Ultrarapid Inductive Rewarming of Vitrified Biomaterials with Thin Metal Forms
Ultrarapid Inductive Rewarming of Vitrified Biomaterials with Thin Metal Forms
Department of Mechanical Engineering 1 2
University of Minnesota 1 2
Church Street SE 1 2
Minneapolis 1 2
Department of Biomedical Engineering 1 2
University of Minnesota 1 2
Church Street SE 1 2
Minneapolis 1 2
School of Energy 1 2
Power Engineering 1 2
Xi'an Jiaotong University 1 2
Xi'an 1 2
People's Republic of China 1 2
Bioinspired Engineering 1 2
Biomechanics Center (BEBC) 1 2
Xi'an Jiaotong University 1 2
Xi'an 1 2
People's Republic of China 1 2
The Key 1 2
0 State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi'an Jiaotong University , Xi'an 710049 , People's Republic of China
1 Laboratory of Biomedical Information Engineering of Ministry of Education, School of Life Science and Technology, Xi'an Jiaotong University , Xi'an 710049 , People's Republic of China
2 work. ing and Biomechanics Center (BEBC), Xi'an Jiaotong University , Xi'an 710049 , People's Republic of China and John Bischof, Department of Mechanical Engineering, University of Minnesota , 111 Church Street SE, Minneapolis, MN 55455 , USA. Electronic mails:
-Arteries with 1-mm thick walls can be successfully vitrified by loading cryoprotective agents (CPAs) such as VS55 (8.4 M) or less concentrated DP6 (6 M) and cooling at or beyond their critical cooling rates of 2.5 and 40 C/min, respectively. Successful warming from this vitrified state, however, can be challenging. For example, convective warming by simple warmbath immersion achieves 70 C/min, which is faster than VS55's critical warming rate of 55 C/min, but remains far below that of DP6 (185 C/min). Here we present a new method that can dramatically increase the warming rates within either a solution or tissue by inductively warming commercially available metal components placed within solutions or in proximity to tissues with non-invasive radiofrequency fields (360 kHz, 20 kA/m). Directly measured warming rates within solutions exceeded 1000 C/min with specific absorption rates (W/g) of 100, 450 and 1000 for copper foam, aluminum foil, and nitinol mesh, respectively. As proof of principle, a carotid artery diffusively loaded with VS55 and DP6 CPA was successfully warmed with high viability using aluminum foil, while standard convection failed for the DP6 loaded tissue. Modeling suggests this approach can improve warming in tissues up to 4-mm thick where diffusive loading of CPA may be incomplete. Finally, this technology is not dependent on the size of the system and should therefore scale up where convection cannot.
Vitrification; Rewarming; Ultrarapid warming
MENG SHI,3,4 PRIYATANU ROY,1 ZONGHU HAN,1 JINBIN QIU,4,5 FENG XU,4,5
TIAN JIAN LU,4,6 and JOHN BISCHOF1,2
The use of low temperatures to indefinitely bank
and store tissues for eventual transplantation is a main
goal of the field of cryobiology.15,19,24 This approach,
often termed cryopreservation, has been successfully
used for long-term storage of cells, aggregates, and
some smaller tissues.10,15,19,35 However, the availability
of many tissues and almost all organs is limited due to
several important bottlenecks, including the need for
faster warming in larger and thicker tissue
One of the best options for cryopreservation of
tissues and larger systems involves vitrification or storage
in a glassy state that avoids ice crystal damage. This
requires tissues and other biomaterials (i.e.,
suspensions) to be loaded with cryoprotective agents (CPAs)
to block ice crystal formation during cooling to
temperatures below the glass transition temperature of the
CPA, usually 2 140 C.10
CPA toxicity can generally be avoided by using
lower concentration CPAs, but this means that the
critical warming rate (CWR) increases from 55 C/min
for 8.4 M VS55 to 185 C/min for 6 M DP67,22,34 to
avoid devitrification during warming.7,8,18,22,34
Similarly, as tissue thickness increases, longer loading time
(hours) would be needed to equilibrate the
distrubution of CPA in the tissue. As this time increases beyond
normal loading times (4?5 steps of roughly 15 min
each), the potential for toxicity and therefore lower
viability at the edge of the tissue being loaded will
in2018 The Author(s)
crease. Therefore, all tissues (thick or thin) are loaded
with the least amount of CPA over the least time to
avoid toxicity. As a result, there will always be a lower
concentration in the center of the loaded tissue which,
especially in the case of thicker tissue, will necessitate
faster rates of warming to successfully avoid
To address these issues, microwave
warming9,17,23,25,26,36 and nanowarming with
nanoparticles8,18 have been proposed to achieve faster warming
of tissues than convection. Microwave warming,
however, can be non-uniform, resulting in ??hot spots??
which can drive subsequent cracking and/or thermal
runaway. Moreover, its application varies by size and
shape within a system.3,4,9,25 Alternatively,
nanowarming adds biocompatible magnetic (iron
oxide) nanoparticles to the CPA prior to vitrification
and storage. Rewarming is achieved within an
electromagnetic coil producing a uniform radiofrequency
field that inductively heats the nanoparticles and then,
by extension, the whole system.8,18 This technology has
achieved uniform warming rates up to 100 C/min for
porcine tissues regardless of volume,18 and has
successfully warmed ~ 1 mm arteries loaded with VS55 in
1?50 mL systems. Nevertheless, the rates necessary to
successfully warm DP6 solutions, loaded arteries, or
thicker arteries (i.e., aorta) are difficult to achieve with
achievable rates from convection or nanowarming.
In this study, we developed an ultra-rapid
volumetric heating method to heat solutions or tissue
systems at ? 1000 C/min, which is a rate that is an order
of magnitude faster than convection, nanowarming or
the CWR of DP6 and VS55.8,18,22 Solutions or tissues
were vitrified and placed in contact with thin metal
forms (foam, foil, or mesh) as shown in Fig. 1. The
alternating magnetic field induced eddy currents in the
metal with concurrent resistive losses that heated the
sample from within (Figure S2A). As a demonstration
of use, this approach was then used to successfully
rewarm DP6 loaded carotid arteries where convection
MATERIALS AND METHODS
Preparation of Thin Metal Forms: Foam, Foil, and Mesh
In this study, metal forms consisted of copper foam
(YiYang Foammetal New Materials Co., Ltd., Hunan,
China), 100-lm thick aluminum foil (Reynolds Wrap,
Lake Forest, IL), and 500-lm thick nitinol mesh
(Boston Scientific, Saint Paul, MN) structures as
shown in Tables 1 and 2. These choices were made to
test a range of metals with variable electrical properties
and ease of shaping.
Preliminary tests were performed with copper foams
with 20 pores per inch and 89percent porosity. These
were formed by wire electrical discharge machining
into a cylindrical shape with diameter and height of 9.8
and 23 mm, respectively. Two fluoroptic probes
(Qualitrol Company LLC, Fairport, NY) were used to
monitor the temperature at the center and edge of the
foam with a vertical position of 30 mm from the top of
a 1.8-mL cryovial. The metal foams were placed in the
cryovial (Cole Parmer, Vernon Hills, IL), and CPA
was added until reaching 1.8-mL volume (Fig. 2a). The
metal foil and mesh were formed into a cylindrical shell
(annulus) shape with properties mentioned in Table 2.
Cooling and heating under these conditions without
the presence of an artery or tissue are understood to
represent limiting cases.
The two CPAs, VS55 and DP6, have very different
critical cooling rates, so two separate cooling protocols
were used to achieve vitrification at rates that exceed
the critical cooling rate (Fig. 2b).
Fast and Direct Cooling (DP6)
DP6 solution requires a high critical cooling rate
(2 40 C/min) for vitrification. To achieve this, the
1.8mL cryovials loaded with the metal and CPA were
lowered into a large flask filled with liquid nitrogen and
held in the vapor phase (2 160 C) just above the
surface of the liquid. Temperature was monitored using
two fluoroptic probes placed at the center and edge of
the vial (Qualitrol Company LLC, Fairport, NY)
connected to a T/GUARD 405 temperature monitoring
system (Neoptix, Canada). One of the probes measured
the centerline temperature of the CPA solution in the
vial while the other was placed on the outside near the
vial wall. When the center reached 2 115 C, the vial
was allowed to anneal by taking the cryovial out of the
flask for 5?7 s to allow the center and the edge of the
CPA inside the cryovial to equilibrate and stabilize. By
performing this just above the glass transition
temperature (2 123 C for VS5520 and 2 119 C for DP622),
residual thermal stresses are reduced, thereby lowering
the chance of cracking when the sample transitions into
a glass. Finally, the samples were cooled to 2 140 C,
and monitored for any cracking (more than 90% of
samples achieved vitrification without cracking). A
number of these successfully vitrified samples were then
either placed in the RF system or convective water bath
to compare warming processes.
Choice of thermal seed
(c) Traditional convection
VS55 has a lower critical cooling rate (2 2.5 C/
min) than DP6, so a multi-flask cooling method for a
1.8-mL system was used as previously described.8,18 In
brief, the cryovials were placed in a series of
concentric, successively larger containers, with liquid nitrogen
filling the outside of most containers. This layering of
containers provided thermal barriers for heat transfer
between the liquid nitrogen and the cryovial and
slowed down the heat transfer rate. To monitor the
temperature during cooling, two fluoroptic probes
were positioned in the center and on the edge of the
cryovial as described in the DP6 cooling section above.
Once the center reached 2 115 C, the sample was
annealed for 5?7 s and finally cooled to 2 140 C. The
vast majority of these samples were vitrified and
noncracked. A number of these were then placed either in
an RF system or convective water bath to compare
The vitrified samples were transferred from the
liquid nitrogen container and immersed into a 37 C
water bath while the temperature variation was
recorded using fluoroptic probes placed in the middle
and edge of the sample (Fig. 2c?top).
Heating rates and experimental SARs are calculated from the linear portion of the heating profile.
As shown in Fig. 2c?bottom, 1.8-mL vitrified
samples consisting of metal (foam, foil and mesh)
loaded in DP6 and VS55 at 2 140 C were quickly
transferred into the coil of a 1-kW Hotshot inductive
heating system. The RF system has a 2.5?turn
watercooled copper coil (Ameritherm Inc., Scottsville, NY),
and experiments were carried out at a magnetic field
strength of 20 kA/m (peak, volume-averaged field
strength) and frequency of 360 kHz. The cryovial was
placed within a Styrofoam container within the coil to
lessen direct loss to the environment. The time of RF
exposure was characterized for each case of metal
forms (copper foam, aluminum foil and nitinol mesh)
to ensure the final temperature of 2 20 C (near melt
of CPA) was reached prior to turning off the field.
Typically, the temperature would then continue to rise
more slowly to room temperature prior to any further
studies. To assess the warming efficacy, we considered
warming rates from 2 140 C vitrified state to
2 20 C, where CPA is liquid and the low temperature
leads to a reduction in toxicity. We noted that the
resulting heat generation or specific absorption rate
(SAR) depends on the metal type, shape, structure,
weight, volume and orientation of placement in RF
coil. Therefore, samples from different metal forms
warm at different rates and lead to different volumetric
SAR (W/cm3) or mass-based SAR (W/g) as shown in
Table 2. The sample temperature was achieved
continuously at a frequency of 5 Hz by means of
For viability experiments, we chose to work with
aluminum foil warming due to ease of deployment in
DP6 and VS55 samples and compared this to
convective warming controls. Porcine arteries were obtained
postmortem from skeletally immature domestic
Yorkshire cross farm pigs (65?80 kg, aged 16?
18 weeks). Arteries were removed within 30 min of
death following Institutional Animal Care and Use
Committee (IACUC) approved protocols at University
of Minnesota. The animals were sacrificed as part of
other IACUC approved studies at the Visible Heart
Lab and the arteries were considered bona fide excess.
Arteries were submerged in a Krebs?Henseleit buffer
and placed on ice before being transported to our
laboratory. Upon receipt (hours later), arteries were
dissected to reproducible segments ~ 1-cm height.
Fresh artery segments were rinsed with growth media
[Dulbecco?s modified Eagle?s medium (Thermo Fisher)
with 1% antibiotic-antimycotic (Thermo Fisher)], and
cleared of fatty tissue. Carotid arteries were sectioned
into 1 cm-long segments with inner diameters of 4?
6 mm and wall thicknesses 1?2 mm. Experiments were
carried out on several independent days with 3?4
arteries per test and 4?6 slices per artery for ultrarapid
warming and convective warming tests.
Viability was assessed by incubation with 10%
alamarBlue (Thermo Fisher) media solution at 37 C
for 3 h before (control) and after any warming
experiments. Fluorescence was read on a plate reader
(Synergy HT, BioTek) at 590 nm from an aliquot of
the media to establish a baseline. For arteries
undergoing ultrarapid or convective methods, tissues were
stepwise loaded with CPA as previously published.1,18
Once the arteries experienced the final step of loading
at full-strength VS55 or DP6, the aluminum foil was
placed against the interior (i.e., luminal) and exterior
artery walls to create a sandwich, and the remainder
was filled with the CPA. All samples were successfully
vitrified by the protocols explained above and
equilibrated at 2 140 C prior to transfer to the warming
Ultrarapid rewarming was achieved by either
inductive RF warming at 20 kA/m, 360 kHz, or by
convective warming using 37 C water bath
immersion, considered here as a gold- standard control. After
warming to room temperature (18?20 C), the VS55
and DP6 was step-wise removed as previously
reported.1 After the removal of the CPA, the tissue
segments were sectioned into small pieces and
incubated with fresh media at 37 C for one hour
(recovery) and then incubated with 10% alamarBlue for 3 h
and compared with fresh controls. The viability of each
tissue piece was normalized to fresh control. Raw
results are presented as the mean ? standard error of
relative fluorescence units (RFU) after correction to
RFU/mg dry weight prior to normalization.
Heat Transfer Modeling
Temperature modeling was approached using a 2-D
cylindrical energy equation for solving the
heat-transfer problem. Different solid domains were assigned as
shown in Fig. 3 for metal, cryovial and tissue (when
present), and the heat diffusion equation was solved:
where k represents the thermal conductivity, q the
density, cp the specific heat capacity, T the
temperature, and SAR (W/m3) the volumetric heat generation
rate from the metals due to RF heating. Initial and
boundary conditions and other parameters are listed in
the Supplemental Material under ??heat-transfer
modeling?? and are listed for specific cases in Fig. 3.
The solution domain consists of two concentric
cylinders. In case of metal foam (Fig. 3a), the inner
cylinder X1 is made up of CPA and foam. Thermal
properties for the different domains are listed in
Table S2A. In the case of CPA and foam in the middle
of the cylinder, the properties are estimated by mass
averaging using this equation:
Xeffective ? /XCPA ? ?1 /?Xmetal;
where XCPA and Xmetal are the corresponding
properties for the pure CPA and pure metal, respectively, and
/ is the mass porosity of the metal foam. Volumetric
heat generation is confined in the domain X1, and
domain X2 mimics the polypropylene cryovial.
Figure 3b describes the case of convective warming.
In this model, the domain X1 consists of only CPA
with no internal heat source, and warming is achieved
only by boundary heating. The boundary conditions
and initial condition for the heat-transfer problem are
also indicated in Fig. 3. In both Figs. 3a and 3b, the
top and left (symmetry) boundaries are assigned
adiabatic conditions, while the bottom and right side of
the container are assigned convective conditions. The
free convection heat transfer coefficient in air (Fig. 3a)
was taken as 8 (W/(m2?K)) based on an empirical
correlation from Incropera and DeWitt,14 whereas in
water (Fig. 3b) it is assumed to be 100 (W/(m2?K))
based on the ability to fit the experimentally
determined convective heating response shown in Fig. 4c.
Solid Mechanics Modeling
While the heat transfer is unaffected by solid
mechanics, the inverse is not true. Specifically, the
mechanical response of the material is driven by
thermal strain caused by temperature distribution within
the domains as discussed in detail in the Supplemental
Material. To assess this coupling, mechanical and
thermal properties were used in simulations as listed in
the supplementary Table S2A.5,6,33 The CPA in
domain X1 was modeled as a viscoelastic linear Maxwell
fluid with a single-branch spring-dashpot behavior.32
The viscosity of the fluid increases as per
supplementary Table S2B with drop in temperature until the fluid
behaves as a solid at close to its glass-transition
temperature. The total strain rate is calculated as the sum
of elastic, creep, and thermal strain rates.5,29
e_ ? e_creep ? e_elastic ? e_thermal
Domain X2 was the container, and it was set to act
as an elastic solid over the temperature range
considered. As shown in Figs. 3a and 3b, two different
geometries were used corresponding to metal foam +
CPA and CPA-only cases. The bottom center of the
cylinder was used as a pinned boundary condition,
while all other boundaries could move freely. Here, the
shear stress is assumed to be negligible, and since the
circumferential stress is much smaller than axial
stress,5 it is not considered in the modeling. The
commercial FEA package COMSOL Multiphysics was
used for all the numerical heat and mechanics based
simulations. In all cases, numerical stability and
Direct cooling (DP6)
0 45 10 15 20100
Coil off Time(sec)
vergence were ensured as further mesh reduction and
discretization left the solution unchanged.
Diffusional (CPA) Loading Model
To model CPA loading, a 1D cylindrical annulus
model of mass (i.e., CPA) diffusion based on Fick?s
2nd Law, was applied with the concept that the CPA
concentration, C, is governed by an effective
diffusivity, D (m2/s) in the tissue:
with the boundary conditions and initial conditions as
noted in Supplemental Methods. The method of
separation of variables (analytical closed form) was used
to obtain an exact solution for C(r, t) as shown in the
Supplemental Material. This closed-form solution was
then plotted and visualized using MATLAB
The value of diffusivity was estimated by fitting the
theoretical curve to historical experimental data for
VS55 loading into a carotid artery.18 More specifically,
the boundary conditions were normalized with respect
to the external CPA solution concentration at the first
18-min time step. The coefficient of determination, R2,
was used to assess how well the model was able to
predict the experimental data. The value of R2 was
where yi is the experimental data, fi is the theoretical
value for the same radius, y is the average of
experimental data. The range of R2 is from 0 to 1, with values
closer to 1 indicating a better fit of the model to the
Figures 4a and 4b and the images in Fig. 2
demonstrate that we can exceed the critical cooling
rates of VS55 (2.5 C/min) and DP6 (40 C/min) to
achieve vitrified solutions as shown by the clarity of the
solution and absence of cracks. Cooling rates
measured were 10 C/min for VS55 and 40?60 C/min for
DP6. Further, the slower VS55-controlled cooling
method and the metal foam samples show minimal
thermal gradients in the sample (Fig. 4a). Both
samples were annealed at roughly 2 115 C, which is just
above the glass-transition temperatures of 2 123 C
for VS5520 and 2 119 C for DP6.34
Figures 4c and 4d show an experimental
comparison of inductive and convective warming of these
vitrified materials from 2 140 C, respectively.
Warmbath immersion leads to convective rates up to 70 C/
min while inductive heating achieves ? 1200 C/min
reaching 2 20 C in seconds. Indeed, it was necessary
to shut the RF coil off at 2 50 C to avoid overheating
of the sample (Fig. 5d). Temperature profiles at the
center or origin (O) to wall (W) are similar for
ultrarapid warming; however, a significant gradient is
shown in the convective water bath (Fig. 4c). These
results show our ability to exceed CWR of DP6 and
VS55 by ultrarapid warming of copper foams. Similar
measurements showing our ability to exceed CCR and
CWR were made for other metals in VS55 as shown in
the Supplemental Material and summarized in Table 2
and Figure S2.
The predicted thermal and mechanical response of
the systems during convective and inductive ultrarapid
warming are shown in Figs. 5 and 6 respectively. For
instance, there is a maximum thermal gradient of 35 C
in a convective water-bath method (Figs. 5a and 5b),
resulting in thermal stress beyond the yield stress,
specifically at the center or origin of ~ 4 MPa, which
will likely lead to failure by cracking (Figs. 5c and 5d).
On the other hand, the computed thermal response
(Figs. 6a and 6b) compares favorably to the
experimental warming profiles (Fig. 4d) of a metal foam
heating with RF. Figures 6c and 6d illustrate the
corresponding thermomechanical stress response. The
positive sign in Fig. 6c represents tension, and the
negative sign represents compression in a biomaterial.
Note that a vitrified biomaterial would fail at much
lower tension than compression, so we look for areas
where the positive stress is maximum (e.g., at the wall
(W) in Fig. 6d). The simulated stress level is 40% less
than the critical yield stress of 3.2 MPa, suggesting
that failure by cracking is unlikely.
Even with an order-of-magnitude higher warming
rate, this technique will still be limited by the amount
of CPA that can be effectively loaded into the artery.
To address this, VS55 diffusive loading into carotid
arteries was studied (Figs. 7a?7c), and warming of
CPA loaded arteries of variable thickness was
attempted experimentally (Fig. 7d). By matching the
diffusion equation to the experimental data at 18 min,
a mass diffusivity of 3.18 910211 m2/s was extracted as
shown in (Fig. 7a). The final R2 for the data set at 4 C
at 18 min was 0.94 indicating a good fit.18 To assess the
impact of differential loading experimentally Fig. 7b
shows loading of CPA into a thin carotid artery.
Clearly, the viability drops as the amount of CPA that
can be delivered to the tissue center is reduced in the
aorta. Using the diffusion loading model, spatial and
temporal distribution of VS55 concentration within the
carotid artery is shown to reach more than 60% in the
center after 60 min in Fig. 7b whereas the 2-mm thick
aorta reached only 10% loading in the center over the
same time frame with the same boundary loading
(Fig. 7c). To assess the impact of differential loading,
the viability of thin (femoral), average (carotid), and
thick (aorta) arteries loaded by the same step protocol
was assessed after nanowarming (Fig. 7d). As can be
seen, the carotid and femoral arteries (roughly 1-mm
thick) had high viability, while the aorta showed low
viability. Thus, CPA loading is critical as lower loading
leads to lower yields from nanowarming.
One approach to successfully rewarm tissues with
less CPA is to increase the warming rate beyond both
convection and nanowarming with metal forms. To
explore this more generally, the heat generation of
copper foams, aluminum foil and nitinol were all
predicted and tested. Table 1 summarizes the theoretical
SAR predictions based on Stauffer31 for a solid rod
with a diameter of .965 mm heated in an RF system
working at frequency of 360 kHz magnetic field
intensity of 20 kA/m. The results show nitinol
volumetric heat generation at almost six times that of
aluminum and copper. Table 2 summarizes the
experimental SAR generation for copper foam,
aluminum foil and nitinol mesh.
Finally, the viability of warmed carotid artery
segments was assessed with varying amounts of CPA
loading (Fig. 8a). Importantly, to avoid temperature
variations within the artery during ultrarapid warming,
the foil was deployed as a sandwich around the artery
prior to cooling and warming. After convective
warming for DP6-loaded arteries showed a ~ 35%
drop in viability vs. VS55-loaded arteries (p < 0.05).
However, there was no statistically significant viability
changes between VS55 or DP6 control arteries after
ultrarapid warming. While this demonstrates the
ability for ultrarapid warming to recover tissues with
suboptimal CPA penetration (i.e., DP6 carotid), it also
suggests that ultrarapid warming may work for thicker
tissues. To evaluate this theoretically, we varied the
heat generation of the warming method in an annular
model of an artery as shown in Fig. 8b.18 Here a
baseline volumetric SAR of 2.5 W/cm3 represents
nanowarming. By increasing this SAR by an order of
magnitude (i.e., 109 SAR), one obtains a trend that
??arteries?? or annular tissues up to 4-mm-thick can be
warmed at rates beyond the CWRs of VS55 and DP6.
Importantly, these SARs and higher are achievable by
deploying the metal forms in the lumen and around the
outside of the artery (Table 2). As shown in the Fig. 8c
sub-table, CWRs increase rapidly as CPA
concentration decreases thereby also showing the need for faster
warming techniques such as from metal forms.
This study demonstrates a new approach to increase
the warming rates of vitrified biomaterials (solutions or
tissues) using inductive heating of thin metal forms.
The rates achievable are in excess of 1000 C/min and
hence far exceed the critical warming rates of
numerous common CPAs. Indeed, the warming rates can be
controlled by both choice of metal (type, amount and
distribution), and field (frequency and magnetic field
intensity) of the RF system. This in turn allows for the
eventual rescue of samples that are sub-optimally
loaded with CPAs and/or the use of lower
concentration CPAs such as DP6. Furthermore, it suggests an
opportunity to design the mechanical stress history of
Convective n=2, Ultrarapid
rewarmed N=4 rewarmed
SAR =2.5 W/cm3
the sample to avoid cracking failures as recently
explored within computational studies of inductively
The ability to heat with metal forms is reliant on
induced currents in the metal that do not distribute
uniformly based on an effect called ??skin depth.?? In
practice, over 98% of the current flow, and thus the
bulk of the heating, will occur within a layer four
times the skin depth from the surface. Thus, to
increase the efficacy of heating, the thickness of the
metal forms should be designed as ? 4 times the
skin depth at the frequency of tuning. Otherwise the
induced eddy currents will cancel each other that
results in reduced heating as described further in
the Supplemental Material. A summary of skin
depth of different metals used in this study is given
in Table 1. In brief, metal type, size and shape (i.e.,
thickness according to skin depth) and frequency of
RF field operation are all important in ultrarapid
Although convection is routinely used on small
volumes (< 3 mL),1,2 the ability to use convection in
larger systems will eventually fail due to cracking as
the thermal stress continues to rise with size to be
above the yield stress. However, properly designed
ultra-rapid warming should be able to achieve uniform
and fast warming within a few millimeters from the
metal form regardless of the size of the system. This
approach is likely to find utility in large-cell suspension
or tissues that have lower concentrations of CPA after
diffusive loading either due to the lower concentration
of the CPA cocktail (i.e., DP6) or due to the increased
thickness of the tissue (i.e., aorta).
As an example diffusive loading of VS55 into an
artery only 0.8-mm thick achieves only 6 M at the
centerline after 3 h.18 This physical study was much
longer than the conventional loading protocols, which
are closer to 75 min to avoid toxicity.1,2 Therefore, in
practice, the center of boundary-loaded tissues will
likely require faster warming rates than currently
reported for the CPA alone. This will be particularly
important in 2-mm thick aortic tissue (Fig. 7) and
other tissues which are routinely 1.5?3.5-mm thick and
are known to poorly load with CPA.28
Thus, a key advantage of ultrarapid warming is
both the low cost of metal forms and the high
achievable rates of over 1000 C /min. For example,
SAR from iron oxide nanoparticles for nanowarming
are usually 160 W/g Fe at a cost of dollars/mg
nanoparticles, whereas the SAR from metal forms
ranges from 80 to 1000 W/g at estimated cost for
aluminum foil of only cents/g metal. The metal forms
can also be designed for easy removal in regular planar
(e.g., heart valve, cartilage, suspension) and annular
(e.g., artery) geometries.
It is important to mention that the biocompatibility
of the metal used in this technique will be important
when deployed in large-scale cell suspensions or in
proximity to tissue surfaces. Various coating
approaches may be needed to address this.
Furthermore, although ultrarapid warming technology can be
a good alternative for warming of tissues with surfaces
and luminal structures, the need for nanowarming for
vascularized bulk biomaterial at present cannot be
addressed by distributed heating other than by
deployment of nanoparticles within the vascular
ELECTRONIC SUPPLEMENTARY MATERIAL
The online version of this article (https://doi.org/10.
1007/s10439-018-2063-1) contains supplementary
material, which is available to authorized users.
We thank the Visible Heart Laboratory?s Tinen Iles
for access to porcine arteries.
This work was supported by NSF CBET #1336659
and the Kuhrmeyer Chair to J.C.B. We are also
grateful for the financial support provided by the
National Natural Science Foundation of China
(11532009) and the National 111 Project of China
(B06024). Author contributions: N.M. and M.S.
conceived of and carried out experiments with analysis and
support from J.C.B. N.M. performed tissue viability
work. N.M. and P.R. performed and/or analyzed the
heating experiments and thermal and mechanical
modeling. N.M. wrote the manuscript with support
and input from all the authors.
Apatent on the ultrarapid warming technology has
been published with International Application No.
PCT/US2017/018331 and is entitled ??Cryoprotection
Compositions and Methods.?? All other authors
declare that they have no competing interests.
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