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-µm thick aluminum foil (Reynolds Wrap, Lake Forest, IL), and 500-µm 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.

Table 1 Thermal and electrical properties of metals used in study. Theoretical SAR is calculated for a solid rod with the diameter of 0.965 mm heated in an RF system working at frequency of f = 360 kHz and magnetic field intensity of H 0 = 20 kA/m. Full size table

Table 2 Physical properties of copper foam, aluminum foil and nitinol mesh. Full size table

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.

Figure 2 Ultrarapid warming steps using metal forms (foams, foils or meshes). (a) Loading of VS55 or DP6 in a 1.8-mL cryovial containing copper foams, aluminum foil or nitinol mesh at room temperature. (b) Success and failure of cooling solutions to sub-glass transition temperature − 140 °C. (c) Rewarming vitrified solutions by convection or inductive RF heating (ultrarapid warming). Full size image

Cooling Approaches

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 (− 40 °C/min) for vitrification. To achieve this, the 1.8-mL cryovials loaded with the metal and CPA were lowered into a large flask filled with liquid nitrogen and held in the vapor phase (− 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 − 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 (− 123 °C for VS5520 and − 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 − 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.

Slow and Controlled Cooling (VS55)

VS55 has a lower critical cooling rate (− 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 − 115 °C, the sample was annealed for 5–7 s and finally cooled to − 140 °C. The vast majority of these samples were vitrified and non-cracked. A number of these were then placed either in an RF system or convective water bath to compare warming processes.

Warming Approaches

Convective Warming

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).

Ultrarapid Warming

As shown in Fig. 2c—bottom, 1.8-mL vitrified samples consisting of metal (foam, foil and mesh) loaded in DP6 and VS55 at − 140 °C were quickly transferred into the coil of a 1-kW Hotshot inductive heating system. The RF system has a 2.5–turn water-cooled 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 − 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 − 140 °C vitrified state to − 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 fluoroptic probes.

Viability Studies

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 − 140 °C prior to transfer to the warming apparatus.

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:

Figure 3 Schematic of the combined thermal and solid mechanics modeling. Boundary conditions and initial conditions are given for both ultrarapid warming of solutions using foam (a) and convective warming in water bath (b). Full size image

$$\frac{1}{r}\frac{\partial }{\partial r}\left( {kr\frac{\partial T}{\partial r}} \right) + \frac{\partial }{\partial z}\left( {k\frac{\partial T}{\partial z}} \right) + {\text{SAR}} = \rho c_{\text{p}} \frac{\partial T}{\partial t} ,$$ (1)

where k represents the thermal conductivity, ρ the density, c p 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 Ω 1 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:

$$X_{\text{effective}} = \phi X_{\text{CPA}} + (1 - \phi )X_{\text{metal}} ,$$ (2)

where X CPA and X metal are the corresponding properties for the pure CPA and pure metal, respectively, and ϕ is the mass porosity of the metal foam. Volumetric heat generation is confined in the domain Ω 1 , and domain Ω 2 mimics the polypropylene cryovial.

Figure 3b describes the case of convective warming. In this model, the domain Ω 1 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.

Figure 4 Experimental measurement of cooling and warming rates of vitrified vials. The cooling response of CPA and metal implanted cryovials are shown for VS55 (a) and DP6 (b). The respective rates of 10 and 40–60 °C/min exceed the critical cooling rates needed for VS55 (2.5 °C/min) and DP6 (40 °C/min). The warming responses during convection (c) and ultrarapid warming (d) are shown to achieve rates of 70 and 1200 °C/min, respectively. In (d), the RF coil was shut down at − 50 °C to avoid overheating the sample. Full size image

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 Ω 1 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

$$\dot{\varepsilon } = \dot{\varepsilon }_{\text{creep}} + \dot{\varepsilon }_{\text{elastic}} + \dot{\varepsilon }_{\text{thermal}}$$ (3)

Domain Ω 2 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 convergence 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:

$$\frac{1}{D} \cdot \frac{\partial C}{\partial t} = \frac{1}{r} \cdot \frac{\partial }{\partial r}\left( {r \cdot \frac{\partial C}{\partial r}} \right)$$ (4)

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 (MathWorks).

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 estimated as:

$$R^{2} \equiv 1 - \frac{{\sum

olimits_{i} {(y_{i} - f_{i} )^{2} } }}{{\sum

olimits_{i} {(y_{i} - \bar{y})^{2} } }},$$ (5)