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\begin{document}

\title{Optimized Tip-Sonication Temperature and Mixing using Finite Element
Modeling for High-Yield Bacterial Cell-Free Extract}



\author[1]{Sakib Ferdous}%
\author[1]{Jared Dopp}%
\author[1]{Nigel Reuel}%
\affil[1]{Iowa State University}%


\vspace{-1em}



  
  \date{May 25, 2024}


\begingroup
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\selectlanguage{english}
\begin{abstract}
Optimal tip sonication settings, namely tip position, input power, and
pulse durations, are necessary to ensure proper mixing and maintain
solution temperature below a critical temperature. This is significant
for temperature sensitive procedures like preparation of viable cell
extract for in vitro protein synthesis. In this paper, the optimum tip
immersion depth is estimated which ensures maximum mixing thereby
enhancing thermal dissipation of local cavitation hotspots inside the
sonication tube; from modeled velocity field streamlines this is found
at immersion depths between 20-30\% height below the liquid surface. A
simplified finite element (FE) heat transfer model is presented and
validated experimentally with (R2 \textgreater{} 97\%) which can predict
the temperature rise over time in a tip-sonicated vessel. This model is
used to observe the effect of temperature rise on cell extract
performance of E. coli BL21 DE3 star strain and estimate the temperature
threshold. From the combined heat map of yield and temperature it is
observed that yield is correlated with final steady state temperature.
Relative yields in the top 10\% are observed for solution temperatures
maintained below 32\selectlanguage{ngerman}°C; this reduces below 50\% relative yield at
temperatures above 47°C. To extend utility of these finite element
models to other temperature sensitive sonication processes, we also
present a generalized workflow for direct simulation using the FE code
as well as master plots for estimation of sonication parameters (power
input and pulse settings) without need of running the code.%
\end{abstract}\selectlanguage{ngerman}%



\sloppy


\textbf{Optimized Tip-Sonication Temperature and Mixing using Finite
Element Modeling for High-Yield Bacterial Cell-Free Extract}

By Sakib Ferdous\textsuperscript{1}, Jared L. Dopp\textsuperscript{1},
and Nigel F. Reuel\textsuperscript{1}*

1. Department of Chemical and Biological Engineering, Iowa State
University

*reuel@iastate.edu

*Corresponding author: Dr Nigel F. Reuel

Address: 3051 Sweeney 618 Bissell Rd. Ames, IA 50011-1098

Email:~reuel@iastate.edu

Phone:~515-294-4592

Running title: Tip-sonication optimization for cell-free extract

\textbf{Funding}

This work was supported by NIGMS MIRA ESI Award \#1R35GM138265-01



\textbf{Abstract}

Optimal tip sonication settings, namely tip position, input power, and
pulse durations, are necessary to ensure proper mixing and maintain
solution temperature below a critical temperature. This is significant
for temperature sensitive procedures like preparation of viable cell
extract for \emph{in vitro} protein synthesis. In this paper, the
optimum tip immersion depth is estimated which ensures maximum mixing
thereby enhancing thermal dissipation of local cavitation hotspots
inside the sonication tube; from modeled velocity field streamlines this
is found at immersion depths between 20-30\% height below the liquid
surface. A simplified finite element (FE) heat transfer model is
presented and validated experimentally with
(R\textsuperscript{2}\textgreater{} 97\%) which can predict the
temperature rise over time in a tip-sonicated vessel. This model is used
to observe the effect of temperature rise on cell extract performance of
\emph{E. coli} BL21 DE3 star strain and estimate the temperature
threshold. From the combined heat map of yield and temperature it is
observed that yield is correlated with final steady state temperature.
Relative yields in the top 10\% are observed for solution temperatures
maintained below 32C; this reduces below 50\% relative yield at
temperatures above 47C. To extend utility of these finite element models
to other temperature sensitive sonication processes, we also present a
generalized workflow for direct simulation using the FE code as well as
master plots for estimation of sonication parameters (power input and
pulse settings) without need of running the code.

\emph{Keywords: Cell free protein synthesis, tip-sonication,
protein-denaturation, bacterial cell lysis}

\emph{}

\textbf{Introduction}

Cell free protein synthesis (CFPS) is a method of producing
proteins\emph{in vitro} , which is widely used to manufacture synthetic
biology sensors (Pardee et al., 2016; Salehi et al., 2017; Takahashi et
al., 2018), prototype proteins (Dopp \& Reuel, 2020; Dopp, Rothstein,
Mansell, \& Reuel, 2019), discover metabolic pathways (Dudley, Nash, \&
Jewett, 2019; Jaroentomeechai et al., 2018), and to manufacture some
protein therapies (Cai et al., 2015; Yin et al., 2012; Zawada et al.,
2011). In a typical reaction, the protein is expressed by combining cell
extract with energy supplements and a DNA template. Bacterial cells,
most commonly a productive \emph{E. coli} strain with protease knockouts
(BL21 DE3 star), are lysed to produce the cell extract which contains
required intercellular machinery for the reaction, like ribosomes and
metabolic enzymes (Smith, Wilding, Hunt, Bennett, \& Bundy, 2014). As an
active cell extract is key for optimal CFPS, many groups have focused on
optimizing and streamlining the extract production procedure (Kwon \&
Jewett, 2015; Shrestha, Holland, \& Bundy, 2012). Sonication is a
convenient and cost-effective method for lysing small cell batches
(\textless{}20 g wet cell weight), as opposed to use of more
capital-intensive homogenizer or French press at larger scale (Dopp \&
Reuel, 2018; Kwon \& Jewett, 2015; Shrestha et al., 2012).

Sonication uses oscillating ultrasonic waves to lyse the outer membranes
of cells via cavitation. A probe transducer (Harrison, 1991; Islam,
Aryasomayajula, \& Selvaganapathy, 2017) is inserted into the fluid
vessel (Fig 1a) and its tip oscillates causing rapid back and forth
fluid motion, leading to pressure waves that create and compress bubbles
(Jamshidi, 2013). The resulting shock waves from collapsing bubbles are
sufficient to rupture cell membranes. The local temperature, in a very
small region of cavitation, increases by thousands of degrees K (Wang,
Yuan, \& Hale, 2016), but quickly dissipates. Over time this causes
buildup of thermal energy in the sonication tube causing temperature
rise (Islam et al., 2017; Wang et al., 2016). Additionally, sonication
induces fluid flow via ultrasonic waves in a process called acoustic
streaming (Nyborg, 1953). Proper mixing in the cell suspension vessel is
necessary for efficient sonication, to eliminate local hot spots (Zhou
et al., 2010); otherwise a small fraction of suspension will be over
sonicated (causing unwanted temperature rise) and the bulk of the
suspension will sit idle. For cells collected from typical shake flask
growths (\textasciitilde{}1-20 g wet cells, prepared at 1 g/ml buffer),
sonication is typically performed in snap-cap microcentrifuge 1.5 mL
tubes, but can also be done in 5, 15, and 50 mL conical vessels (Fig
1b). Most protocols carefully specify tip height placement or suggest
manual motion of the tip to ensure the suspension is mixed and subject
to the same level of ultrasonic exposure. The production of viable cell
lysate is proportional to cavitation and the extent of cavitation is
dependent on the power input (Harrison, 1991; Sutkar \& Gogate, 2009;
Wang et al., 2016). Higher power density results in faster cell lysis,
but greater heat accumulation. Researchers concluded that the total
sonication energy input from the tip ultimately converts to thermal
energy very near to the tip (Chivate \& Pandit, 1995; Prabhu, Gogate, \&
Pandit, 2004). It is documented that extract conditioning temperature
rise affects CFPS yield (Kigawa et al., 2004), which agrees with our
biophysical understanding of denaturing and loss of function at elevated
temperatures, typically \textgreater{} 42C (de Groot \& Ventura, 2006;
Farewell \& Neidhardt, 1998). It is also observed that prolonged
ultrasound exposure can have adverse effects on biological molecules,
namely the formation of hydrogen, hydroxide and peroxide radicals and
degradation of protein and enzymes (Islam et al., 2017; Miller, Miller,
\& Brayman, 1996; Rokhina, Lens, \& Virkutyte, 2009; Save, Pandit, \&
Joshi, 1997).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

\textbf{Figure 1} -- (a) Schematic depicting cell lysis by tip
sonication: (i) sonicator tip is inserted into the sonication vessel,
submerging tip in liquid. (ii) Controller for specifying pulse,
amplitude \& duration iii) The tube sits in ice-bath for cooling iv)
Input energy from controller (ii) is set as a function of signal
amplitude (translates to tip power based on fluid volume and vessel),
pulse durations, and total sonication time v) Thermal energy transfers
to ice-bath from cell suspension domain vi) The sonicated liquid is
divided into circulated zone \& dead zone (b) Axis-symmetric models
(right half) of common laboratory tubes: i) 1.5 mL microcentrifuge tube
ii) 5 mL microcentrifuge tube iii) 15 mL Falcon tube iv) 50 mL Falcon
tube

It is also important to note that adverse temperature effects of
sonication extend beyond this paper's focusing example of cell lysate
preparation. For example, mass loss of graphene nano particles is caused
by temperature rise in sonication (Baig et al., 2018). In ultrasonic
extraction of corn, overexposure causes reduction of glucose release due
to denaturation of enzyme due to temperature rise. There is a reduction
in taste, vitamin content and loss of texture in foods that over
processed with ultrasonic extraction (Tobergte \& Curtis, 2013). In
another example, single walled carbon nanotubes (SWCNT) bundle ends are
frayed due to temperature rise caused by ultrasonic exposure (Hassan,
Reddy, Haque, Minett, \& Gomes, 2013; Strano et al., 2003). Thus, a
model for mixing and temperature rise caused by sonication will find
uses in broader biotechnology applications.

Sonication protocols are designed to mitigate this influence of
temperature rise and improve mixing; however, they currently require
much empirical testing to determine. Typically, the probe is operated in
a pulsed fashion with defined on and off cycles. Additionally, the
sonication vessel is submerged in an ice bath or chiller line. There is
a tradeoff between the number of cells lysed and the extract viability
which decreases when over-sonicated. From a physical standpoint, it is
logical that there exists a threshold temperature for each type of
extract, and corresponding sets of optimum parameters to stay below this
threshold, but in practice, finding this threshold and controlling
temperature rise experimentally can be difficult. The sonicator
parameters of input power, pulse durations, and total sonication times
are empirically optimized for a given vessel, often necessitating a
large number of experiments to cover the design space (Kwon \& Jewett,
2015). Characterization tools can help direct such experiments, but
their utility for small volume lysate preparations are limited (Sutkar
\& Gogate, 2009). The velocity field inside a sonoreactor can be
monitored by particle image velocimetry (PIV) techniques (G. S. B.
Lebon, Tzanakis, Pericleous, Eskin, \& Grant, 2019; Donato Rubinetti,
Weiss, Wahlen, \& M\selectlanguage{ngerman}üller, 2016), but for opaque lysate in a small tube
such techniques cannot be used to conveniently measure the velocity
pattern. It is also difficult to routinely measure temperature in such
small volumes by thermocouple and as the vessel is seated in an ice
bath, it is also difficult to monitor the inner vessel temperature by
NIR imaging. Thus, to more efficiently design optimal sonication
protocols for thermally sensitive procedures like cell extract
preparation, we propose finite element modeling of mixing and thermal
effects.

Finite element modeling of ultrasound systems has been demonstrated in
literature, especially for larger reactors. Fluid flow in large
sonoreactor (\textgreater{} 500 mL) has been extensively studied (B.
Lebon, Tzanakis, Pericleous, \& Eskin, 2019; D. Rubinetti \& Weiss,
2018; Xu, Yasuda, \& Koda, 2013). The temperature-rise in large
reactors, however, is less prevalent, likely due to temperature rise
being negligible in a large vessel when subjected to low power density
input and having a larger surface area for thermal dissipation (Trujillo
\& Knoerzer, 2011). Effects of ultrasound (temperature rise and fluid
streaming) are mostly studied for medical applications of
high-intensity, focused ultrasound (Moriyama, Yoshizawa, \& Umemura,
2012; Solovchuk, Sheu, Lin, Kuo, \& Thiriet, 2012). Conversely, in cell
extract preparation, much smaller, laboratory scale tubes (Fig 1b) are
used and both mixing and temperature effects will need to be managed.
This can be done using a similar framework of finite element modeling.

This paper provides a computational model to predict the effects of tip
sonication parameters on mixing and temperature rise in small vessels,
commonly used for cell extract preparation. First the relationship
between fluid flow patterns and tip immersion depth is modeled; this is
used to estimate the optimum tip depth which maximizes mixing. This is
done by numerically calculating the stationary velocity field inside the
sonication tubes for different tip immersion depths and comparing the
fractional volume with regular, circulating streamlines. Next a heat
transfer model is used to predict temperature rise over time due to
sonication in lab scale tubes which is then experimentally validated.
This model is then used to estimate the optimal threshold temperature in
a common cell extract strain (BL21 DE3 star) using optimized CFPS
experiments presented in literature (Kwon \& Jewett, 2015). This model
coupled to experimental data can then provide insight on the effect of
sonication temperature on cell lysis yield. A stepwise workflow is then
presented for use of these numerical models in obtaining optimized
parameters for other novel sonication set ups. Lastly, we provide
convenient master-plots for determination of optimal sonication
conditions for new temperature thresholds without need of running the
modeling code.

\textbf{Result and Discussion}

\emph{Effect of sonication tip position on extent of mixing}

Before determining thermal effects of sonication, a simple acoustic
streaming model is used to study the effect of sonication tip position
on extent of mixing. A tip placement that induces near to complete
mixing is necessary to simplify the heat transfer model (assumption of
uniform mixing, decoupling acoustic model from thermal). From our finite
element model (see methods), we obtain stationary flow velocities at
each point inside the sonication tube. As estimated from other
literature sources (Trujillo \& Knoerzer, 2011), it is observed that the
liquid flows as a uniform jet downward from the sonicator tip, gets
deflected by the bottom of the vessel and flows upward, turning near the
vessel neck back towards the tip creating a circulation zone of rotating
streamlines (yellow color in Fig 2a). Outside the circulation zone there
are two regions with moderate to low, irregular velocity (`dead zones'
at the top and bottom of the tube, indicated by the grey area in Fig
2a). Our goal is to maximize the circulation zone and reduce the dead
zone in each tube based on tip position.

This simulation was run for different tip depths starting at 0.5 cm and
increasing at intervals of 0.5 cm for each of the four standard tube
sizes used in tip sonication of cell extract (1.5, 1.5, 5, 15 and 50 mL)
with volumes of 1.5, 1, 5, 10, and 15 mL respectively. Simulation
results are shown as streamline diagrams, indicating the boundary of the
circulation zone in each of the four tubes (1.5 mL diagram is shown in
Figure 2, remainder can be found in Supplementary Fig 1-5). The
circulation zone fraction to total fluid volume is quantified with
ImageJ and percent circulation zone is plotted as function of tip
immersion depth from surface percentage to total liquid depth. It is
observed that for each of the tubes simulated the greatest percentage of
volume is mixed, if the tip depth is within 20-30\% from the top of the
total liquid height and is best mixed in a 50 mL tube (with 15 mL total
volume).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

\textbf{Figure 2} : Modeling effect of tip depth on mixing. a)
Circulation zone (yellow) and dead zone (gray) with different tip depths
for 1.5 mL Microcentrifuge tube obtained from simulation. b) Percentage
of volume in circulation zone with changing tip height for four sizes of
tubes 1.5,1.5, 5, 15, and 50 mL with 1.5,1, 5, 10, 15 mL sample
respectively.

For the common 1.5 mL snap-cap microcentrifuge tubes the vessel cavity
is narrow (low clearance between tip and wall) and the liquid has a
smaller circulation zone; when the tip depth is more than 60\% of the
liquid height, the circulation zone percentage falls below 50\% of the
total capacity, in simulation. Another interesting observation is
reduced mixing at the shallower tip depths for the 15 mL centrifuge
tube; this tube has the highest length to diameter aspect ratio of the
tubes screened and we observe a dead zone build up at bottom of the tube
if the depth is less than 20\% from the top; likewise, there is reduced
mixing if depth is more than 40\% (dead zone near the top surface). The
50 mL tube is the only one simulated that can achieve nearly 100\%
mixing (at depths less than 40\% total fluid height). We attribute this
to the superior circulation zone observed in this vessel size. However,
the 50 mL tube has the limitation of poorer heat dissipation (smaller
area to volume ratio) leading to greater potential of heat build-up and
damage to cell extract preparation. This laminar model does not take
into account the improved mixing cause by turbulent eddies caused by
sonication; thus we progress to the heat transfer model by making the
assumption of complete mixing for all tubes and then use experimental
validation to confirm use of this assumption.

\emph{2) Heat transfer model and experimental validation}

Temperature rise due to sonication was simulated using a finite element
heat transfer model (see methods) for four sets of pulse length, total
power, and vessel size conditions: (1) 10 s, 5.5 W, 1.5 mL, (2) 20 s,
5.5 W, 1.5 mL, (3) 10 s, 12.5 W, 5 mL, (4) 10 s, 1.73W, 1.5 ml tubes.
These were then experimentally validated under the same conditions using
a thermocouple probe (Fig 3, supplementary figure 9). It is observed
that the simulated temperature profile matches well with the experiment
(R\textsuperscript{2} = 0.9947, 0.9989, 0.9926 and 0.9849). This
indicates that the model assumptions made (namely complete mixing in the
tube) are adequate and that the model can be used to assess published
data and to calculate optimized conditions.

\textbf{Hosted file}

\verb`image3.emf`  available at \url{https://authorea.com/users/398739/articles/511356-optimized-tip-sonication-temperature-and-mixing-using-finite-element-modeling-for-high-yield-bacterial-cell-free-extract}

\textbf{Figure 3} - Temperature rise over time determined experimentally
(blue line) and estimated with the finite element simulation (orange
line). a) 1.5 mL microcentrifuge tube with 1.5 mL sample at 50\%
amplitude using a 3mm tip (corresponding to \textasciitilde{}5.5 Watt)
and 10 second on and 10 second off pulse, initial temperature 1.6C. b)
1.5 mL microcentrifuge tube with 1.5 mL sample at 50\% amplitude using a
3mm tip (corresponding to \textasciitilde{}5.5 Watt) and 20 second on
and 20 second off pulse, initial temperature 3.4C. c) 1.5 mL
microcentrifuge tube with 1.5 mL sample at 25\% amplitude using a 3mm
tip (corresponding to \textasciitilde{}2 Watt) and 10 second on and 10
second off pulse, initial temperature 1.1C. d) 5 mL microcentrifuge tube
with 5 mL sample at 50\% amplitude using a 6mm tip (corresponding to
\textasciitilde{}12.5 Watt) and 20 second on and 20 second off pulse,
initial temperature at 14.4 C.

From the model and experimental data, we observe that the temperature
starts rising immediately as the sonication starts and within a
relatively short time (300-500 s) it reaches a steady state, a point
where the energy added by sonication is equal to the energy lost to the
ice-bath. It is also observed that the temperature follows a very
predictive parabolic pattern while rising and the model could capture
this effect. The model can then be used to estimate temperature rise for
different sonication conditions with different power input, vessel
geometry, sample volume and pulsing.

\emph{3) Estimation of optimum temperature in cell extract preparation
\& role of power density}

With a valid heat transfer model in place, we can next estimate the
maximum temperature threshold during cell lysis for optimum yield from
the common \emph{E. coli} BL21 DE3 star strain. This can be estimated
using the published data by Kwon et al. (Kwon \& Jewett, 2015) where
relative CFPS yields were measured from 144 samples of extract prepared
by sonication at different volumes (1500, 1000, 700, 500, 300, and 100
\selectlanguage{greek}µ\selectlanguage{english}L) and input energy; other parameters such as sonication amplitude, tip
size, pulse on duration, and pulse off duration were held constant at
50\%, 3 mm, 10 s, and 10 s respectively and the tube was cooled by an
ice bath, starting at 277K. From this, a contour map was produced by
plotting energy added (x-axis), volume of sample (y-axis) and yield
(z-axis) (reproduced from original data in Fig 5a). This plot shows the
effect of sample volume and energy added on yield.

To convert this data to temperature, we first needed to determine the
power input for each of the sample volumes. We empirically determined
the power at each of the measured volumes using the same sonicator
(Qsonica 125) set at 50\% amplitude (Supplement Fig 6,7), observing that
the power input at a given amplitude setting on the sonicator is
dependent on the volume of the liquid. This measured input power was
then divided by the sample volume to get the volumetric heat source used
in the heat transfer model (Q\textsubscript{g} term, discussed in
methods). The pulse time (10 s on and off), cooling condition and all
associated geometric and thermal parameters were supplied as model
inputs according to the simulation outlined in the methods section.
Using the model, the temperature is estimated over time for each volume.
The peak temperature in a cycle of on-off pulses is observed at the last
second of the on pulse (Fig 3, top of each saw tooth wave). From the
temperature vs. time data, we select the temperature at each peak and
convert the sonication time data (cumulative of pulse on time only) to
energy by multiplying with the effective power value. By this we obtain
temperature vs. energy data and interpolate to determine the temperature
value for a given input energy value (over the range of 0 to 1600 Joules
used by Kwon et al., see Supplement table 16 for example calculation).
This data is then used to create a temperature matrix (supplementary
table 17,18) and this data is superimposed as contour lines on the same
yield plot from Kwon et al. (Fig 4a). Temperature and normalized yield
for individual sample volumes are also plotted in Supplementary Figure
8.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

\textbf{Figure 4} -- a) Heat map of normalized sfGFP yield from BL21 DE3
Star cell extracts prepared at different volumes and total energies,
with z-axis color bar presenting relative amounts of expression
(replotted from (Kwon \& Jewett, 2015)). Thick dashed lines depict
temperatures (K) at these sonication conditions obtained by the finite
element simulation. Thin solid lines indicate energy density values
(J/mL). b) The same normalized yield data plotted in a more generalized
fashion as power density vs. total energy; dashed lines again show
temperatures estimated by simulation.

These modeled temperatures allow us to observe the effect of temperature
on different yields. From the graph, it can be observed that the yield
is \textgreater{} 90\% relative yield in regions where temperature is
below 305K; beyond 320K the yield reduces below 50\% relative yield. Our
finding that protein yield is influenced by temperature is well
supported by cell free literature (Kigawa et al., 2004). We also observe
from the Kwon data that increased energy at larger volume has little
effect on yield; this is again attributed to temperature effect as we
see from the model that the mixture reaches a steady state temperature
below the 305K limit. Again, the steady state is reached when the heat
added by sonication and removed by cooling is equal, which depends on
rate of energy supplied, as we discuss next.

In the Kwon et al. study, a linear equation is presented that determines
total energy needed based on sample volume to optimize protein yield,
but this is only at a set specific amplitude and pulse on/off times. It
makes intuitive sense that the yield is not only dependent on total
energy supplied per volume (energy density), but also the rate at which
energy is supplied per unit volume (power density and pulsing times). In
the Kown et al. framework a certain amount of energy has to be given per
volume for optimal lysing. However, the energy could be supplied slowly
(less power density and short pulse on time) or quickly (more power
density long pulse on time). Intuitively, if the energy is supplied too
fast the temperature would rise above an undesired point, and the yield
should fall. This power density effect can be studied with the heat
transfer model. For example, the optimum energy for a 1000 \selectlanguage{greek}μ\selectlanguage{english}L sample
according to the Kwon et al. equation is (1000-33.4)
\(\times\)1.8\textsuperscript{-1} = 553 Joules. If this 553
Joules is supplied using 15 Watt power corresponding to 0.015 W/\selectlanguage{greek}μ\selectlanguage{english}L power
density with 20 second on-off pulse, it would take only two bursts to
supply the required energy and the total processing time required would
be one minute; however, the final temperature would be above 340K and
yield would suffer despite use of the optimal energy density.

Thus, to observe the role of power density more clearly, we transform
the same data into another contour plot (Fig 4b). Here the y-axis is
changed from volume to power density by dividing the tip input power at
that liquid volume (empirically derived -- Supplement figure 7) by the
volume. The x and z-axis are kept the same as before (energy and yield,
temperature values respectively). At these sonication conditions (50\%
amplitude and 10 s pulse settings) the relative yield is above 90\% in
the small window of power densities between 0.005 to 0.01 W/\selectlanguage{greek}μ\selectlanguage{english}L and 200
to 1000 J total energy. If the power density is more than 0.015 W/\selectlanguage{greek}μ\selectlanguage{english}L,
the yield is low (\textless{}60\%) regardless of energy input and the
modeled temperature increases above 320K for total energies above 100 J.
Another interesting observation from inspecting the data in terms of
power density, is that at each power density the temperature rises to a
steady state very quickly (horizontal isotherms). This means that at
each sonication setting (under active cooling, ice bath) the steady
state temperature can be determined by the finite element heat transfer
model. In other words, the maximum temperature that can be reached in a
sonication system can be tuned using the heat transfer model by altering
power density and pulsing.

\emph{4) Optimizing temperature sensitive sonication using the heat
transfer model}

The finite element heat transfer model (COMSOL code in Supplement, also
as a module) is readily adaptable and can be used to efficiently
determine optimal sonication settings for new temperature sensitive
processes. For cell-free extract, this could be using a different
sonication vessel, cooling method, or cell extract density. This also
has utility beyond cell-free, such as preparation of temperature
sensitive emulsions, nanoparticles, or nano-sensors in which the same
model can predict temperature rise (after adjusting fluid intrinsic
properties). This can be done in a logical stepwise process (summarized
in Fig 5).

First, the vessel materials and associated thermal parameters, vessel
geometry, sample volume, cooling method (water bath, ice water bath, ice
water bath with cooler, insulation or no cooling) are specified as
scalar values and proper boundary conditions within COMSOL. The energy
requirement per volume is determined according to process requirement
(\emph{e.g.} for cell extract, the energy needed to lyse the cells). In
most cases, this is done by empirical measurement. For cell lysis of
BL21 DE3 cells, the Kwon et al. data shows yield \textgreater{} 90\%
lies between 0.27 J/\selectlanguage{greek}μ\selectlanguage{english}L\selectlanguage{ngerman} to 0.85 J/\selectlanguage{greek}μ\selectlanguage{english}L
(solid blue slopes shown on Fig 5a). In our model the midpoint, optimal
energy density of 0.55 J/\selectlanguage{greek}μ\selectlanguage{english}L is used.

Next, the minimum power density and threshold temperature for the
specific sonication task should also be specified. In cases of larger
volume sonication, if the power density is too low there will not be
sufficient power to cause cavitation (and thereby lysis of cells,
formation of nanoparticles, etc.) (Chemat et al., 2017). Again, one
estimates the minimum power density from process knowledge or empirical
data, but this is used as a starting point for the simulation and is
adjusted to meet the target threshold temperature (which is again found
empirically). For BL21 DE3 star cells, good yield was obtained using a
power density between 0.003 and 0.01 W/\(\mu\)L.

The optimum power density and pulse time is obtained iteratively from
the model. First the duration of sonication is calculated using the
equations in the third process model block (Fig 5) using an initial
guess of power density higher than minimum and set pulsing times. The FE
model is then used to calculate temperature rise over time. If
temperature surpasses the threshold, the power density and pulsing are
changed (less power, shorter pulses to drop temperature) and the
simulation is again repeated until pulse timing and set power density is
obtained for which temperature is below threshold.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image5/image5}

\end{center}
\end{figure}

\textbf{Figure 5:} Workflow diagram to obtain optimized sonication
parameters for temperature sensitive procedure using the finite element
model directly (access to COMSOL required to run provided process code).

Next, the total power requirement is calculated by multiplying the power
density used in the model with the sample volume. If a single tip is not
capable of supplying this total power (10 and 17 W from the 2 and 3 mm
QSonica tips) the sample can be divided into more than one tube or a
larger tip can be used (however, this again affects the model geometry
which takes into account total fluid and tip size). After the input
power is selected, the mixing is optimized by using the CFD calculation
by adjusting the sonicator transducer position using the geometrical and
fluid parameter in the first block. Installing baffles could enhance
mixing but is beyond the scope of this simple model.

With this workflow one can obtain a set of optimized sonication
parameters, namely transducer position, power density, pulsing and
sonication duration that will ensure better mixing and safe temperature
rise. This same workflow is applicable to other geometries such as a
sonication bath in beakers, automated sonication systems, or miniature
lab on a chip cell lysis device (making sure to change geometry of the
model and correctly specifying the sonication transducer surface).
However, this iterative process requires resources to run the finite
element model, and in the case of tip-sonication of cell extract, a set
of master data would be sufficient to interpolate most process
conditions, without need of solving the finite element equations.

\emph{5) Optimizing sonication with master plots for common cell extract
parameters}

Noting that both software access and computation time necessary to run
our finite element model may limit its utility, we also devised a set of
master plots that can likewise be used to efficiently select sonication
conditions for cell extract processing, but still gives the flexibility
to use strains that have different temperature and power density
limitations. Here we model the maximum temperature that can be reached
in aqueous samples by a standard tip sonication set up (cooling in
ice-bath with sufficiently large volume) for four common sonication tube
sizes, while varying power density and pulse settings (Fig 6). These
plots can be used directly to find optimal sonication parameters at a
set temperature threshold without having to run the FE model.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image6/image6}

\end{center}
\end{figure}

\textbf{Figure 6:} Maximum temperature (y-axis) estimated for different
power density (x-axis) and pulse time (5-10,10-10,15-10 and 20-10 on-off
pulses respectively) for each of the four tubes -- a) 1.5 mL
microcentrifuge tube b) 5 mL microcentrifuge tube c) 15 mL conical tube
d) 50mL conical tube.

To provide clarity on use of these master plots we provide an example.
Assume a cell growth yields 3 g of cells, to make 3 mL of cell
suspension for sonication and the specific strain threshold temperature
is 320K (empirically observed). First a sonication tube with adequate
volume is selected -- in this case the 1.5 mL tube is too small, and the
5 mL tube is a suitable choice. Next, draw a horizontal line at the max
temperature (in this case 320K) for the selected tube (dotted line in
Fig 6b) which will intersect lines for four different pulse condition
(5-10,10-10,15-10 and 20-10 on off pulses). The power density for these
pulse conditions are then read from the x-axis at these points (4.5, 3,
2.5, and 2.2 W/mL respectively). Then the sample volume (in mL) is
multiplied with the power density for the selected pulse condition to
get the maximum permissible power. In the case of 3 mL samples in the 5
mL tube at the 5-10, 10-10, 15-10 and 20-10 s on/off pulse settings, the
max power settings obtained are 13.5, 9, 7.5, 6.6 W respectively. Now
one can tune the power setting with reference to the sonicator
calibration chart (provided by vendor or empirically determined, see
Supplement Fig 6,7) to select an input power that will not exceed the
threshold temperature. In the case of this example, if less than 6.6 W
power is used with 20-10 s on/off pulses the maximum temperature will
always be below 320K regardless of time sonicated. The next step would
be to process a few batches of cells at these conditions to determine
the appropriate energy density (J/mL) and thus overall length of
sonication (number of pulse) cycles on yield. Using the optimal energy
density of 550 J/mL from the BL21 DE3 star cells, the sonication
duration would be 570 seconds or 19 cycles.

\textbf{Conclusion}

The optimum tip immersion depth which facilitates mixing is estimated
from the relationship between fluid flow pattern and tip position using
a simplified acoustic streaming model. A time dependent heat transfer
model is also presented which can estimate temperature rise in
laboratory scale sonication given process inputs. Assumptions were made
and validated by experiments which enabled us to decouple heat transfer
model from acoustic pressure and velocity distribution. Using the model
and previous experimental data, effect of temperature on yield of BL21
DE3 Star strain is calculated. The model offers us process insight on
how input parameters like power, sample volume and pulse time affects
temperature rise. This model can also be used to tune the parameters to
control temperature in other lab scale sonication procedures like
extraction of biological and food samples where temperature rise is a
concern; this model allows one to narrow in on a range of suitable power
and pulse setting without the need for lengthy iterative laboratory
experiments. Use of this model can be extended to any tip sonicator,
irrespective of vendors, by empirically determining input power as a
function of amplitude setting and volume. Although this model is used
for laboratory scale tubes, in future work, it could also be applied for
scale up in larger vessels. Finally, the central finding of an optimal
temperature range for cell extract preparation can be used in design of
a closed loop sonication system with real time temperature control.

\textbf{Methods}

Simulations were conducted as axisymmetric models (2D interface) in
COMSOL multiphysics 5.4. To find model dimensions, the sonication tubes
were dismantled, and height, thickness, and width were measured with
slide calipers. The model was then drawn directly in the COMSOL computer
aided design interface with specified acoustic and flow boundary
conditions (Fig 7, Table 1,2,3). The sonication tubes as well as tips
are cylindrical and can be represented by taking half of the cross
section along the mid plane (axisymmetric geometry). Finite element
analysis demands the simulation domain to be discretized to number of
elements, and the solution is obtained at each of the nodes.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image7/image7}

\end{center}
\end{figure}

\textbf{Figure 7} : Model drawing in COMSOL with specified boundary
conditions for a) Pressure acoustics, b) Laminar flow and c) Heat
transfer

\textbf{Table 1 - Pressure Acoustic Boundary Conditions}\selectlanguage{english}
\begin{longtable}[]{@{}lll@{}}
\toprule
Index & Domain and Boundary condition & Equations\tabularnewline
\midrule
\endhead
1. Boundary & Pressure Boundary & P = Po\tabularnewline
2. Boundary & Sound soft boundary & - n.\((-\frac{1}{\rho_{c}}\nabla\)P) =
0\tabularnewline
3. Boundary & Sound hard boundary & P\textsubscript{t} =
0\tabularnewline
4. Boundary & Axis-symmetric coordinate & r = 0\tabularnewline
\bottomrule
\end{longtable}

\emph{Pressure acoustics and laminar flow modelling}

The pressure distribution in a system can be calculated by inhomogeneous
Helmholtz equation:

\(\nabla.\ \left[\ -\frac{1}{\rho_{c}}\left(\nabla P\right)\right]-\ \frac{\omega^{2}}{\rho_{c}{C_{c}}^{2}}\text{\ P}=\ 0\){[}Eq. 1{]}

where \emph{P} is the acoustic pressure of the media. The angular
frequency \(\omega\) is defined as \(\omega=2\pi f\), where
\emph{f}is the ultrasound frequency.

\(\rho_{c}\) and \emph{C\textsubscript{c}} is the complex density
and complex sound speed, respectively. They can be expressed by the
following equation as --

\(\rho_{c}\) = \(\frac{\rho{C_{s}}^{2}}{{C_{c}}^{2}}\) and {[}Eq. 2{]}

\emph{C\textsubscript{c}} = \(\frac{\omega}{k_{c}}\) {[}Eq. 3{]}

Where \selectlanguage{greek}ρ\selectlanguage{ngerman} and \emph{Cs} are density of the medium and
sound speed, respectively. Complex wave number k\textsubscript{c} can be
expressed as:

\emph{k\textsubscript{c}} = \(\frac{\omega}{C_{s}}\) -\emph{i}
\(\alpha\) {[}Eq. 4{]}

Where C\textsubscript{s} and \selectlanguage{greek}α\selectlanguage{ngerman} are the sound speed and
absorption coefficient in the media respectively.

The input pressure is calculated by equation {[}5{]} -

\(P_{0}\) = \(\sqrt{}(2\ \rho C_{s}I\ )\) {[}Eq.5{]}

Where `\emph{I'} is the intensity of the sound. It is assumed that all
the power enters the tube through the tip of the transducer. The power
input \emph{P\textsubscript{w}} is in watts. Intensity is given by,

\emph{I =} \(\frac{P_{w}}{A}\) {[}Eq. 6{]}

Where A is the area of tip (30.2mm\textsuperscript{2} for the standard
1/8'' or 3mm diameter sonication tip). In this study the input power is
set at 5.5 W because this is corresponding to power delivered by a
Qsonica 125 with 50\% amplitude with 3.1 mm diameter sonication tip
which is the usual sonication parameter for cell lysis. In cavitating
media, the absorption coefficient is very high and difficult to
determine (Louisnard, 2012). For the purpose of this study the
absorption coefficient of the media is considered 1
m\textsuperscript{-1} for water adopted from Xu (Xu et al., 2013). All
the input parameters are listed in (Supplement table 1).

Solving the stationary Helmholtz equation {[}Eq.1{]} gives pressure at
each point of the simulated tube. From the resulting pressure field, the
intensity field can be calculated using equation {[}5{]}.

The stationary laminar flow field is modelled by two equations- 1. The
momentum balance equation {[}Eq. 7{]} and 2. The continuity equation
{[}Eq. 8{]}:

\(\rho(\overrightarrow{u}.\nabla)\overrightarrow{u}=\nabla.\left[-PI+k\right]+F\){[}Eq. 7{]}

\(\rho\nabla.\overrightarrow{u}=0\) {[}Eq. 8{]}

Where \(\rho,\ \overrightarrow{u},\ P,I,\ k\text{\ and\ }F\ \)are fluid density, velocity vector, fluid
pressure, identity tensor, fluid viscosity and volumetric force
respectively.

\textbf{Table 2 - Laminar Flow Boundary Conditions}\selectlanguage{english}
\begin{longtable}[]{@{}lll@{}}
\toprule
\textbf{Index} & \textbf{Domain and Boundary condition} &
\textbf{Equations}\tabularnewline
\midrule
\endhead
1. Boundary & Wall Boundary (slip) & -n.u= 0\tabularnewline
2. Boundary & Wall Boundary (no slip) & u = 0\tabularnewline
3. Boundary & Axial Symmetry & r = 0\tabularnewline
4. Domain & Volumetric Force & F = \(\selectlanguage{greek}\frac{2\ \text{α\ I}}\selectlanguage{greek}\selectlanguage{english}{\text{ρ\ C}}\selectlanguage{english}\)
\(\frac{N}{m^{3}}\)\tabularnewline
\bottomrule
\end{longtable}

The volumetric force term (\emph{F} ) in momentum balance is calculated
from the pressure intensity field \emph{I,} determined from Eq. 9.
Assuming plane wave approximation \emph{F} can be expressed by the
following relationship:

\emph{F =} \(\frac{2\ \alpha}{\ C_{s}}\text{\ I}\) {[}Eq. 9{]}

Detail of this derivation can be obtained from (Huang, Holt, Cleveland,
\& Roy, 2004).

Where \emph{F} , \(\alpha,\) \emph{C\textsubscript{s}} and
\emph{I} are volumetric force, sound attenuation coefficient, sound
speed and intensity, respectively. Solving this with finite element
analysis in COMSOL using the specified boundary conditions (Table 2) and
input parameters (Supplementary table 2) yields the velocity field at
each point of the sonication tube (Fig 7b). Velocity streamline
indicates the direction of fluid flow. The area inside the streamlines
are marked yellow and quantified with ImageJ. (details in supplementary
figure 1-5, table 3- 12)

\emph{Temperature modeling simulation}

Temperature rise due to sonication is modelled using the `Heat transfer
in solid and fluid interface' module in COMSOL Multiphysics v5.4 as a
time dependent study. The simulated model has three domains (Fig 7c): 1)
sonication tube domain, 2) polypropylene tube wall domain, and 3) ice
bath domain. The thermal and physical properties of each of the domains
is listed in supplement (Supplement Table 13).

The time dependent heat transfer equation is:

\(\rho\)\textsubscript{s} C\textsubscript{p}\(\frac{\partial T}{\partial t}\)
=\(\kappa\)\textsubscript{s}\(\nabla\)\textsuperscript{2}
T
+\(\rho_{s}C_{\text{p\ }}\overrightarrow{u}\ \nabla.T+\ \)Q\textsubscript{g}\(\ +\ \)Q\textsubscript{loss}{[}Eq.
10{]}

Where \(\rho_{s},\) \emph{C\textsubscript{p}} , \emph{T}
,\emph{k\textsubscript{s}} , \(\overrightarrow{u}\), Q\textsubscript{g}and
Q\textsubscript{s} are domain material density, specific heat,
temperature, thermal conductivity, velocity vector, heat generation term
and heat loss term, respectively.

Returning to the velocity field solution above, the assumption of
laminar flow should not be used for this calculation, only for
generalization of fluid volume affected by the tip (Fig 2). Rather, in
an extremely turbulent environment with nonlinear cavitation constrained
to a small cavity it is difficult to determine the time dependent
velocity field coupled with heat transfer. Due to turbulence, there is a
time-dependent change in thermal properties such as the thermal
conductivity `k'. Due to high conductivity, small scale and assumed
complete turbulent mixing, the cell suspension domain is considered
isothermal and the velocity term can be neglected. This simplifies the
heat transfer in the tube to the following equation --

\(\rho\)\textsubscript{s}
\emph{C\textsubscript{p}}\(\frac{\partial T}{\partial t}\)
=\(\kappa\)\textsubscript{s}\(\nabla\)\textsuperscript{2}
T\(+\ \)Q\textsubscript{g} {[}Eq. 11{]}

The ice-bath is considered large enough so that it can effectively act
as a heat sink without much temperature rise. The material and thermal
property of ice bath is assumed similar to ice. The total outside domain
can be considered insulated (no heat flow in or out) as outside
temperature has negligible effect in temperature of the domains.

The heat generation term Qg is active only inside the sonication tube
domain as a volumetric heat source in W/m\textsuperscript{3}. The power
delivered is measured empirically from the sonicator and multiplied with
a tip conversion factor to account for realistic loss of power of 0.85
from literature (Pasumarthi, 2016) and divided by the sample volume to
get the volumetric heat source term. The volumetric heat source is
multiplied by a piecewise time function to incorporate pulsing. The
function value is 1 while the pulse is on and 0 when pulse is off.
Temperature value is stored for each second.

\textbf{Table 3 - Heat Transfer Boundary Conditions}\selectlanguage{english}
\begin{longtable}[]{@{}lll@{}}
\toprule
\begin{minipage}[b]{0.30\columnwidth}\raggedright\strut
\textbf{Index}\strut
\end{minipage} & \begin{minipage}[b]{0.30\columnwidth}\raggedright\strut
\textbf{Domain and Boundary condition}\strut
\end{minipage} & \begin{minipage}[b]{0.30\columnwidth}\raggedright\strut
\textbf{Equations}\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
1. Domain\strut
\end{minipage} & \begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
Cell suspension domain (volumetric heat source active, isothermal)\strut
\end{minipage} & \begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
Q\textsubscript{g} = \(\frac{Input\ Power\times conv.\ factor}{\text{sample\ volume}}\)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
2. Domain\strut
\end{minipage} & \begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
Tube wall domain (tube material -- polypropylene)\strut
\end{minipage} & \begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
3. Domain\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Ice-bath domain\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
4. Boundary\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Insulation\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
n.q = -n.q = 0\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
5. Boundary\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Axial Symmetry\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
r=0\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

\emph{Experimental Temperature measurement for Model Validation}

Cell suspensions are prepared as described before (Dopp, Jo, \& Reuel,
2019). In brief, starter culture is prepared by taking 20 mL of LB media
(prepared by protocol outlined in {[}2{]}) and a cell pick of BL21 DE3
Star. This starter culture is left to grow overnight and used to
inoculate 1 L growth media of 2x YTPG (prepared by protocol outlined in
{[}2{]}) in a 2.5 L Tunair flask. The cells are harvested after 4 hours.
The cell pellets are resuspended in S30 buffer, centrifuged (at 3000g
for 20 minutes in 4C temperature) and pelleted again. These cells are
mixed with equal volume of S30 buffer and vortexed to produce cell
suspension which is aliquot in tubes.

The sonication tubes are placed in an ice bath containing ground ice in
water, stabilized with a clamp. The sonication tip is dipped in the
suspension 0.5 cm from top as per the optimum depth found from this
study (Fig 2). A k-type probe data logger thermometer (Fluke TC-2000) is
used for temperature measurement and logging. The probe head was
carefully held manually inside the sonication tube so that it did not
touch the tube wall or the sonication tip due to vibration. The
amplitude and pulse settings were specified and the sonication and data
logging was started at once. The experiments were conducted with
different power setting, pulse setting, tip radius, tubes and initial
temperatures to observe the experimental response in different
conditions and validate the finite element model. For each of the
experimental runs, simulations were also conducted using the model
inputs. The experimental runs were -

\begin{enumerate}
\tightlist
\item
  1.5 mL microcentrifuge tube with 1.5 mL sample \& 50\% amplitude 3mm
  tip (corresponding to 5.5 Watt) and 10 second on and 10 second off
  pulse, initial temperature 1.6 C. (Fig 3a)
\item
  1.5 mL microcentrifuge tube with 1.5 mL sample \& 50\% amplitude 3mm
  tip (corresponding to 5.5 Watt) and 20 second on and 20 second off
  pulse, initial temperature 3.4 C. (Fig 3b)
\item
  1.5 mL microcentrifuge tube with 1.5 mL sample \& 25\% amplitude 3mm
  tip (corresponding to 1.73 Watt) and 10 second on and 10 second off
  pulse, initial temperature 1.1 C. (Fig 3c)
\item
  5 mL microcentrifuge tube with 5 mL sample \& 50\% amplitude 6mm tip
  (corresponding to 12.5 Watt) and 20 second on and 20 second off pulse,
  initial temperature 14.4 C. (Fig 3d)
\end{enumerate}

\textbf{Acknowledgements}

We thank Prof. Kwon for sending us original sonication data to fit to
our thermal model in Figure 4.

\textbf{Conflict of Interest Statement}

The authors have no conflict of interest to declare

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\textbf{Tables}

\textbf{Table 1 - Pressure Acoustic Boundary Conditions}\selectlanguage{english}
\begin{longtable}[]{@{}lll@{}}
\toprule
Index & Domain and Boundary condition & Equations\tabularnewline
\midrule
\endhead
1. Boundary & Pressure Boundary & P = Po\tabularnewline
2. Boundary & Sound soft boundary & - n.\((-\frac{1}{\rho_{c}}\nabla\)P) =
0\tabularnewline
3. Boundary & Sound hard boundary & P\textsubscript{t} =
0\tabularnewline
4. Boundary & Axis-symmetric coordinate & r = 0\tabularnewline
\bottomrule
\end{longtable}\selectlanguage{english}
\begin{longtable}[]{@{}lll@{}}
\toprule
\textbf{Index} & \textbf{Domain and Boundary condition} &
\textbf{Equations}\tabularnewline
\midrule
\endhead
1. Boundary & Wall Boundary (slip) & -n.u= 0\tabularnewline
2. Boundary & Wall Boundary (no slip) & u = 0\tabularnewline
3. Boundary & Axial Symmetry & r = 0\tabularnewline
4. Domain & Volumetric Force & F = \(\selectlanguage{greek}\frac{2\ \text{α\ I}}\selectlanguage{greek}\selectlanguage{english}{\text{ρ\ C}}\selectlanguage{english}\)
\(\frac{N}{m^{3}}\)\tabularnewline
\bottomrule
\end{longtable}

\textbf{Table 2 - Laminar Flow Boundary Conditions}

\textbf{Table 3 - Heat Transfer Boundary Conditions}\selectlanguage{english}
\begin{longtable}[]{@{}lll@{}}
\toprule
\begin{minipage}[b]{0.30\columnwidth}\raggedright\strut
\textbf{Index}\strut
\end{minipage} & \begin{minipage}[b]{0.30\columnwidth}\raggedright\strut
\textbf{Domain and Boundary condition}\strut
\end{minipage} & \begin{minipage}[b]{0.30\columnwidth}\raggedright\strut
\textbf{Equations}\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
1. Domain\strut
\end{minipage} & \begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
Cell suspension domain (volumetric heat source active, isothermal)\strut
\end{minipage} & \begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
Q\textsubscript{g} = \(\frac{Input\ Power\times conv.\ factor}{\text{sample\ volume}}\)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
2. Domain\strut
\end{minipage} & \begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
Tube wall domain (tube material -- polypropylene)\strut
\end{minipage} & \begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
3. Domain\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Ice-bath domain\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
4. Boundary\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Insulation\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
n.q = -n.q = 0\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
5. Boundary\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Axial Symmetry\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
r=0\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

\textbf{List of Figures}

\begin{enumerate}
\tightlist
\item
  (a) Schematic depicting cell lysis by tip sonication: (i) sonicator
  tip is inserted into the sonication vessel, submerging tip in liquid.
  (ii) Controller for specifying pulse, amplitude \& duration iii) The
  tube sits in ice-bath for cooling iv) Input energy from controller
  (ii) is set as a function of signal amplitude (translates to tip power
  based on fluid volume and vessel), pulse durations, and total
  sonication time v) Thermal energy transfers to ice-bath from cell
  suspension domain vi) The sonicated liquid is divided into circulated
  zone \& dead zone (b) Axis-symmetric models (right half) of common
  laboratory tubes: i) 1.5 mL microcentrifuge tube ii) 5 mL
  microcentrifuge tube iii) 15 mL Falcon tube iv) 50 mL Falcon tube.
\item
  Modeling effect of tip depth on mixing. a) Circulation zone (yellow)
  and dead zone (gray) with different tip depths for 1.5 mL
  Microcentrifuge tube obtained from simulation. b) Percentage of volume
  in circulation zone with changing tip height for four sizes of tubes
  1.5,1.5, 5, 15, and 50 mL with 1.5,1, 5, 10, 15 mL sample
  respectively.
\item
  Temperature rise over time determined experimentally (blue line) and
  estimated with the finite element simulation (orange line). a) 1.5 mL
  microcentrifuge tube with 1.5 mL sample at 50\% amplitude using a 3mm
  tip (corresponding to \textasciitilde{}5.5 Watt) and 10 second on and
  10 second off pulse, initial temperature 1.6C. b) 1.5 mL
  microcentrifuge tube with 1.5 mL sample at 50\% amplitude using a 3mm
  tip (corresponding to \textasciitilde{}5.5 Watt) and 20 second on and
  20 second off pulse, initial temperature 3.4C. c) 1.5 mL
  microcentrifuge tube with 1.5 mL sample at 25\% amplitude using a 3mm
  tip (corresponding to \textasciitilde{}2 Watt) and 10 second on and 10
  second off pulse, initial temperature 1.1C. d) 5 mL microcentrifuge
  tube with 5 mL sample at 50\% amplitude using a 6mm tip (corresponding
  to \textasciitilde{}12.5 Watt) and 20 second on and 20 second off
  pulse, initial temperature at 14.4 C.
\item
  a) Heat map of normalized sfGFP yield from BL21 DE3 Star cell extracts
  prepared at different volumes and total energies, with z-axis color
  bar presenting relative amounts of expression (replotted from (Kwon \&
  Jewett, 2015)). Thick dashed lines depict temperatures (K) at these
  sonication conditions obtained by the finite element simulation. Thin
  solid lines indicate energy density values (J/mL). b) The same
  normalized yield data plotted in a more generalized fashion as power
  density vs. total energy; dashed lines again show temperatures
  estimated by simulation.
\item
  Workflow diagram to obtain optimized sonication parameters for
  temperature sensitive procedure using the finite element model
  directly (access to COMSOL required to run provided process code).
\item
  Maximum temperature (y-axis) estimated for different power density
  (x-axis) and pulse time (5-10,10-10,15-10 and 20-10 on-off pulses
  respectively) for each of the four tubes -- a) 1.5 mL microcentrifuge
  tube b) 5 mL microcentrifuge tube c) 15 mL conical tube d) 50mL
  conical tube.
\item
  Model drawing in COMSOL with specified boundary conditions for a)
  Pressure acoustics, b) Laminar flow and c) Heat transfer
\end{enumerate}

\textbf{Figures}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image8/image8}

\end{center}
\end{figure}

\textbf{Figure 1} -- (a) Schematic depicting cell lysis by tip
sonication: (i) sonicator tip is inserted into the sonication vessel,
submerging tip in liquid. (ii) Controller for specifying pulse,
amplitude \& duration iii) The tube sits in ice-bath for cooling iv)
Input energy from controller (ii) is set as a function of signal
amplitude (translates to tip power based on fluid volume and vessel),
pulse durations, and total sonication time v) Thermal energy transfers
to ice-bath from cell suspension domain vi) The sonicated liquid is
divided into circulated zone \& dead zone (b) Axis-symmetric models
(right half) of common laboratory tubes: i) 1.5 mL microcentrifuge tube
ii) 5 mL microcentrifuge tube iii) 15 mL Falcon tube iv) 50 mL Falcon
tube.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image9/image9}

\end{center}
\end{figure}

\textbf{Figure 2} : Modeling effect of tip depth on mixing. a)
Circulation zone (yellow) and dead zone (gray) with different tip depths
for 1.5 mL Microcentrifuge tube obtained from simulation. b) Percentage
of volume in circulation zone with changing tip height for four sizes of
tubes 1.5,1.5, 5, 15, and 50 mL with 1.5,1, 5, 10, 15 mL sample
respectively.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/imagf0/default-figure}

\end{center}
\end{figure}

\textbf{Figure 3} - Temperature rise over time determined experimentally
(blue line) and estimated with the finite element simulation (orange
line). a) 1.5 mL microcentrifuge tube with 1.5 mL sample at 50\%
amplitude using a 3mm tip (corresponding to \textasciitilde{}5.5 Watt)
and 10 second on and 10 second off pulse, initial temperature 1.6C. b)
1.5 mL microcentrifuge tube with 1.5 mL sample at 50\% amplitude using a
3mm tip (corresponding to \textasciitilde{}5.5 Watt) and 20 second on
and 20 second off pulse, initial temperature 3.4C. c) 1.5 mL
microcentrifuge tube with 1.5 mL sample at 25\% amplitude using a 3mm
tip (corresponding to \textasciitilde{}2 Watt) and 10 second on and 10
second off pulse, initial temperature 1.1C. d) 5 mL microcentrifuge tube
with 5 mL sample at 50\% amplitude using a 6mm tip (corresponding to
\textasciitilde{}12.5 Watt) and 20 second on and 20 second off pulse,
initial temperature at 14.4 C.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/imagf1/imagf1}

\end{center}
\end{figure}

\textbf{Figure 4} -- a) Heat map of normalized sfGFP yield from BL21 DE3
Star cell extracts prepared at different volumes and total energies,
with z-axis color bar presenting relative amounts of expression
(replotted from (Kwon \& Jewett, 2015)). Thick dashed lines depict
temperatures (K) at these sonication conditions obtained by the finite
element simulation. Thin solid lines indicate energy density values
(J/mL). b) The same normalized yield data plotted in a more generalized
fashion as power density vs. total energy; dashed lines again show
temperatures estimated by simulation.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/imagf2/imagf2}

\end{center}
\end{figure}

\textbf{Figure 5:} Workflow diagram to obtain optimized sonication
parameters for temperature sensitive procedure using the finite element
model directly (access to COMSOL required to run provided process code).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/imagf3/imagf3}

\end{center}
\end{figure}

\textbf{Figure 6:} Maximum temperature (y-axis) estimated for different
power density (x-axis) and pulse time (5-10,10-10,15-10 and 20-10 on-off
pulses respectively) for each of the four tubes -- a) 1.5 mL
microcentrifuge tube b) 5 mL microcentrifuge tube c) 15 mL conical tube
d) 50mL conical tube.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/imagf4/imagf4}

\end{center}
\end{figure}

\textbf{Figure 7} : Model drawing in COMSOL with specified boundary
conditions for a) Pressure acoustics, b) Laminar flow and c) Heat
transfer

\selectlanguage{english}
\FloatBarrier
\end{document}

