A quantitative analysis of the thermal properties of porcine liver with glycerol at subzero and cryogenic temperatures

Freezing of Solute-Laden Aqueous Solutions: Kinetics of Crystallization and Heat- and Mass-Transfer-Limited Model

Following an earlier study, we reexamined the latent heat of fusion during freezing at 5 K/min of twelve different pre-nucleated solute-laden aqueous solutions using a Differential Scanning Calorimeter (DSC) and correlated it with the amount of initially dissolved solids or solutes in the solution. In general, a decrease in DSC-measured heat release (in comparison to that of pure water, 335 mJ/mg) was observed with an increasing fraction of dissolved solids or solutes, as observed in the earlier study. In addition, the kinetics of ice crystallization was also obtained in three representative biological media by performing additional experiments at 1, 5 and 20 K/min. A model of ice crystallization based on the phase diagram of a water–NaCl binary solution and a modified Avrami-like model of kinetics was then developed and fit to the experimental data. Concurrently, a heat and mass transfer model of the freezing of a salt solution in a small container is also presented to account for the effect of the cooling rate as well as the solute concentration on the measured latent of freezing. This diffusion-based model of heat and mass transfer was non-dimensionalized, solved using a numerical scheme and compared with experimental results. The simulation results show that the heat and mass transfer model can predict (± 10%) the experimental results.

Supplemented phase diagrams for vitrification CPA cocktails: DP6, VS55 and M22

DP6, VS55 and M22 are the most commonly used cryoprotective agent (CPA) cocktails for vitrification experiments in tissues and organs. However, complete phase diagrams for the three CPAs are often unavailable or incomplete (only available for full strength CPAs) thereby hampering optimization of vitrification and rewarming procedures. In this paper, we used differential scanning calorimetry (DSC) to measure the transition temperatures including heterogeneous nucleation temperatures (T_het), glass transition temperatures (T_g), rewarming phase crystallization (devitrification and/or recrystallization) temperatures (T_d) and melting temperatures (T_m) while cooling or warming the CPA sample at 5 °C/min and plotted the obtained transition temperatures for different concentrations of CPAs into the phase diagrams. We also used cryomicroscopy cooling or warming the sample at the same rate to record the ice crystallization during the whole process, and we presented the cryomicroscopic images at the transition temperatures, which agreed with the DSC presented phenomena.

Experimental Investigation on Thermal Conductivity and Thermal Diffusivity of Ex-Vivo Bovine Liver from Room Temperature down to -60 °C

Ex vivo animal tissues (e.g., bovine liver) as well as water-agar gel are commonly used to simulate both experimentally and numerically the response of human tissues to cryoablation treatments. Data on the low temperature thermal properties of bovine liver are difficult to find in the literature and very often are not provided for the whole temperature range of interest. This article presents the thermal conductivity and thermal diffusivity measurements performed on ex-vivo bovine liver samples using the transient plane source method. Regression coefficients are provided to determine these properties in different temperature ranges except for the phase transition during which no results were obtained, which suggests an ad hoc calorimetric analysis. A quick procedure is also suggested to determine the water mass fraction in the tissue. Moreover, an attempt to estimate the liver density in the frozen state using measurements performed solely at room temperature is also presented. The measured thermal conductivity and thermal diffusivity values are compared with data reported in literature highlighting a spread up to 40%. Moreover, it emerges that water-agar gel usually made with 2% by weight of agar does not show the same thermal properties as the bovine liver.

Measurement of Ex Vivo Liver, Brain and Pancreas Thermal Properties as Function of Temperature

The ability to predict heat transfer during hyperthermal and ablative techniques for cancer treatment relies on understanding the thermal properties of biological tissue. In this work, the thermal properties of ex vivo liver, pancreas and brain tissues are reported as a function of temperature. The thermal diffusivity, thermal conductivity and volumetric heat capacity of these tissues were measured in the temperature range from 22 to around 97 °C. Concerning the pancreas, a phase change occurred around 45 °C; therefore, its thermal properties were investigated only until this temperature. Results indicate that the thermal properties of the liver and brain have a non-linear relationship with temperature in the investigated range. In these tissues, the thermal properties were almost constant until 60 to 70 °C and then gradually changed until 92 °C. In particular, the thermal conductivity increased by 100% for the brain and 60% for the liver up to 92 °C, while thermal diffusivity increased by 90% and 40%, respectively. However, the heat capacity did not significantly change in this temperature range. The thermal conductivity and thermal diffusivity were dramatically increased from 92 to 97 °C, which seems to be due to water vaporization and state transition in the tissues. Moreover, the measurement uncertainty, determined at each temperature, increased after 92 °C. In the temperature range of 22 to 45 °C, the thermal properties of pancreatic tissue did not change significantly, in accordance with the results for the brain and liver. For the three tissues, the best fit curves are provided with regression analysis based on measured data to predict the tissue thermal behavior. These curves describe the temperature dependency of tissue thermal properties in a temperature range relevant for hyperthermia and ablation treatments and may help in constructing more accurate models of bioheat transfer for optimization and pre-planning of thermal procedures.

Multiscale Thermal Property Measurements for Biomedical Applications

Bioheat transfer-based innovations in health care include applications such as focal treatments for cancer and cardiovascular disease and the preservation of tissues and organs for transplantation. In these applications, the ability to preserve or destroy a biomaterial is directly dependent on its temperature history. Thus, thermal measurement and modeling are necessary to either avoid or induce the injury required. In this review paper, we will first define and discuss thermal conductivity and calorimetric measurements of biomaterials in the cryogenic (<-40 °C), subzero (<0 °C), hypothermic (<37 °C), and hyperthermic (>37 °C) regimes. For thermal conductivity measurements, we review the use of 3ω and laser flash techniques for measurement of thermal conductivity in thin (1 μm-2 mm thick), anisotropic, and/or multilayered tissues. At the nanoscale, we review the use of pump-probe and scanning probe methods to measure thermal conductivity at short temporal scales (10 ps-100 ns) and spatial scales (1 nm-1 μm), particularly in the coating and surrounding medium around metallic nanoparticles (1 nm-20 nm). For calorimetric techniques, we review differential scanning calorimetry (DSC), which is intrinsically at the microscale (e.g., tissue pieces or millions of cells in media). DSC is used with large sample mass (∼3-100 mg) over wide temperature ranges (-180 to 750 °C) with low-temperature scanning rates (<750 °C/min). The need to assess smaller samples at higher rates has led to the development of nanocalorimetry on a silicon based membrane. Here the sample weight is as low as 10 ng, thereby allowing ultra-rapid heating rates (∼1 × 10⁷ C/min). Finally, we discuss various opportunities that are driving the need for new micro- and nanoscale thermal measurements.

A Micro-Thermal Sensor for Focal Therapy Applications

There is an urgent need for sensors deployed during focal therapies to inform treatment planning and in vivo monitoring in thin tissues. Specifically, the measurement of thermal properties, cooling surface contact, tissue thickness, blood flow and phase change with mm to sub mm accuracy are needed. As a proof of principle, we demonstrate that a micro-thermal sensor based on the supported "3ω" technique can achieve this in vitro under idealized conditions in 0.5 to 2 mm thick tissues relevant to cryoablation of the pulmonary vein (PV). To begin with "3ω" sensors were microfabricated onto flat glass as an idealization of a focal probe surface. The sensor was then used to make new measurements of 'k' (W/m.K) of porcine PV, esophagus, and phrenic nerve, all needed for PV cryoabalation treatment planning. Further, by modifying the sensor use from traditional to dynamic mode new measurements related to tissue vs. fluid (i.e. water) contact, fluid flow conditions, tissue thickness, and phase change were made. In summary, the in vitro idealized system data presented is promising and warrants future work to integrate and test supported "3ω" sensors on in vivo deployed focal therapy probe surfaces (i.e. balloons or catheters).

High accuracy thermal conductivity measurement of aqueous cryoprotective agents and semi-rigid biological tissues using a microfabricated thermal sensor

An improved thermal-needle approach for accurate and fast measurement of thermal conductivity of aqueous and soft biomaterials was developed using microfabricated thermal conductivity sensors. This microscopic measuring device was comprehensively characterized at temperatures from 0 °C to 40 °C. Despite the previous belief, system calibration constant was observed to be highly temperature-dependent. Dynamic thermal conductivity response during cooling (40 °C to -40 °C) was observed using the miniaturized single tip sensor for various concentrations of CPAs, i.e., glycerol, ethylene glycol and dimethyl sulfoxide. Chicken breast, chicken skin, porcine limb, and bovine liver were assayed to investigate the effect of anatomical heterogeneity on thermal conductivity using the arrayed multi-tip sensor at 20 °C. Experimental results revealed distinctive differences in localized thermal conductivity, which suggests the use of approximated or constant property values is expected to bring about results with largely inflated uncertainties when investigating bio-heat transfer mechanisms and/or performing sophisticated thermal modeling with complex biological tissues. Overall, the presented micro thermal sensor with automated data analysis algorithm is a promising approach for direct thermal conductivity measurement of aqueous solutions and soft biomaterials and is of great value to cryopreservation of tissues, hyperthermia or cryogenic, and other thermal-based clinical diagnostics and treatments.

Reusable bi-directional 3ω sensor to measure thermal conductivity of 100-μm thick biological tissues

Accurate knowledge of the thermal conductivity (k) of biological tissues is important for cryopreservation, thermal ablation, and cryosurgery. Here, we adapt the 3ω method-widely used for rigid, inorganic solids-as a reusable sensor to measure k of soft biological samples two orders of magnitude thinner than conventional tissue characterization methods. Analytical and numerical studies quantify the error of the commonly used "boundary mismatch approximation" of the bi-directional 3ω geometry, confirm that the generalized slope method is exact in the low-frequency limit, and bound its error for finite frequencies. The bi-directional 3ω measurement device is validated using control experiments to within ±2% (liquid water, standard deviation) and ±5% (ice). Measurements of mouse liver cover a temperature ranging from -69 °C to +33 °C. The liver results are independent of sample thicknesses from 3 mm down to 100 μm and agree with available literature for non-mouse liver to within the measurement scatter.

Methods for characterizing convective cryoprobe heat transfer in ultrasound gel phantoms

While cryosurgery has proven capable in treating of a variety of conditions, it has met with some resistance among physicians, in part due to shortcomings in the ability to predict treatment outcomes. Here we attempt to address several key issues related to predictive modeling by demonstrating methods for accurately characterizing heat transfer from cryoprobes, report temperature dependent thermal properties for ultrasound gel (a convenient tissue phantom) down to cryogenic temperatures, and demonstrate the ability of convective exchange heat transfer boundary conditions to accurately describe freezing in the case of single and multiple interacting cryoprobe(s). Temperature dependent changes in the specific heat and thermal conductivity for ultrasound gel are reported down to -150 °C for the first time here and these data were used to accurately describe freezing in ultrasound gel in subsequent modeling. Freezing around a single and two interacting cryoprobe(s) was characterized in the ultrasound gel phantom by mapping the temperature in and around the "iceball" with carefully placed thermocouple arrays. These experimental data were fit with finite-element modeling in COMSOL Multiphysics, which was used to investigate the sensitivity and effectiveness of convective boundary conditions in describing heat transfer from the cryoprobes. Heat transfer at the probe tip was described in terms of a convective coefficient and the cryogen temperature. While model accuracy depended strongly on spatial (i.e., along the exchange surface) variation in the convective coefficient, it was much less sensitive to spatial and transient variations in the cryogen temperature parameter. The optimized fit, convective exchange conditions for the single-probe case also provided close agreement with the experimental data for the case of two interacting cryoprobes, suggesting that this basic characterization and modeling approach can be extended to accurately describe more complicated, multiprobe freezing geometries. Accurately characterizing cryoprobe behavior in phantoms requires detailed knowledge of the freezing medium's properties throughout the range of expected temperatures and an appropriate description of the heat transfer across the probe's exchange surfaces. Here we demonstrate that convective exchange boundary conditions provide an accurate and versatile description of heat transfer from cryoprobes, offering potential advantages over the traditional constant surface heat flux and constant surface temperature descriptions. In addition, although this study was conducted on Joule-Thomson type cryoprobes, the general methodologies should extend to any probe that is based on convective exchange with a cryogenic fluid.

Review of biomaterial thermal property measurements in the cryogenic regime and their use for prediction of equilibrium and non-equilibrium freezing applications in cryobiology

It is well accepted in cryobiology that the temperature history and cooling rates experienced in biomaterials during freezing procedures correlate strongly with biological outcome. Therefore, heat transfer measurement and prediction in the cryogenic regime is central to the field. Although direct measurement of temperature history (i.e. heat transfer) can be performed, accuracy is usually achieved only for local measurements within a given system and cannot be readily generalized to another system without the aid of predictive models. The accuracy of these models rely upon thermal properties which are known to be highly dependent on temperature, and in the case of significant cryoprotectant loading, also on crystallized fraction. In this work, we review the available thermal properties of biomaterials in the cryogenic regime. The review shows a lack of properties for many biomaterials in the subzero temperature domain, and especially for systems with cryoprotective agents. Unfortunately, use of values from the limited data available (usually only down to -40 degrees C) lead to an underestimation of thermal property change (i.e. conductivity rise and specific heat drop due to ice crystallization) with lower temperatures. Conversely, use of surrogate values based solely on ice thermal properties lead to an overestimation of thermal property change for most biomaterials. Additionally, recent work extending the range of available thermal properties to -150 degrees C has shown that the thermal conductivity will drop in both PBS and tissue (liver) due to amorphous/glassy phases (versus crystalline) of biomaterials with the addition of cryoprotective additives such as glycerol. Thus, we investigated the implications of using approximated or constant property values versus measured temperature-dependent values for predicting temperature history during freezing in PBS (phosphate-buffered saline) and porcine liver with and without cryoprotectants (glycerol). Using measured property values (thermal conductivity, specific heat, and latent heat of phase change) of porcine liver, a standard was created which showed that values based on surrogate ice properties under-predicted cooling times, while constant properties (i.e. based on limited data reported near the freezing point) over-predicted cooling times. Additionally, a new iterative numerical method that accommodates non-equilibrium cooling effects as a function of time and position (i.e. crystallization versus amorphous phase) was used to predict temperature history during freezing in glycerol loaded systems. Results indicate that in addition to the increase in cooling times due to the lowering of thermal diffusivity with more glycerol, non-equilibrium effects such as the prevention of maximal crystallization (i.e. amorphous phases) will further increase required cooling times. It was also found that the amplified effect of non-equilibrium cooling and crystallization with system size prevents the thermal history to be described with non-dimensional lengths, such as was possible under equilibrium cooling. These results affirm the need to use accurate thermal properties that incorporate temperature dependence and crystallized fraction. Further studies are needed to extract thermal properties of other important biomaterials in the subzero temperature domain and to develop accurate numerical methods which take into account non-equilibrium cooling events encountered in cryobiology when partial or total vitrification occurs.

Frontiers in biotransport: water transport and hydration

Biotransport, by its nature, is concerned with the motions of molecules in biological systems while water remains as the most important and the most commonly studied molecule across all disciplines. In this review, we focus on biopreservation and thermal therapies from the perspective of water, exploring how its molecular motions, properties, kinetic, and thermodynamic transitions govern biotransport phenomena and enable preservation or controlled destruction of biological systems.

Frontiers in Biotransport: Water Transport and Hydration

Biotransport, by its nature, is concerned with the motions of molecules in biological systems while water remains as the most important and the most commonly studied molecule across all disciplines. In this review, we focus on biopreservation and thermal therapies from the perspective of water, exploring how its molecular motions, properties, kinetic, and thermodynamic transitions govern biotransport phenomena and enable preservation or controlled destruction of biological systems.