshold was applied to create a 1-bit mask. B z / m T radial distance /mm 0 100 200 300 0 15 30 B x / m T radial distance /mm FIG. 2: Calculated and measured vertical (top) and lat-eral (bottom) field components at the height level of thechannel slide. Assuming a remanent magnetisation of1 .
27 T, the field is predicted accurately.
The “Analyze Particles ...” script was run to countthe number of particles using a lower size threshold.Both the intensity threshold and size threshold werevaried. The ImageJ script that automates this pro-cess and generates the overlay image is available assupplementary material.
IV. RESULTS AND DISCUSSIONA. Field and forces
The force field above the permanent magnet varieswith distance to the magnet surface in both strengthand direction. For experiments with magneticnanoparticles inside the channel slide, we want thelateral forces in the plane of the channel to be assmall as possible, yet the vertical force to be as highas possible and very uniform over the area of interest.Using the soft sphere model of equation (II), we de-termined that the optimal height of the channel slidefor both conditions is 10 . B z ) and alongthe channel ( B x ) at this optimum height, comparedwith field measurements in the center and at the edgeof the magnet. A fit of the calculation to the measure- area of interest z x permanent dipolesoft sphere FIG. 3: Calculated force densities in vertical (red) andlateral (black) direction as a function of the position overthe length of the channel slide. The top curve indicatesthe case where the particle is a permanent magnet withremanent moment I r (equation 2). To obtain the force,multiply by V p I r . The bottom curve indicates the casewhere the particle is a sphere of volume V p and suscep-tibility χ (equation II). To obtain the force, multiply thevalue on the vertical axis by 3 V p χ/ (3 + χ ). ment results in a magnetisation of 1 . ± ° .Figure 3 shows the forces on particles for both thepermanent dipole magnet (top) and soft sphere (bot-tom) models. For the permanent dipole model, theforces are normalised to the particle magnetic mo-ment I r V p [Tm ]. A typical particle has a magneti-sation in the range from 0 . / m . For comparison,the gravitation force density on a typical iron-oxideparticle is 40 kN / m (gravitation acceleration timesmass density difference with water).For the soft sphere model, the forces are normalisedto 3 V p χ/ (3+ χ ), which ranges from 0 to 3 V p . A typicaliron-oxide particle has a susceptibility greater than1 [20], meaning that force densities are in the samerange as for the permanent dipole approximation.Both models show a variation of 14 % in the verticalcomponent of the force over the length of the 30 mmchannel. The soft sphere model has a much weakerlateral force. At the entry of the channel, the forceonly tilts about 1 ° inward, whereas for the permanentdipole model, it tilts at 10 ° .The large magnet produces a very uniform distribu- after filling5 hours
30 mm
FIG. 4: Channel filled with magnetic nanoparticles of5 nm diameter in water. Immediately after filling, theconcentration is very uniform over the channel. Only af-ter several hours can a slight increase in concentrationbe observed in the center. The concentration gradient isnegligible over the region of interest. tion of magnetic particles. Figure 4 shows a channelslide filled with a diluted suspension of 5 nm iron-oxide particles. Immediately after filling, no concen-tration gradient can be observed. After several hours,a slight reduction in concentration is observed closeto the channel entries, yet the concentration appearsoptically uniform over the area of interest. There-fore, this magnet configuration applies forces that areat least 25 times higher than the gravitational force,perpendicular to the surface and uniform over mostof the channel slide.
B. Cell viability
Two different fluorescent magnetic particles wereused: cross-linked dextran iron-oxide composite par-ticles (from Micromod) and iron oxide incorporatedconjugated polymer particles (from Sigma-Aldrich).Both particles have an average diameter of 100 nm.These particles are expected to be non-toxic as theywere developed especially for cell studies. To con-firm this, we performed a cell viability test on HepG2cells exposed for 24 hour to approximately 10 000 par-ticles per cell. Experiments were performed both withand without application of a magnetic field. Figure 5shows a typical result with a very small number ofdead cells (red). Analysis of thirty images from threeindependent measurements shows that the survivalrate is higher than 90 %, which is equal to the controlwithout particles within measurement uncertainty.
C. Particle counting
Only the fluorescent particles can be imaged bymeans of an optical filter. To eliminate observer bias,and for practical reasons, particle counting was auto-mated using ImageJ software (see Section III). Theimage analysis procedure has two adjustable param- μ m S i g m a - A l d i r c h M i c r o m od no magnet magnet FIG. 5: Composite images of a live/dead cell vi-ability assay of 5 × HepG2cells / mL exposed to5 × nanoparticles / mL for 24 hours. Dead cells are dis-played in red, live cells in green. Top: Cells exposed to100 nm diameter cross-linked dextran iron-oxide compos-ite particles (Micromod). Bottom: 100 nm diameter ironoxide incorporated conjugated polymer particles (Sigma-Aldrich). The right-hand images are of cultures that wereplaced on the magnet. The cell survival for both types ofparticles and with or without field is higher than 90 %,which is equal within measurement error to the control.Therefore, we conclude that these particles are non-toxicfor a period of 24 hours, as expected. eters. The first is the threshold size of the observedparticle in pixels. This value should be sufficientlyhigh to avoid false detection due to noise, yet smallenough not to miss particles. With a 20 × lens, thepixel size is 324 nm, which is lower than the wave-length of the emitted light, so the minimum thresholdsize should be larger than 2 pixel × × ×
100 200 300 400 500 600 700 800 0 10 20 30 40 50 pa r t i c l e s de t e c t ed threshold area / pixels 0 50 100 150 200 250 300 350 400 0 5 10 15 20 25 30 35 40 pa r t i c l e s de t e c t ed threshold level /bit FIG. 6: Number of detected red fluorescent particles as afunction of the minimum size in pixels (top, using an in-tensity threshold of 25) and detection threshold (bottom,using a size threshold of 9 pixels). The number of detectedparticles is very sensitive to these settings, especially tothe intensity threshold level. tion algorithm shown in Figure 7. At a threshold of24, the non-uniform illumination disturbs the image,whereas the output seems reasonable from 26 to 28.However, the particle count varies by a factor of 10over this small range.The total number of particles expected from theconcentration of 5 × particles / mL is approxi-mately 1 × in the field of view. It is clear that,whatever the settings, the method grossly underesti-mates the number of particles. This is very likelydue to particle agglomeration, but one should notrule out that particles lose their fluorescent proper-ties. This does not render the method entirely use-less. By using an identical method to detect parti-cles in different images, a relative comparison can bemade between the case with and without the magnet.Therefore, we analysed images with a size thresholdof 3 pixel ×
24 25 26 27 28
Threshold
Particles μ m FIG. 7: Image of Micromod particles taken with red filter (left) and detected particles using automated image analysiswith a size threshold of 9 pixels as a function of the intensity threshold (indicated above the images). The number ofdetected particles (indicated below the images) is very sensitive to the threshold chosen for optimal particle detection.
D. Cell and particle count
The image analysis method was applied to hu-man liver cell cultures with Micromod and Sigma-Aldrich particles, both with and without magneticfield. Figure 8 shows composite images of typicalresults for these four cases. We superimposed thelocation of detected particles in red (Micromod par-ticles) and green (Sigma-Aldrich particles) on top ofthe greyscale bright field images. The cell and particledensities appear more or less similar. We performedstatistical analyses of 61 images (for Micromod 17and 7, for Sigma-Aldrich 23 and 14, away from andon top of the magnet, respectively). Figure 9 showsthere is no clear difference in particle density amongthe four cases. There is a hint that the particle den-sity is lower in the experiment with the MicroModparticles (left) on the magnet (red). Given the uncer-tainty in the particle detection algorithm, however,we refrain from drawing a definite conclusion.In addition to particles, we also analysed the num-ber of cells. Figure 10 shows the observed cell densityfor the four different cases. As the particles do not af-fect cell viability, we do not expect major differences.Indeed, the cell density does not exhibit a statisti-cally significant dependency on particle type or fieldcondition. The cell density is in agreement with thecell concentration in the administered solution (Sec-tion III), indicated by the black line labeled “theory”.We also counted the number of particles registeredwith cells in the bright field image. Figure 11 showsthat, again, there is no clear difference between thecells that were away from and those on top of themagnet. However, it is surprising that we observedless than ten particles on top of cells, which is far μ m S i g m a - A l d i r c h M i c r o m od no magnet magnet μ m FIG. 8: Composite image of HepG2 liver cells (greyscale)and detected Micromod red fluorescent particles (red, toprow) and Sigma-Aldrich green fluorescent particles (green,bottom row). There is no significant difference betweenthe sample that has been away from (left) or on top of(right) the magnet for 24 hours. too few. From the cell and particle densities shownin Figures 9 and 10, one would expect approximately40 particles per cell. A possible explanation couldbe that particles do not adhere well to the cell mem-brane. Nevertheless, one should not rule out thatparticles may be incorporated into the cell and losetheir fluorescent properties.From these observations we conclude that the typeof particles used in this experiment is not very suit-able to determine whether there is an enhanced up-take of magnetic particles under application of astrong field gradient. Compared to the uncertain- pa r t i c l e s / mm no magnetmagnet FIG. 9: Particle density obtained from image analysis forsamples with two different magnetic particles, away from(grey) and on top of (red) the magnet. A box is drawnaround the region between the first and third quartiles,with a horizontal line at the median value. Whiskers ex-tending from the box encapsulate two-thirds of the datapoints. Data outside that range is indicated by points.There is no statistically significant difference in the fourcases. For the Micromod particles, there is a hint of areduction in particle density when the sample was on themagnet. theory c e ll s / mm no magnetmagnet FIG. 10: Observed cell density for samples with two dif-ferent magnetic particles, away from (grey) and on top of(red) the magnet. The cell density is on the order of theexpected value (black line labeled “theory”) and there isno significant influence of the magnetic field. ties caused by the image analysis and spread betweenindividual images, the differences between the casesare small. This uncertainty prohibits us from draw-ing robust conclusions. Rather, one will have to applymore complicated methods such as measuring the ironcontent by mass spectrometry, transmission electronmicroscopy or transfection.
V. CONCLUSIONS
We constructed a magnetic system that exerts astrong force on fluorescent magnetic nanoparticles in-side a channel slide with a human liver cell culture. pa r t i c l e s / c e ll no magnetmagnet FIG. 11: Number of particles that coincide with a cell fortwo different magnetic particles, away from (grey) and ontop of (red) the magnet. The differences are not signifi-cant. As in the particle count for the Micromod particles(Figure 9), there might be some reduction in particles percell under application of a field.
By using a cylindrical magnet with a diameter of70 mm, the vector components of the field and force inthe vertical direction were dominant, with a strengthin excess of 300 mT and 6 MN / m , respectively. Overthe length of the 30 mm channel, the force strengthremains within 14 % and the force direction varies byless than 1 ° .HepG2 human liver cells exposed for 24 hoursshowed no significant change in cell viability whenexposed to cross-linked dextran iron-oxide compos-ite particles (Micromod) or iron oxide incorporatedconjugated polymer particles (Sigma-Aldrich), bothof 100 nm diameter and with a concentration of10 000 particles / cell.The number of fluorescent particles detected by op-tical microscopy depends by at least one order of mag-nitude on the settings of the automated image detec-tion algorithm. The number of detected particles isespecially sensitive to the intensity level threshold.Analysis of over 60 images did not show an increasein the number of observed magnetic particles overlap-ping with cells when a magnetic force is applied. Onthe contrary, the particle density seems to be a factorof 40 lower on cells than in regions without cells.From these measurements, we conclude that usingfluorescent magnetic nanoparticles to demonstrateenhanced particle uptake in magnetic fields is far fromtrivial, and may not be the optimal approach. [1] A. Elsaesser and C. V. Howard, AdvancedDrug Delivery Reviews , 129 (2012),doi:10.1016/j.addr.2011.09.001.[2] A. C. Anselmo and S. Mitragotri, Bioengi-neering & translational medicine , 10 (2016),doi:10.1002/btm2.10003.[3] S. Mornet, S. Vasseur, F. Grasset, and E. Duguet,Journal of Materials Chemistry , 2161 (2004),doi:10.1039/b402025a.[4] Q. A. Pankhurst, J. Connolly, S. K. Jones, andJ. Dobson, Journal of physics D: Applied physics ,R167 (2003), doi:10.1088/0022-3727/36/13/201.[5] G. Zabow, S. Dodd, E. Shapiro, J. Moreland, andA. Koretsky, Magnetic Resonance in Medicine ,645 (2011), doi:10.1002/mrm.22647.[6] S. J. Soenen and M. D. Cuyper, Nanomedicine ,1261 (2010), doi:10.2217/nnm.10.106.[7] J. G. Teeguarden, P. M. Hinderliter, G. Orr, B. D.Thrall, and J. G. Pounds, Toxicological Sciences ,300 (2006), doi:10.1093/toxsci/kfl165.[8] K. Pondman, N. Bunt, A. Maijenburg, R. vanWezel, U. Kishore, L. Abelmann, J. tenElshof, and B. Ten Haken, Journal of Mag-netism and Magnetic Materials , 299 (2014),doi:10.1016/j.jmmm.2014.10.101.[9] D. . H. Kim, E. A. Rozhkova, I. V. Ulasov, S. D.Bader, T. Rajh, M. S. Lesniak, and V. Novosad, Na-ture Materials , 165 (2010), doi:10.1038/nmat2591.[10] D. Kilinc, C. Dennis, and G. Lee, Advanced Materialspp. 5672–5680 (2016), doi:10.1002/adma.201504845.[11] M. Colombo, S. Carregal-Romero, F. Casula M.,L. Guti´errez, P. Morales M., B. Bahm I.,J. T. Heverhagen, D. Prosperi, and W. J.Parak, Chemical Society Reviews , 4306 (2012),doi:10.1039/c2cs15337h.[12] S. Prijic, J. Scancar, R. Romih, M. Cemazar, V. B. Bregar, A. Znidarsic, and G. Sersa, TheJournal of Membrane Biology , 167 (2010),doi:10.1007/s00232-010-9271-4.[13] H. Haim, I. Steiner, and A. Panet, Journal ofVirology , 622 (2004), doi:10.1128/jvi.79.1.622-625.2005.[14] F. Scherer, M. Anton, U. Schillinger, J. Henke,C. Bergemann, A. Kr¨uger, B. G¨ansbacher,and C. Plank, Gene therapy , 102 (2002),doi:10.1038/sj.gt.3301624.[15] M. Pickard and D. Chari, Nanomedicine , 217(2010), doi:10.2217/nnm.09.109.[16] T. Dejardin, J. de la Fuente, P. del Pino,E. P. Furlani, M. Mullin, C.-A. Smith, andC. C. Berry, Nanomedicine , 1719 (2011),doi:10.2217/nnm.11.65.[17] I. Venugopal, S. Pernal, A. Duproz, J. Bentley,H. Engelhard, and A. Linninger, Materials Re-search Express , 095010 (2016), doi:10.1088/2053-1591/3/9/095010.[18] J. Park, N. R. Kadasala, S. A. Abouelmagd,M. A. Castanares, D. S. Collins, A. Wei,and Y. Yeo, Biomaterials , 285 (2016),doi:10.1016/j.biomaterials.2016.06.007.[19] B. Delinchant, D. Duret, L. Estrabaut, L. Gerbaud,H. Nguyen Huu, B. Du Peloux, H. L. Rakotoarison,F. Verdi`ere, and F. Wurtz, COMPEL-The interna-tional journal for computation and mathematics inelectrical and electronic engineering , 368 (2007),doi:10.1108/03321640710727728.[20] H. Yun, X. Liu, T. Paik, D. Palanisamy, J. Kim,W. D. Vogel, A. J. Viescas, J. Chen, G. C. Pa-paefthymiou, J. M. Kikkawa, et al., ACS Nano8