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\begin{document}

\title{Multiphysics simulation of a compression - perfusion combined bioreactor
to predict the mechanical microenvironment during bone metastatic breast
cancer loading experiments}



\author[1]{Boyuan Liu}%
\author[1]{Suyue Han}%
\author[1]{Yahya Modarres-Sadeghi}%
\author[2]{Maureen Lynch}%
\affil[1]{University of Massachusetts Amherst}%
\affil[2]{University of Colorado Boulder}%


\vspace{-1em}



  
  \date{June 18, 2024}


\begingroup
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\selectlanguage{english}
\begin{abstract}
Incurable breast cancer bone metastasis causes widespread bone loss,
resulting in fragility, pain, increased fracture risk, and ultimately
increased patient mortality. Increased mechanical signals in the
skeleton are anabolic and protect against bone loss, and they may also
do so during osteolytic bone metastasis. Skeletal mechanical signals
include interdependent tissue deformations and interstitial fluid flow,
but how metastatic tumor cells respond to each of these individual
signals remains under-investigated, a barrier to translation to the
clinic. To delineate their respective roles, we report computed
estimates of the internal mechanical field of a bone-mimetic scaffold
undergoing combinations of high and low compression and perfusion using
multiphysics simulations. Simulations were conducted in advance of
multi-modal loading bioreactor experiments with bone metastatic breast
cancer cells to ensure that mechanical stimuli occurring internally were
physiological and anabolic. Our results show that mechanical stimuli
throughout the scaffold were within the anabolic range of bone cells in
all loading configurations, were homogenously distributed throughout,
and that combined high magnitude compression and perfusion synergized to
produce the largest wall shear stresses within the scaffold. These
simulations, when combined with experiments, will shed light on how
increased mechanical loading in the skeleton may confer anti-tumorigenic
effects during metastasis.%
\end{abstract}%



\sloppy


\textbf{Introduction}

Roughly three in four patients with advanced breast cancer develop
incurable bone metastases (Siegel, Miller, \& Jemal, 2018). Once bone
metastasis occurs, the lesions are overwhelmingly osteolytic, putting
patients at great risk of suffering skeletal related events (SREs),
including severe bone pain and fracture (Coleman, 2005). The mechanical
environment in the skeleton is well-known to control bone tissue
homeostasis, with increased loading preventing or reversing osteoporotic
bone loss and associated fracture risk (von Stengel, Kemmler, Kalender,
Engelke, \& Lauber, 2007). Similarly, mechanical signals are emerging as
a critical factor in bone metastasis and tumor-induced bone disease
(TIBD) (Beaton et al., 2009; Sheill, Guinan, Peat, \& Hussey, 2018). A
few promising reports showed that in patients with existing bone
metastases, physical therapy resulted in multiple positive physical
outcomes (\emph{e.g.} increased muscle strength) without SREs (Cormie et
al., 2013; Galvao et al., 2018), although changes to bone mass and
architecture were not explicitly evaluated. In preclinical models,
increased loading was protective against TIBD, such as tibial
compression (Fan et al., 2020; Lynch et al., 2013), low intensity
vibrations (Pagnotti et al., 2016), and ankle loading (Yang et al.,
2019). But, the impacts of loading on tumor cell function may be
dose-dependent, where high damage-causing forces may reverse the
protective effects of loading against TIBD (Fan et al., 2020). Clearly,
more work is needed to clarify the impacts of anabolic loading on TIBD
before successful translation to the clinic.

When forces are applied to the skeleton during physical activity, the
deforming tissue pressurizes the interstitial fluid, resulting in fluid
flow from high to low pressure. These interdependent physical signals
are then translated into intracellular biochemical signals, thereby
stimulating bone formation when increased (Robling \& Turner, 2009;
Thompson, Rubin, \& Rubin, 2012). Thus, elucidating the mechanisms of
how each of these mechanical signals is translated into stimuli in
cancer cells within a bone microenvironment is needed to understand how
anabolic loading is anti-tumorigenic. To this end, tissue
engineering-based approaches have been an indispensable tool.
Loading-induced interstitial fluid flow is widely recognized as an
anabolic signal for stimulating osteogenesis and bone formation (McCoy
\& O'Brien, 2010), and can be generated in scaffolds via
directly-applied perfusion or compression of a hydrated scaffold.
Recently, these approaches have been leveraged to help uncover how
skeletal mechanical signals impact cancer cells in bone. Dynamic
compression applied to breast cancer cells in a mineral-containing
polymeric scaffold downregulated expression of osteolytic genes (Lynch
et al., 2013). In contrast, dynamic compression applied to Ewing Sarcoma
cells in a hydrogel increased their drug resistance (Marturano-Kruik et
al., 2018; Santoro, Lamhamedi-Cherradi, Menegaz, Ludwig, \& Mikos,
2015), underscoring that cancer type and microenvironment are important
factors in bone cancer mechanobiology. Mechanical signals also regulate
tumor cell interactions with resident bone cells. For example,
mesenchymal stem cells (MSCs) increased their osteopontin production
upon exposure to breast cancer-derived soluble factors during
compression-induced osteogenic differentiation (Lynch et al., 2016),
indicating that tumor cells may stimulate bone cells to secrete proteins
that promote tumor cell adhesion. Further, mechanically loaded,
paclitaxel-releasing MSCs inhibited the growth of multiple myeloma cells
in the Rotary Cell Culture System (Bonomi et al., 2017; Ferrarini et
al., 2013).

While fluid flow is clearly important for bone homeostasis, the impact
of matrix deformations is much less understood. Matrix deformations and
fluid flow occur together (Robling \& Turner, 2009), thus delineating
the individual roles of each signal in cancer cell mechanobiology
studies is challenging. One approach is to apply perfusion and
compression in combination and isolation, and several recent studies
using this approach report that fluid flow- and compression-induced
signals together enhance bone anabolism (Ramani-Mohan et al., 2018;
Zhao, Mc Garrigle, Vaughan, \& McNamara, 2018; Zhao, Vaughan, \&
McNamara, 2015). For example, multiscale computational modeling of a
hydrogel scaffold undergoing perfusion, compression, or both predicted
that the combination of low magnitude (0.5\% peak strain) compression
and pore pressure (10 kPa) would induce more osteogenic differentiation
and bone mass (Zhao et al., 2018), perhaps as a result of greater cell
deformation (Zhao et al., 2015). Further, when computational approaches
were combined with combinatorial experiments involving MSCs with an AP-1
(an intracellular strain sensor) luciferase reporter, applied
compression resulted in the greatest cellular deformation and
osteogenesis, suggesting physical strain is the main driver of bone
anabolism rather than fluid flow alone (Ramani-Mohan et al., 2018).
Thus, both mechanical signals should be considered when investigating
the role of anabolic loading on tumor cells in the skeleton. Further,
computational simulations may help shed light on their respective roles.

Here, we report on multiphysics computational simulations of multi-modal
loading bioreactor experiments in advance of the metastatic breast
cancer cellular experiments to ensure a mechanical environment in the
anabolic range. Our bioreactor delivers compression and perfusion
individually or in combination to multiple bone-mimetic 3D constructs
(Fig. 1A). We have previously determined the necessary inlet flow
velocity to engender physiological and anabolic wall shear stresses
(WSSs) in our bone-mimetic scaffold (Liu, Han, Hedrick,
Modarres-Sadeghi, \& Lynch, 2018), and we also determined an osteogenic
level of dynamic compression that also impacted bone cell-tumor cell
interactions (Lynch et al., 2016). Here, we extend our previous work to
include simulations of multiple magnitudes as well as dynamic
compression, and we anticipate that the combination of applied
compression and perfusion will synergize to produce the greatest
mechanical signals (Zhao et al., 2018).

\textbf{Materials and Methods}

\textbf{Overview of Experimental Setup used for Simulations}

Our experimental setup includes a multi-modal loading bioreactor and
bone-mimetic scaffold. With our bioreactor (Bangalore integrated System
Solutions), we can apply compression and perfusion, which are
independently controlled, either in isolation or in combination.
Mechanical stimuli is applied to breast cancer cells seeded in highly
porous scaffolds fabricated from poly(lactide-co-glycolide) (PLGA)
microspheres and hydroxyapatite (HA) scaffolds (Lynch et al., 2013;
Pathi, Kowalczewski, Tadipatri, \& Fischbach, 2010). We simulated eight
experiments with dynamic compression and steady perfusion in various
combinations with a static, nonloaded control (Fig. 1B). The compression
conditions included no compression (C-), low compression (5\% peak bulk
strain, C+), and high compression (10\% peak bulk strain, C++) applied
at 1 Hz. The high compression value (10\% peak strain) previously
inhibited expression of resorption genes in breast cancer cells within
the same PLGA-HA scaffold modeled here (Lynch et al., 2013), and
modulated their interactions with bone marrow mesenchymal stems during
osteogenic differentiation (Lynch et al., 2016). The low compression
value (5\% peak strain) serves as a lower stimulus, but is within the
range of commonly used strains in experiments to stimulate osteogenic
responses (Bhatt et al., 2007).

The inlet perfusion velocity conditions included no perfusion (P-),
steady low perfusion (0.3 mL/min, P+), and steady high perfusion (0.6
mL/min, P++). Our rationale for applying steady, as opposed to dynamic,
perfusion is that no clear consensus currently exists as to which
profile is better for osteoinductive responses in bone cells in tissue
engineered constructs (McCoy \& O'Brien, 2010). The low perfusion rate
(0.3 mL/min) was previously simulated via CFD, and resulted in internal
shear stresses that are in the osteogenic range and flow velocities
similar to intracanalicular flow velocities during in vivo tibial
loading (Liu et al., 2018).

\textbf{Geometry Reconstruction from MicroCT Images}

Previously acquired micro-computed tomographic (microCT) images of the
scaffold (Liu et al., 2018) (Fig. 2A) were used to generate
computational models (Fig. 2B). Image data were imported into Simpleware
ScanIP (Synopsys, Inc.) for segmentation and directly transformed into a
volumetric mesh containing both solid and fluid domains. Images were
filtered to remove noise and smoothed by applying a mean filter (filter
radius = 1 pixel). Grayscale stacked images were then segmented to
separate solid from the air (threshold value taken from our previous
model (Liu et al., 2018)). The scaffold image data were presented as a
voxel model after the segmentation. Next, a voxel model of a cylinder
was created to trim the scaffold into a smaller domain (1.2 mm
thickness, 2 mm diameter) for shorter computation. Boolean operation
intersection between the cylinder and scaffold voxel model was used to
create the final solid domain (Foley, 1996). Boolean operation
subtraction was used to generate the fluid domain from the image
(scaffold) voids (Fig. 2C). Finally, the two domains were meshed
together by replacing existing voxels directly to volumetric tetrahedral
elements. The final mesh contains both solid and fluid domain with
watertight assembly and interfaces with shared nodes (Fig. 3A).

\textbf{Multiphysics Computational Model Creation}

Eight experimental treatments were simulated (static control omitted).
The 2 perfusion alone cases (C-P+ and C-P++) were simulated using only
Fluent (Workbench 19.0, ANSYS, Inc.), a CFD solver. The remaining six
cases were solved using a multiphysics solver, which utilized Fluent,
Transient Structural (FE solver), and System Coupling {[}Fluid-Structure
Interface (FSI){]} (Workbench 19.0, ANSYS, Inc.). To establish the CFD
and multiphysics models, the solid domain was imported to Transient
Structural, where the equations of motion was solved in matrix form:

\(\left[M\right]\left\{\ddot{x}\right\}+\left[C\right]\left\{\dot{x}\right\}+\left[K\right]\left\{x\right\}\)=\(\left\{F\left(t\right)\right\}\)

where \(\left[M\right]\left\{\ddot{x}\right\}\)represents the inertia forces,\(\left[C\right]\left\{\dot{x}\right\}\)
represents the damping forces, \(\left[K\right]\left\{x\right\}\)represents elastic
forces, and\(\left\{F\left(t\right)\right\}\ \)is the dynamic load vector. The material of
the solid domain, which is a mixture of PLGA polymer and HA, was assumed
to be isotropic elastic. A Young's modulus and Poisson's ratio of 2 GPa
and 0.3, respectively, were taken from similar PLGA-based scaffolds
(Agrawal \& Ray, 2001; Holland, Jolly, Yasin, \& Tighe, 1987; Zhao et
al., 2015). The material density, 2100 kg/m\textsuperscript{3}, was
calculated from PLGA (Blasi, D'Souza, Selmin, \& DeLuca, 2005) and HA
(Larra\selectlanguage{ngerman}ñaga, Richard J. Lewis, \& Lewis, 2007) with 1:1 weight ratio
according to the fabrication protocol (Pathi et al., 2010). To simulate
the dynamic compression applied to the top of the scaffold (Fig. 1A), a
transient 60 \selectlanguage{greek}μ\selectlanguage{english}m displacement (5\% bulk strain, C+) or 120 \selectlanguage{greek}μ\selectlanguage{english}m
displacement (10\% bulk strain, C++) was applied at the top surface of
the solid domain with a 1 Hz sine wave. Bottom surfaces were modeled as
fixed supports. The side walls were constrained to allow only in-plane
displacements. Finally, fluid-solid shared interfaces were set to allow
data transfer (Fig. 3B).

The fluid domain, which filled with Dulbecco's Modified Eagle Medium,
was assumed to be an incompressible fluid with a constant density (1000
kg/m\textsuperscript{3}) and dynamic viscosity
(1.45\selectlanguage{ngerman}×10\textsuperscript{-3} Pa\(\bullet\)s) (Olivares, Marsal,
Planell, \& Lacroix, 2009). In Fluent, Navier-Stokes equations written
as a continuity equation:

\begin{equation}
\nabla\bullet\left(\rho\overset{}{u}\right)=0\nonumber \\
 \end{equation}

and a conservation of momentum equation:

\begin{equation}
\frac{\partial\overset{}{u}}{\partial t}+\left(\overset{}{u}\bullet\nabla\right)\overset{}{u}-\nu\nabla^{2}\overset{}{u}=-\nabla\left(\frac{p}{\rho}\right)\nonumber \\
 \end{equation}

were solved, where \selectlanguage{greek}\emph{ρ} \selectlanguage{english}is the flow density, \(\overset{}{u}\) is
the flow velocity, \emph{p} is the static pressure, and \selectlanguage{greek}ν \selectlanguage{english}is the dynamic
viscosity. The Pressure-Based Coupled Algorithm of Fluent was used with
a convergence criterion of 10\textsuperscript{-3} for the velocity
residual in each direction and for the continuity residual.

In each CFD model, the lateral side boundary was set as a no-slip wall.
Boundary conditions of 100 \selectlanguage{greek}μ\selectlanguage{english}m/sec velocity and 0 Pa pressure were
defined at the bottom inlet and top outlet, respectively, to simulate
the direct perfusion in conditions with low perfusion (0.3 mL/min, P+).
Similarly, 200 \selectlanguage{greek}μ\selectlanguage{english}m/sec bottom inlet velocity was applied to models with
high perfusion (0.6 mL/min, P++). To simulate fluid flow induced by
compression (C+P-, C++P-), a separate boundary condition in the CFD
models was utilized in which both inlet and outlet were instead set at 0
Pa pressure. In order to couple CFD with deforming solid domains, CFD
models simulating treatments with compression were set to have
deformable mesh with a remesh algorithm. Finally, fluid-solid interfaces
were constant (Fig. 3C).

For the multiphysics models, the FE and CFD solvers were linked together
by System Coupling in order to perform FSI simulations. During the
simulation, the 1 Hz loading cycle was broken into time steps while the
equations in either the FE or CFD solver were solved following a
staggered iteration strategy. In each time step, the fluid mesh updated
its shape following solid deformation, and subsequently, the CFD
simulation was solved using the new mesh. Simultaneously, the remesh
algorithm was deployed when necessary to avoid highly skewed elements.
Then, Transient Structural solved the FE simulation considering the
applied boundary and the fluid forces that were transferred from the
fluid-solid interface based on the results from the previous CFD
calculation. All simulations in this study were performed on remote
Linux clusters {[}The Massachusetts Green High Performance Computing
Center (MGHPCC){]} with 16 cores {[}Intel(R) Xeon(R) CPU E5-2650 v3 @
2.30GHz with 128GB RAM{]}. After simulations, FE and CFD solvers were
linked to PostCFD (Workbench 15.0, ANSYS) for results exporting and
visualization, where velocity vectors, WSS color maps, and solid strain
color maps were created.

\textbf{Model Sensitivity Tests}

Multiple simulations were carried out for testing model sensitivities. A
mesh sensitivity test was performed to determine the appropriate element
size. A total of four different models were generated in which the fluid
domains were simulated in CFD using the P+ loading condition (low
perfusion,100 \selectlanguage{greek}μ\selectlanguage{english}m/sec inlet velocity). The models had an element number
range from \textasciitilde{}44,000 to \textasciitilde{}504,000, with the
highest element number model was four times smaller in element sizes
(both maximum and minimum element lengths) than the lowest. The
resulting WSS distributions of each model were nearly identical (Suppl.
Fig. 1A), indicating that our starting sensitivity model had
sufficiently fine element sizes, similar to other models of tissue
engineered scaffold (Zhao, Melke, Ito, van Rietbergen, \& Hofmann,
2019). In fact, coarser models did not pass mesh quality tests or had
internal errors. We selected the mesh with the same element sizes as our
previous CFD study (minimum element length of 0.02 mm, roughly four
times of initial micro-CT voxel size) to maintain consistency (Liu et
al., 2018).

A second sensitivity test was performed to determine time step length
used in multiphysics models. The C+P+ loading condition was applied in
three different simulations with 40, 100 and 200 time steps per loading
cycle (1 cycle, 1 second). Distributions of fluid-solid interface WSS of
each model at 0.25 s were virtually identical (Suppl. Fig. 1B). Thus, we
chose 100 time steps per loading cycle to achieve a balance between data
points and simulating time. Next, we assumed the scaffold was
sufficiently stiff to prevent the fluid from causing reciprocal solid
deformations. To verify this, we conducted two-way FSI coupled models to
compare the solid strain distributions to the compression-alone FE
simulation. Identical solid strain distributions verifyied that fluid
forces did not deform solid structures (Suppl. Fig. 1C). Thus, we
utilized one-way coupling simulations, allowing only solid deformation
transfers. Finally, to determine the number of loading cycles to
simulate, the C+P+ loading condition was used to simulate two full
loading cycles (2 sec). WSSs were calculated from the fluid-solid
interface on each loading cycle, and median values of these WSS showed
identical curves between the first and the second cycle (Suppl. Fig.
1D). Thus, 1 second of loading was simulated.

\textbf{Results}

\textbf{Local scaffold strains were evenly dispersed throughout the
scaffold and doubled in intensity from 5\% to 10\% peak strain.}

As discussed previously, scaffold deformation was independent of fluid
flow (i.e. the fluid did not `push' back). Thus, the solid deformations
resulting from applied compression in six configurations (C+P-, C+P+,
C+P++, C++P-, C++P+, C++P++) of the total eight conditions could be
represented by the 2 compression magnitude groups alone (C+ and C++).
The maximum deformations of the 1 Hz loading cycle occurred at 0.5 sec,
the time of peak compressive strain, as we expected. At this moment,
heat maps on the fluid-solid interface revealed evenly distributed
principal strains throughout the entire scaffold (Suppl. Fig. 2, Fig.
4A) with few sites of strain concentrations. Distributions of principal
strains in C+ showed that the majority of strains (\textgreater{}70\%)
were within 5,000-20,000 \selectlanguage{greek}με. \selectlanguage{english}In C++, strain values were twice as much
with 10\% bulk strain compared to 5\% (mean values 13,300 \selectlanguage{greek}με \selectlanguage{english}in C+,
265,000 \selectlanguage{greek}με \selectlanguage{english}in C++), indicating that the scaffold deformed linearly
despite the complexity of the geometry (Fig. 4B).

\textbf{Applied compression resulted in interstitial fluid flow with and
without applied perfusion.}

The resulting WSSs of each model were calculated at all saved time steps
(20 in 1s) from fluid-solid interfaces. The median values of WSSs showed
dynamic waveforms in all six multiphysics models during the full cycle
length (Fig. 5). Bulk compressive strains of 5\% and 10\% resulted in
substantial interstitial fluid flow that generated dynamic WSS
throughout the scaffold even in the absence of applied perfusion, as
shown in other FSI models of tissue engineered scaffolds
(Marturano-Kruik et al., 2018; Zhao et al., 2015). Heat maps of the
scaffold interior showed uniformly dispersed WSS throughout the scaffold
at peak point (0.25s, Fig. 5), similar to our previous results
simulating perfusion alone in irregular scaffolds (Liu et al., 2018) and
that of others (Maes et al., 2012; Maes, Van Ransbeeck, Van Oosterwyck,
\& Verdonck, 2009). In addition, both histograms (Suppl. Fig. 3) and
heat maps (Fig. 5) revealed that the majority of WSS values (1-100 mPa)
were within the physiological range (Maes et al., 2012; McCoy \&
O'Brien, 2010; Sladkova \& de Peppo, 2014).

\textbf{Co-existence of applied compression and perfusion created
asymmetry in WSS waveforms.}

WSSs induced by applied compression alone (C+P-, C++P-) revealed
symmetrical waveforms, in which no WSS was observed at 0, 0.5, and 1
seconds (see Supplemental Video 1 for WSSs of C+P- in whole loading
cycles). In compression only configurations, peak WSS values were found
at 0.25 sec and 0.75 sec when the moving solid boundary was at maximum
velocity, according to our loading sine waveform. The peak values of
median WSS were 50 mPa and 100 mPa for C+P- and C++P- configurations,
respectively. In contrast, when compression and perfusion were combined,
WSS waveforms showed temporal asymmetry in the resulting median WSS.
Peak WSSs were higher in the first half of the loading cycle (see
Supplemental Video 2\&3 for WSSs of C+P+ and C+P++ in whole loading
cycles), suggesting that compression-induced fluid flow `cancels'
applied perfusion in the second half of the loading cycle. To
investigate interstitial flow more deeply, we selected C+P- and C+P+
simulations to generate fluid velocity vectors and WSS heat maps at
0.25, 0.5, and 0.75 sec (Fig. 6). At 0.25 sec, the scaffold walls had
maximum downward velocity (\textasciitilde{}200 um/sec at the top
boundary), while at 0.75 sec, the walls had maximum upward velocity. In
the compression only (C+P-) simulation, compression pushed the fluid out
with the moving scaffold boundary at 0.25 sec, which was then resorbed
at 0.75 sec with a similar velocity profile as compression was unloaded
(Fig. 6A). Hence the double peak symmetrical WSS waveform. However, in
C+P+ simulation, the moving scaffold walls opposed the applied steady
fluid flow for the first 0.5 sec. As the fluid was incompressible, the
opposing velocity augmented the total upward fluid flow in the scaffold,
thus generated much higher WSSs (Fig. 6B). In contrast, at 0.75 sec, the
scaffold walls synergized with the direction of applied fluid flow in
the upper portion of the scaffold, which reduced the total velocity and
WSSs, and even created a downward flow at some local sites.

\textbf{Discussion}

Here, we report estimates of the internal mechanical field from
multiphysics simulations of a bone scaffold undergoing combinations of
high and low compression and perfusion. Simulations were conducted in
advance of multi-modal experiments with bone metastatic breast cancer
cells to ensure that mechanical stimuli occurring internally were
anabolic. Our results show that mechanical stimuli throughout the
scaffold were within the anabolic range of bone cells in all loading
configurations, and local distributions were homogenously distributed
throughout.

Overall, the wall shear stresses within the scaffold during loading were
found to be in the physiological and anabolic range. We reported peak
median wall shear stresses in the range of \textasciitilde{}5 -- 25 mPa
across all of our loading configurations, which is in line with values
reported to stimulate osteogenesis in tissue-engineered scaffolds
(Fernandez-Yague et al., 2015; Stops, Heraty, Browne, O'Brien, \&
McHugh, 2010). Some studies reported significant osteoblastic cell loss
at higher WSS ranges (\textasciitilde{}1 -- 50 mPa) (Jaasma \& O'Brien,
2008; Partap, Plunkett, Kelly, \& O'Brien, 2010; Plunkett, Partap, \&
O'Brien, 2010), though how breast cancer cells will adhere to our bone
scaffold at the higher WSS values is unknown. In vivo, breast cancer
cells have been shown to localize to osteogenic niches at the endosteal
surface (Wang et al., 2015), a site that can experience very high shear
stresses according to simulations, particularly under applied loading
(as high as 5 Pa) (Birmingham et al., 2015; Coughlin \& Niebur, 2012).
Even so, at our higher magnitude loading configurations, we and other
should take care to investigate this. When breast cancer cells were
seeded in the same scaffold modeled here and underwent 10\% dynamic
compression, the breast cancer cells' expression of genes that
controlled downstream remodeling (Runx2) was altered with no apparent
loss of cellularity (based on imaging) (Lynch et al., 2013). Here, our
modeling results of this experiment would indicate that these cells
would have experienced peak median WSS of \textasciitilde{}10 mPa. Ewing
Sarcoma cells in a compressed hydrogel experienced peak fluid velocities
\textasciitilde{}4 -- 6 um/sec (Marturano-Kruik et al., 2018), which is
3 orders of magnitude different compared to our peak of 2 mm/sec. This
highlights that differences in tumor cell response may occur across
different cancer types and microenvironments.

Though our WSS values are in the range for osteogenesis and bone
formation by osteoblastic cells, we utilized steady flow, which is not
physiological. However, in vitro, whether steady or dynamic flow is more
beneficial remains an open question. In 2D studies that directly
compared steady versus dynamic flow, no differences were observed (Case
et al., 2011; Kreke, Sharp, Lee, \& Goldstein, 2008). In contrast, one
study demonstrated oscillatory flow stimulated greater Ca2+ flickers in
osteoblasts (Roy, Das, Mishra, Maiti, \& Chakraborty, 2014). Similarly,
using a microfluidic approach, oscillatory fluid flow was more
stimulatory to osteocytes (Middleton, Al-Dujaili, Mei, Gunther, \& You,
2017). In 3D, most studies utilize steady flow to stimulate osteogenesis
and bone formation (Bancroft et al., 2002; Cartmell, Porter, Garcia, \&
Guldberg, 2003; Sikavitsas, Bancroft, Holtorf, Jansen, \& Mikos, 2003;
Sikavitsas et al., 2005; Zhao, Chella, \& Ma, 2007), but overall,
studies that utilized either steady or dynamic (oscillatory, pulsatile)
have reported osteogenesis. Few studies have compared steady and dynamic
flow side to side in 3D, and the results are mixed. In favor of dynamic
flow, intermittent flow caused greater stimulation of osteoblasts than
steady flow (Jaasma \& O'Brien, 2008). Pulsatile flow appeared best for
bone protein formation relative to steady flow (Sharp, Lee, \&
Goldstein, 2009), and pulsatile flow more strongly upregulated
osteoblast production of cyclooxygenase-2 while oscillatory flow more
strongly upregulated prostaglandin E2 (Jaasma \& O'Brien, 2008), both
important osteogenic signaling factors. Even if applying steady flow,
rest periods of static or low flow are recommended to overcome cellular
desensitization (Robling, Burr, \& Turner, 2000), with similarly mixed
results in vitro (Batra et al., 2005; Jaasma \& O'Brien, 2008; Kreke,
Huckle, \& Goldstein, 2005; Kreke et al., 2008; Partap et al., 2010;
Plunkett et al., 2010; Vance, Galley, Liu, \& Donahue, 2005).

Few studies have studied dynamic versus steady or static mechanical
signals on tumor cells. Static flow in 2D resulted in apoptosis of
cancer cells across multiple lines (Hep3B hepatocarcinoma cells, MG63
osteosarcoma cells, SCC25 oral squamous cells and A549 carcinomic
alveolar basal epithelial cells) while oscillatory flow did not (Lien et
al., 2013). Pulsed magnetic forces applied to TCC-S leukemic cells with
a magnetic bead increased tumor cell death both in vitro and in vivo, a
response that enhances when combined with an anti-cancer therapy
(Ogiue-Ikeda, Sato, \& Ueno, 2003; Yamaguchi, Sato, Sekino, \& Ueno,
2006). In a novel microfluidic device, when mechanically-flow osteocytes
were adjacent to breast cancer cells, breast cancer extravasation was
significantly reduced with mechanically-stimulated osteocytes compared
to static osteocytes, though the breast cancer cells remained under
static conditions (Mei et al., 2019). When considering the effects of
strain, 2D stretching is typically applied acutely and held steady for a
period of time with a variety of results across multiple cell types (Gao
\& Carson, 2016; Manome, Saeki, Yoshinaga, Watanabe, \& Mizuno, 2003;
McKenzie, Svec, Williams, \& Howe, 2020; Panzetta, Fusco, \& Netti,
2019; Riching et al., 2014). One study reported that 2D cyclic
compression of breast cancer cells plated underneath an agarose gel by a
platen regulated necrosis vs apoptosis, and the mode of death was
sensitive to loading frequency, peak applied compressive displacement,
and duration of loading bout (Takao, Taya, \& Chiew, 2019). Similarly,
in 3D, dynamic compression of a hydrogel with Ewing Sarcoma cells
altered drug sensitivity compared to static controls, and the response
was sensitive to peak strain magnitude (Marturano-Kruik et al., 2018).
As mentioned previously, breast cancer cells in our scaffold altered
their gene expression under dynamic compression relative to static
controls, though no change in viability was observed (Lynch et al.,
2013). Overall, these results emphasize that future work is needed to
study the impacts of steady versus dynamic mechanical signals
experimentally.

One of our goals is to delineate the individual roles of matrix
deformation and fluid flow on tumor cell behavior, which is challenging
as they are coupled together in the body. Our approach to achieving this
goal is to correlate the estimated internal mechanical signals with
biological outputs following applied perfusion and compression
experimentation. By comparing the effects of perfusion alone to
configurations that include deformation and interstitial fluid flow
(i.e. compression alone and compression + perfusion), we expect to be
able to isolate their respective effects. The asymmetry among the
various mechanical signals will be a challenge in interpreting results.
For example, compression alone, which best represents the in vivo
mechanical environment by causing deformations and interstitial fluid
flow, exhibits a phase lag between peak strains and peak wall shear
stresses that may have biological implications. For our particular
approach, a crucial consideration is that we use steady rather than
dynamic perfusion. As shown by our computational results, this results
in compression-induced flow and applied perfusion acting in concert
(i.e. larger velocities) in the upper scaffold region during part of the
loading cycle, leading to greater WSSs in that region. Conversely, in
the latter half of the loading cycle, compression-induced flow and
applied perfusion act in concert at the lower portion of the scaffold.
Dynamic perfusion should be incorporated in future experiments to better
reflect in vivo physiology, but mechanical signal asymmetries will still
remain. Some approaches for dealing with the asymmetries could be to
incorporate live imaging during loading to sense Ca2+ signaling (a known
intracellular flow signal (Chen et al., 2000)), and/or intracellular
strain signals (i.e. AP-1 (Ramani-Mohan et al., 2018)). Another approach
could be to apply larger magnitudes of loading to help augment the
signal-to-noise ratio in various strain- and flow-response pathways.

In summary, we have generated multiphysics models of our multimodal
loading experiments to estimate interior scaffold strains and
interstitial fluid velocities and wall shear stresses during loading
experiments with breast cancer cells in a bone microenvironment. Our
long term goal is to study bone metastatic breast cancer cell
mechanobiology, and to understand how anabolic mechanical loading
confers anti-tumorigenic effects to breast cancer cells (Fan et al.,
2020; Lynch et al., 2013; Pagnotti et al., 2016). We confirmed that our
imposed mechanical signals are within the range known to stimulate an
anabolic response in bone cells, thus our experiments will reflect
conditions during anabolic loading in preclinical models of bone
metastasis.

\textbf{Acknowledgements} : We are grateful for the funding support
provided for this research by NSF CBET 1605060. We highlight support
from The Massachusetts Green High Performance Computing Center (MGHPCC).

\textbf{Conflict of Interest:} The authors have no conflicts to declare.

\textbf{References} :

Agrawal, C. M., \& Ray, R. B. (2001). Biodegradable polymeric scaffolds
for musculoskeletal tissue engineering. \emph{J Biomed Mater Res, 55}
(2), 141-150.
doi:10.1002/1097-4636(200105)55:2\textless{}141::aid-jbm1000\textgreater{}3.0.co;2-j

Bancroft, G. N., Sikavitsas, V. I., van den Dolder, J., Sheffield, T.
L., Ambrose, C. G., Jansen, J. A., \& Mikos, A. G. (2002). Fluid flow
increases mineralized matrix deposition in 3D perfusion culture of
marrow stromal osteoblasts in a dose-dependent manner. \emph{Proc Natl
Acad Sci U S A, 99} (20), 12600-12605. Retrieved from
http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve\&db=PubMed\&dopt=Citation\&list\_uids=12242339

Batra, N. N., Li, Y. J., Yellowley, C. E., You, L., Malone, A. M., Kim,
C. H., \& Jacobs, C. R. (2005). Effects of short-term recovery periods
on fluid-induced signaling in osteoblastic cells. \emph{J Biomech, 38}
(9), 1909-1917. Retrieved from
http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve\&db=PubMed\&dopt=Citation\&list\_uids=16023480

Beaton, R., Pagdin-Friesen, W., Robertson, C., Vigar, C., Watson, H., \&
Harris, S. R. (2009). Effects of exercise intervention on persons with
metastatic cancer: a systematic review. \emph{Physiother Can, 61} (3),
141-153. doi:10.3138/physio.61.3.141

Bhatt, K. A., Chang, E. I., Warren, S. M., Lin, S. E., Bastidas, N.,
Ghali, S., . . . Gurtner, G. C. (2007). Uniaxial mechanical strain: an
in vitro correlate to distraction osteogenesis. \emph{J Surg Res, 143}
(2), 329-336. doi:10.1016/j.jss.2007.01.023

Birmingham, E., Kreipke, T. C., Dolan, E. B., Coughlin, T. R., Owens,
P., McNamara, L. M., . . . McHugh, P. E. (2015). Mechanical stimulation
of bone marrow in situ induces bone formation in trabecular
explants.\emph{Ann Biomed Eng, 43} (4), 1036-1050.
doi:10.1007/s10439-014-1135-0

Blasi, P., D'Souza, S. S., Selmin, F., \& DeLuca, P. P. (2005).
Plasticizing effect of water on poly(lactide-co-glycolide). \emph{J
Control Release, 108} (1), 1-9. doi:10.1016/j.jconrel.2005.07.009

Bonomi, A., Steimberg, N., Benetti, A., Berenzi, A., Alessandri, G.,
Pascucci, L., . . . Mazzoleni, G. (2017). Paclitaxel-releasing
mesenchymal stromal cells inhibit the growth of multiple myeloma cells
in a dynamic 3D culture system. \emph{Hematol Oncol, 35} (4), 693-702.
doi:10.1002/hon.2306

Cartmell, S. H., Porter, B. D., Garcia, A. J., \& Guldberg, R. E.
(2003). Effects of medium perfusion rate on cell-seeded
three-dimensional bone constructs in vitro. \emph{Tissue Eng, 9} (6),
1197-1203. Retrieved from
http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve\&db=PubMed\&dopt=Citation\&list\_uids=14670107

Case, N., Sen, B., Thomas, J. A., Styner, M., Xie, Z., Jacobs, C. R., \&
Rubin, J. (2011). Steady and oscillatory fluid flows produce a similar
osteogenic phenotype. \emph{Calcif Tissue Int, 88} (3), 189-197.
Retrieved from
http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve\&db=PubMed\&dopt=Citation\&list\_uids=21165611

Chen, N. X., Ryder, K. D., Pavalko, F. M., Turner, C. H., Burr, D. B.,
Qiu, J., \& Duncan, R. L. (2000). Ca(2+) regulates fluid shear-induced
cytoskeletal reorganization and gene expression in osteoblasts. \emph{Am
J Physiol Cell Physiol, 278} (5), C989-997. Retrieved from
http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve\&db=PubMed\&dopt=Citation\&list\_uids=10794673

Coleman, R. E. (2005). Bisphosphonates in breast cancer. \emph{Ann
Oncol, 16} (5), 687-695. doi:10.1093/annonc/mdi162

Cormie, P., Newton, R. U., Spry, N., Joseph, D., Taaffe, D. R., \&
Galvao, D. A. (2013). Safety and efficacy of resistance exercise in
prostate cancer patients with bone metastases. \emph{Prostate Cancer
Prostatic Dis, 16} (4), 328-335. doi:10.1038/pcan.2013.22

Coughlin, T. R., \& Niebur, G. L. (2012). Fluid shear stress in
trabecular bone marrow due to low-magnitude high-frequency
vibration.\emph{J Biomech, 45} (13), 2222-2229. Retrieved from
http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve\&db=PubMed\&dopt=Citation\&list\_uids=22784651

Fan, Y., Jalali, A., Chen, A., Zhao, X., Liu, S., Teli, M., . . .
Yokota, H. (2020). Skeletal loading regulates breast cancer-associated
osteolysis in a loading intensity-dependent fashion. \emph{Bone
Research, 8} (1), 9. doi:10.1038/s41413-020-0083-6

Fernandez-Yague, M. A., Abbah, S. A., McNamara, L., Zeugolis, D. I.,
Pandit, A., \& Biggs, M. J. (2015). Biomimetic approaches in bone tissue
engineering: Integrating biological and physicomechanical
strategies.\emph{Adv Drug Deliv Rev, 84} , 1-29.
doi:10.1016/j.addr.2014.09.005

Ferrarini, M., Steimberg, N., Ponzoni, M., Belloni, D., Berenzi, A.,
Girlanda, S., . . . Ferrero, E. (2013). Ex-vivo dynamic 3-D culture of
human tissues in the RCCS bioreactor allows the study of Multiple
Myeloma biology and response to therapy. \emph{PLoS One, 8} (8), e71613.
doi:10.1371/journal.pone.0071613

Foley, J. D. (1996). \emph{``12.7 Constructive Solid Geometry''} :
Addison-Wesley Professional.

Galvao, D. A., Taaffe, D. R., Spry, N., Cormie, P., Joseph, D.,
Chambers, S. K., . . . Newton, R. U. (2018). Exercise Preserves Physical
Function in Prostate Cancer Patients with Bone Metastases. \emph{Med Sci
Sports Exerc, 50} (3), 393-399. doi:10.1249/MSS.0000000000001454

Gao, S., \& Carson, J. A. (2016). Lewis lung carcinoma regulation of
mechanical stretch-induced protein synthesis in cultured
myotubes.\emph{Am J Physiol Cell Physiol, 310} (1), C66-79.
doi:10.1152/ajpcell.00052.2015

Holland, S. J., Jolly, A. M., Yasin, M., \& Tighe, B. J. (1987).
Polymers for biodegradable medical devices. II.
Hydroxybutyrate-hydroxyvalerate copolymers: hydrolytic degradation
studies. \emph{Biomaterials, 8} (4), 289-295.
doi:10.1016/0142-9612(87)90117-7

Jaasma, M. J., \& O'Brien, F. J. (2008). Mechanical stimulation of
osteoblasts using steady and dynamic fluid flow. \emph{Tissue Eng Part
A, 14} (7), 1213-1223. doi:10.1089/tea.2007.0321

10.1089/ten.tea.2007.0321

Kreke, M. R., Huckle, W. R., \& Goldstein, A. S. (2005). Fluid flow
stimulates expression of osteopontin and bone sialoprotein by bone
marrow stromal cells in a temporally dependent manner. \emph{Bone, 36}
(6), 1047-1055. Retrieved from
http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve\&db=PubMed\&dopt=Citation\&list\_uids=15869916

Kreke, M. R., Sharp, L. A., Lee, Y. W., \& Goldstein, A. S. (2008).
Effect of intermittent shear stress on mechanotransductive signaling and
osteoblastic differentiation of bone marrow stromal cells. \emph{Tissue
Eng Part A, 14} (4), 529-537. Retrieved from
http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve\&db=PubMed\&dopt=Citation\&list\_uids=18352827

Larra\selectlanguage{ngerman}ñaga, M. D., Richard J. Lewis, S., \& Lewis, R. A. (2007). Hawley's
Condensed Chemical Dictionary. 88. doi:10.1021/ja0769144

Lien, S. C., Chang, S. F., Lee, P. L., Wei, S. Y., Chang, M. D., Chang,
J. Y., \& Chiu, J. J. (2013). Mechanical regulation of cancer cell
apoptosis and autophagy: roles of bone morphogenetic protein receptor,
Smad1/5, and p38 MAPK. \emph{Biochim Biophys Acta, 1833} (12),
3124-3133. doi:10.1016/j.bbamcr.2013.08.023

Liu, B., Han, S., Hedrick, B. P., Modarres-Sadeghi, Y., \& Lynch, M. E.
(2018). Perfusion applied to a 3D model of bone metastasis results in
uniformly dispersed mechanical stimuli. \emph{Biotechnol Bioeng, 115}
(4), 1076-1085. doi:10.1002/bit.26524

Lynch, M. E., Brooks, D., Mohanan, S., Lee, M. J., Polamraju, P., Dent,
K., . . . Fischbach, C. (2013). In vivo tibial compression decreases
osteolysis and tumor formation in a human metastatic breast cancer
model. \emph{J Bone Miner Res, 28} (11), 2357-2367.
doi:10.1002/jbmr.1966

Lynch, M. E., Chiou, A. E., Lee, M. J., Marcott, S. C., Polamraju, P.
V., Lee, Y., \& Fischbach, C. (2016). Three-Dimensional Mechanical
Loading Modulates the Osteogenic Response of Mesenchymal Stem Cells to
Tumor-Derived Soluble Signals. \emph{Tissue Eng Part A, 22} (15-16),
1006-1015. doi:10.1089/ten.TEA.2016.0153

Maes, F., Claessens, T., Moesen, M., Van Oosterwyck, H., Van Ransbeeck,
P., \& Verdonck, P. (2012). Computational models for wall shear stress
estimation in scaffolds: a comparative study of two complete
geometries.\emph{J Biomech, 45} (9), 1586-1592.
doi:10.1016/j.jbiomech.2012.04.015

Maes, F., Van Ransbeeck, P., Van Oosterwyck, H., \& Verdonck, P. (2009).
Modeling fluid flow through irregular scaffolds for perfusion
bioreactors. \emph{Biotechnol Bioeng, 103} (3), 621-630. Retrieved from
http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve\&db=PubMed\&dopt=Citation\&list\_uids=19288440

Manome, Y., Saeki, N., Yoshinaga, H., Watanabe, M., \& Mizuno, S.
(2003). A culture device demonstrates that hydrostatic pressure
increases mRNA of RGS5 in neuroblastoma and CHC1-L in lymphocytic
cells.\emph{Cells Tissues Organs, 174} (4), 155-161.
doi:10.1159/000072718

Marturano-Kruik, A., Villasante, A., Yaeger, K., Ambati, S. R.,
Chramiec, A., Raimondi, M. T., \& Vunjak-Novakovic, G. (2018).
Biomechanical regulation of drug sensitivity in an engineered model of
human tumor. \emph{Biomaterials, 150} , 150-161.
doi:10.1016/j.biomaterials.2017.10.020

McCoy, R. J., \& O'Brien, F. J. (2010). Influence of shear stress in
perfusion bioreactor cultures for the development of three-dimensional
bone tissue constructs: a review. \emph{Tissue Eng Part B Rev, 16} (6),
587-601. Retrieved from
http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve\&db=PubMed\&dopt=Citation\&list\_uids=20799909

McKenzie, A. J., Svec, K. V., Williams, T. F., \& Howe, A. K. (2020).
Protein kinase A activity is regulated by actomyosin contractility
during cell migration and is required for durotaxis. \emph{Mol Biol
Cell, 31} (1), 45-58. doi:10.1091/mbc.E19-03-0131

Mei, X., Middleton, K., Shim, D., Wan, Q., Xu, L., Ma, Y. V., . . . You,
L. (2019). Microfluidic platform for studying osteocyte
mechanoregulation of breast cancer bone metastasis. \emph{Integr Biol
(Camb), 11} (4), 119-129. doi:10.1093/intbio/zyz008

Middleton, K., Al-Dujaili, S., Mei, X., Gunther, A., \& You, L. (2017).
Microfluidic co-culture platform for investigating osteocyte-osteoclast
signalling during fluid shear stress mechanostimulation. \emph{J
Biomech, 59} , 35-42. doi:10.1016/j.jbiomech.2017.05.012

Ogiue-Ikeda, M., Sato, Y., \& Ueno, S. (2003). A new method to destruct
targeted cells using magnetizable beads and pulsed magnetic
force.\emph{IEEE Transactions on NanoBioscience, 2} (4), 262-265.
doi:10.1109/TNB.2003.820276

Olivares, A. L., Marsal, E. l., Planell, J. A., \& Lacroix, D. (2009).
Finite element study of scaffold architecture design and culture
conditions for tissue engineering. \emph{Biomaterials, 30} , 6142-6149.
doi:10.1016/j.biomaterials.20

Pagnotti, G. M., Chan, M. E., Adler, B. J., Shroyer, K. R., Rubin, J.,
Bain, S. D., \& Rubin, C. T. (2016). Low intensity vibration mitigates
tumor progression and protects bone quantity and quality in a murine
model of myeloma. \emph{Bone, 90} , 69-79.
doi:10.1016/j.bone.2016.05.014

Panzetta, V., Fusco, S., \& Netti, P. A. (2019). Cell mechanosensing is
regulated by substrate strain energy rather than stiffness. \emph{Proc
Natl Acad Sci U S A, 116} (44), 22004-22013. doi:10.1073/pnas.1904660116

Partap, S., Plunkett, N. A., Kelly, D. J., \& O'Brien, F. J. (2010).
Stimulation of osteoblasts using rest periods during bioreactor culture
on collagen-glycosaminoglycan scaffolds. \emph{J Mater Sci Mater Med,
21} (8), 2325-2330. doi:10.1007/s10856-009-3966-z

Pathi, S. P., Kowalczewski, C., Tadipatri, R., \& Fischbach, C. (2010).
A novel 3-D mineralized tumor model to study breast cancer bone
metastasis. \emph{PLoS One, 5} (1), e8849. Retrieved from
http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve\&db=PubMed\&dopt=Citation\&list\_uids=20107512

Plunkett, N. A., Partap, S., \& O'Brien, F. J. (2010). Osteoblast
response to rest periods during bioreactor culture of
collagen-glycosaminoglycan scaffolds. \emph{Tissue Eng Part A, 16} (3),
943-951. doi:10.1089/ten.TEA.2009.0345

Ramani-Mohan, R. K., Schwedhelm, I., Finne-Wistrand, A., Krug, M.,
Schwarz, T., Jakob, F., . . . Hansmann, J. (2018). Deformation strain is
the main physical driver for skeletal precursors to undergo osteogenesis
in earlier stages of osteogenic cell maturation. \emph{J Tissue Eng
Regen Med, 12} (3), e1474-e1479. doi:10.1002/term.2565

Riching, K. M., Cox, B. L., Salick, M. R., Pehlke, C., Riching, A. S.,
Ponik, S. M., . . . Keely, P. J. (2014). 3D collagen alignment limits
protrusions to enhance breast cancer cell persistence. \emph{Biophys J,
107} (11), 2546-2558. doi:10.1016/j.bpj.2014.10.035

Robling, A. G., Burr, D. B., \& Turner, C. H. (2000). Partitioning a
daily mechanical stimulus into discrete loading bouts improves the
osteogenic response to loading. \emph{J Bone Miner Res, 15} (8),
1596-1602. Retrieved from
http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve\&db=PubMed\&dopt=Citation\&list\_uids=10934659

Robling, A. G., \& Turner, C. H. (2009). Mechanical signaling for bone
modeling and remodeling. \emph{Crit Rev Eukaryot Gene Expr, 19} (4),
319-338. Retrieved from
http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve\&db=PubMed\&dopt=Citation\&list\_uids=19817708

Roy, B., Das, T., Mishra, D., Maiti, T. K., \& Chakraborty, S. (2014).
Oscillatory shear stress induced calcium flickers in osteoblast
cells.\emph{Integr Biol (Camb), 6} (3), 289-299. doi:10.1039/c3ib40174j

Saarto, T., Sievanen, H., Kellokumpu-Lehtinen, P., Nikander, R.,
Vehmanen, L., Huovinen, R., . . . Blomqvist, C. (2012). Effect of
supervised and home exercise training on bone mineral density among
breast cancer patients. A 12-month randomised controlled
trial.\emph{Osteoporos Int, 23} (5), 1601-1612. Retrieved from
http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve\&db=PubMed\&dopt=Citation\&list\_uids=21892676

Santoro, M., Lamhamedi-Cherradi, S. E., Menegaz, B. A., Ludwig, J. A.,
\& Mikos, A. G. (2015). Flow perfusion effects on three-dimensional
culture and drug sensitivity of Ewing sarcoma. \emph{Proc Natl Acad Sci
U S A, 112} (33), 10304-10309. doi:10.1073/pnas.1506684112

Sharp, L. A., Lee, Y. W., \& Goldstein, A. S. (2009). Effect of
low-frequency pulsatile flow on expression of osteoblastic genes by bone
marrow stromal cells. \emph{Ann Biomed Eng, 37} (3), 445-453.
doi:10.1007/s10439-008-9632-7

Sheill, G., Guinan, E. M., Peat, N., \& Hussey, J. (2018).
Considerations for Exercise Prescription in Patients With Bone
Metastases: A Comprehensive Narrative Review. \emph{PM R, 10} (8),
843-864. doi:10.1016/j.pmrj.2018.02.006

Siegel, R. L., Miller, K. D., \& Jemal, A. (2018). Cancer statistics,
2018. \emph{CA Cancer J Clin, 68} (1), 7-30. doi:10.3322/caac.21442

Sikavitsas, V. I., Bancroft, G. N., Holtorf, H. L., Jansen, J. A., \&
Mikos, A. G. (2003). Mineralized matrix deposition by marrow stromal
osteoblasts in 3D perfusion culture increases with increasing fluid
shear forces. \emph{Proc Natl Acad Sci U S A, 100} (25), 14683-14688.
Retrieved from
http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve\&db=PubMed\&dopt=Citation\&list\_uids=14657343

Sikavitsas, V. I., Bancroft, G. N., Lemoine, J. J., Liebschner, M. A.,
Dauner, M., \& Mikos, A. G. (2005). Flow perfusion enhances the
calcified matrix deposition of marrow stromal cells in biodegradable
nonwoven fiber mesh scaffolds. \emph{Ann Biomed Eng, 33} (1), 63-70.
Retrieved from
http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve\&db=PubMed\&dopt=Citation\&list\_uids=15709706

Sladkova, M., \& de Peppo, G. (2014). Bioreactor Systems for Human Bone
Tissue Engineering. \emph{Processes, 2} (2), 494. Retrieved from
http://www.mdpi.com/2227-9717/2/2/494

Stops, A. J., Heraty, K. B., Browne, M., O'Brien, F. J., \& McHugh, P.
E. (2010). A prediction of cell differentiation and proliferation within
a collagen-glycosaminoglycan scaffold subjected to mechanical strain and
perfusive fluid flow. \emph{J Biomech, 43} (4), 618-626. Retrieved from
http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve\&db=PubMed\&dopt=Citation\&list\_uids=19939388

Takao, S., Taya, M., \& Chiew, C. (2019). Mechanical stress-induced cell
death in breast cancer cells. \emph{Biol Open, 8} (8).
doi:10.1242/bio.043133

Thompson, W. R., Rubin, C. T., \& Rubin, J. (2012). Mechanical
regulation of signaling pathways in bone. \emph{Gene} . Retrieved from
http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve\&db=PubMed\&dopt=Citation\&list\_uids=22575727

Vance, J., Galley, S., Liu, D. F., \& Donahue, S. W. (2005). Mechanical
stimulation of MC3T3 osteoblastic cells in a bone tissue-engineering
bioreactor enhances prostaglandin E2 release. \emph{Tissue Eng, 11}
(11-12), 1832-1839. Retrieved from
http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve\&db=PubMed\&dopt=Citation\&list\_uids=16411829

von Stengel, S., Kemmler, W., Kalender, W. A., Engelke, K., \& Lauber,
D. (2007). Differential effects of strength versus power training on
bone mineral density in postmenopausal women: a 2-year longitudinal
study. \emph{Br J Sports Med, 41} (10), 649-655; discussion 655.
Retrieved from
http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve\&db=PubMed\&dopt=Citation\&list\_uids=17550916

Wang, H., Yu, C., Gao, X., Welte, T., Muscarella, A. M., Tian, L., . . .
Zhang, X. H. (2015). The osteogenic niche promotes early-stage bone
colonization of disseminated breast cancer cells. \emph{Cancer Cell, 27}
(2), 193-210. doi:10.1016/j.ccell.2014.11.017

Winters-Stone, K. M., Dobek, J., Nail, L. M., Bennett, J. A., Leo, M.
C., Torgrimson-Ojerio, B., . . . Schwartz, A. (2012). Impact +
resistance training improves bone health and body composition in
prematurely menopausal breast cancer survivors: a randomized controlled
trial. \emph{Osteoporos Int} . Retrieved from
http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve\&db=PubMed\&dopt=Citation\&list\_uids=22996743

Yamaguchi, S., Sato, Y., Sekino, M., \& Ueno, S. (2006). Combination
Effects of the Repetitive Pulsed Magnetic Stimulation and the Anticancer
Agent Imatinib on Human Leukemia Cell Line TCC-S. \emph{IEEE
Transactions on Magnetics, 42} (10), 3581-3583.
doi:10.1109/TMAG.2006.880866

Yang, S., Liu, H., Zhu, L., Li, X., Liu, D., Song, X., . . . Zhang, P.
(2019). Ankle loading ameliorates bone loss from breast
cancer-associated bone metastasis. \emph{FASEB J, 33} (10), 10742-10752.
doi:10.1096/fj.201900306RR

Zhao, F., Chella, R., \& Ma, T. (2007). Effects of shear stress on 3-D
human mesenchymal stem cell construct development in a perfusion
bioreactor system: Experiments and hydrodynamic
modeling.\emph{Biotechnol Bioeng, 96} (3), 584-595. Retrieved from
http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve\&db=PubMed\&dopt=Citation\&list\_uids=16948169

Zhao, F., Mc Garrigle, M. J., Vaughan, T. J., \& McNamara, L. M. (2018).
In silico study of bone tissue regeneration in an idealised porous
hydrogel scaffold using a mechano-regulation algorithm. \emph{Biomech
Model Mechanobiol, 17} (1), 5-18. doi:10.1007/s10237-017-0941-3

Zhao, F., Melke, J., Ito, K., van Rietbergen, B., \& Hofmann, S. (2019).
A multiscale computational fluid dynamics approach to simulate the
micro-fluidic environment within a tissue engineering scaffold with
highly irregular pore geometry. \emph{Biomech Model Mechanobiol, 18}
(6), 1965-1977. doi:10.1007/s10237-019-01188-4

Zhao, F., Vaughan, T. J., \& McNamara, L. M. (2015). Multiscale
fluid-structure interaction modelling to determine the mechanical
stimulation of bone cells in a tissue engineered scaffold. \emph{Biomech
Model Mechanobiol, 14} (2), 231-243. doi:10.1007/s10237-014-0599-z

\textbf{Figure Legends:}

\textbf{Figure 1: In vitro multi-modal loading system with 3D bone
mimetic scaffolds.} (a) In future experiments, breast cancer cells will
be seeded in bone-mimicking scaffolds fabricated from
poly(lactide-co-glycolide) and bone mineral (hydroxyapatite). (b)
Scaffolds will be loaded in a multi-modal bioreactor system under nine
configurations of dynamic compression and direct perfusion.

\textbf{Figure 2: 3D reconstruction of scaffold from microCT image and
solid-fluid assembly model.} (a) The bone-mimicking scaffold is highly
porous with mean macropore size 432 \selectlanguage{greek}μ\selectlanguage{english}m and mean wall thickness 58 \selectlanguage{greek}μ\selectlanguage{english}m
(Pathi et al., 2010). (b) A scaffold was scanned using high-resolution
microCT images with voxel size 5.4 \selectlanguage{greek}μ\selectlanguage{english}m (Liu et al., 2018). (c) The 3D
voxel model of the scaffold (shown in ivory) as well as the fluid domain
(shown in cyan) was generated using ScanIP. The solid-fluid assembly was
a sub-domain of the whole model, with final dimensions 1.2 mm thick and
2 mm wide.

\textbf{Figure 3: Multiphysics simulation model.} (a) Volumetric meshes
of the fluid and solid domains were directly generated in ScanIP from 3D
voxel models. (b) Fluid and solid surface meshes formed a watertight
assembly along with shared nodes one the interior fluid-solid
interfaces. (c) Boundary conditions were assigned to match the
experimental setup. Interior fluid-solid interface was linked together
in order to transfer coupled data (i.e., solid displacements and fluid
forces).

\textbf{Figure 4: Heat maps and distributions of surface principle
strain of low and high compression.} (a) Surface strain contours of 5\%
compression were distributed evenly in the scaffold with 70\% values
located in 5,000-20,000 \selectlanguage{greek}με \selectlanguage{english}range. (b) Strains of 10\% compression
shifted towards higher range (10,000-40,000 \selectlanguage{greek}με\selectlanguage{english}).

\textbf{Figure 5: Median WSS versus time during the 1 Hz loading
cycle.}WSSs induced by compression alone revealed symmetrical waveforms.
However, when scaffolds were loaded with both compression and perfusion,
the waveforms became asymmetric. Peak WSS values occurred at 0.25 sec of
each cycle and increased with higher magnitude loading. WSS = wall shear
stress.

\textbf{Figure 6: Cyclic compression caused dynamic interstitial fluid
flow.} (a) In the C+P- simulation, velocity vectors showed fluid flow
changed direction during scaffold loading (fluid perfused out) and
unloading (fluid resorbed in). (b) In contrast, during combination
loading (shown C+P+), fluid velocity vectors at 0.25 sec showed greater
fluid flow going upward, the same as the direction of applied perfusion.
Fluid flow was much lower at 0.75 sec with some reversed velocity
vectors seen.\selectlanguage{english}
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