Unfrozen Regions Research Articles

An improved process-oriented hydro-biogeochemical model for simulating dynamic fluxes of methane and nitrous oxide in alpine ecosystems with seasonally frozen soils

Abstract. The hydro-biogeochemical model Catchment Nutrient Management Model – DeNitrification-DeComposition (CNMM-DNDC) was established to simultaneously quantify ecosystem productivity and losses of nitrogen and carbon at the site or catchment scale. As a process-oriented model, this model is expected to be universally applied to different climate zones, soils, land uses and field management practices. This study is one of many efforts to fulfill such an expectation, which was performed to improve the CNMM-DNDC by incorporating a physically based soil thermal module to simulate the soil thermal regime in the presence of freeze–thaw cycles. The modified model was validated with simultaneous field observations in three typical alpine ecosystems (wetlands, meadows and forests) within a catchment located in seasonally frozen regions of the eastern Tibetan Plateau, including observations of soil profile temperature, topsoil moisture, and fluxes of methane (CH4) and nitrous oxide (N2O). The validation showed that the modified CNMM-DNDC was able to simulate the observed seasonal dynamics and magnitudes of the variables in the three typical alpine ecosystems, with index-of-agreement values of 0.91–1.00, 0.49–0.83, 0.57–0.88 and 0.26–0.47, respectively. Consistent with the emissions determined from the field observations, the simulated aggregate emissions of CH4 and N2O were highest for the wetland among three alpine ecosystems, which were dominated by the CH4 emissions. This study indicates the possibility for utilizing the process-oriented model CNMM-DNDC to predict hydro-biogeochemical processes, as well as related gas emissions, in seasonally frozen regions. As the original CNMM-DNDC was previously validated in some unfrozen regions, the modified CNMM-DNDC could be potentially applied to estimate the emissions of CH4 and N2O from various ecosystems under different climate zones at the site or catchment scale.

Freeze-Thawing-Induced Macroporous Catechol Hydrogels with Shape Recovery and Sponge-like Properties.

Catechol-containing hydrogels have been exploited in biomedical fields due to their adhesive and cohesive properties, hemostatic abilities, and biocompatibility. Catechol moieties can be oxidized to o-catecholquinone, a chemically active intermediate, in the presence of oxygen to act as an electrophile to form catechol-catechol or catechol-amine/thiol adducts. To date, catechol cross-linking chemistry to fabricate hydrogels has been mostly performed at room temperature. Herein, we report large increases in catechol cross-linking reaction kinetics by the freeze-thawing process. The formation of ice crystals during freezing steps spatially condenses catechol-containing polymers into nearly frozen (yet unfrozen) regions, resulting in decreases in the polymeric chain distances. This environment allows great increases in catechol cross-linking kinetics, a phenomenon that can also occur during thawing steps. The increased cross-linking rate and spatial condensation in the cryogels provide unique wall and pore structures, which result in elastic, spongelike hydrogels. The moduli of the cryogels prepared by glycol-chitosan-catechol (g-chitosan-c) were improved by 3-6-fold compared to room temperature-cured conventional hydrogels, and the degree of improvement increased depending on the freezing time and the number of freeze-thawing cycles. Unlike typical cell encapsulations before cross-linking, which have often been a source of cytotoxicity, the macroporosity of cryogels allows nontoxic cell seeding with ease. This research offers a new way to utilize catechol cross-linking chemistry by freeze-thawing processes to simultaneously regulate mechanical strength and porous structures in catechol-containing hydrogels.

A Non-Fourier Bioheat Transfer Model for Cryosurgery of Tumor Tissue with Minimum Collateral Damage

Background and objectivesIncorporation of non-Fourier heat conduction while studying heat transfer phenomena in biological materials has emerged has an important approach as it predicts better and more realistic results than Fourier based models. In this article we have proposed a non-Fourier computational model and applied the same to simulate cryosurgery of lung tumor and attempted minimization of freezing damage of healthy lung tissue using pulsed laser irradiation. MethodsA non-Fourier bioheat transfer model for phase change in biological tissues is solved via a Fourier heat conduction based solution approach. A unified model is proposed combining all variants of bioheat models: Fourier's heat conduction based Pennes’ bioheat model, hyperbolic heat conduction model and dual phase lag model. The proposed model takes into account the different thermophysical properties of frozen and unfrozen regions. In order to mimic the actual biotransport process, the blood perfusion and metabolic heat generation are switched off in the frozen region. Implicit source based enthalpy method is used to model phase change process. A new iterative enthalpy update equation is developed for capturing evolution of freezing front implicitly. Finite Volume based numerical discretization technique is used to discretize the governing PDE. The resulting discrete algebraic equation set is solved implicitly by Tri-diagonal Matrix Algorithm. The proposed model is verified with existing results from the literature. ResultsFor Fourier heat conduction, freezing time of 99.99% of tumor is 1247s, which increases to 1267s for τq= 5s (τT= 0s) and again reduces to 1255s for τq= 5s and τT= 3s. τq and τT are phase lag parameters for non-Fourier heat conduction. For τq= 5s and τT= 0.05s, the freezing damage of healthy tissue decreases by 23.76% when pulsed laser irradiation (Io = 106 W/m2) is used to warm the neighboring healthy tissue. ConclusionsSo non-Fourier bioheat transport models are better and more accurate in predicting temperature history, freezing time and freezing front propagation as compared to Fourier based models. Pulsed laser irradiation can prove to be a very efficient technique in minimizing collateral damage during cryosurgery.

Theoretical modeling of a thermal wave technique to determine the extent of the freezing region surrounding a cryoprobe

Cryosurgery is a clinical technique to ablate undesirable tissues by extreme freezing, exhibiting the merits of minimal invasion, fast recovery, and low cost. A low temperature cryoprobe is used to form a freezing region around the target tissue. Monitoring the extent of the freezing region is critical since including the target tissue within the surgery scope is necessary for precise treatment and minimal damage to the surrounding normal tissue. This paper investigates a thermal wave based monitoring technique similar to the 3ω method for thermal property characterization in order to measure the extent of the freezing region. The method takes advantage of the contrast in thermal properties between the frozen and unfrozen regions and employs different locations on the circumference of the probe for the thermal wave generator and thermal wave sensor. A two-dimensional analytical model in cylindrical coordinates was developed for the thermal wave and was validated by finite element simulations. The analytical model was then employed to determine the influence of several parameters on determining the freezing extent including modulation frequency, the wave generator width, the relative locations of the thermal wave generator and sensor, and the diameter of the cryoprobe. The results obtained indicate the feasibility of the proposed technique since the amplitude and particularly the phase of the thermal wave signal are sensitive to the position of the interface between the frozen and unfrozen regions. For frozen and unfrozen layers with water, thermophysical properties of the measurement sensitive region extend to diameters in the cm range.

Concentration Effects in Frozen Polyacrylonitrile Solutions During the Gelation Process as Studied by Viscoelastic Techniques

Dynamic viscoelasticity measurements were carried out for N, N-dimethylacetamide solutions of polyacrylonitrile (PAN) frozen at −40 °C to characterize the effect of concentration in the frozen state in relation to the freezing and thawing method of the PAN gel. The storage (G′) and loss moduli (G″) were measured for samples obtained by separating the frozen and unfrozen regions during the thawing step. The G′ were also acquired for solutions without the separation (referred to as post-thawing solution), written as and for frozen region, unfrozen region, and post-thawing solution, respectively. The relationship, < < was observed, showing that regions of higher and lower concentrations were developed in the thawing step. (/) was considered a relative index of the concentration increase, to be compared for those of the initial and later stages within the thawing step. (/) was much greater than 1 in the initial stage, and then decreased and approached 1 in the later stage. The behavior of (/) was discussed with reference to the effects of freezing time and concentration on the gelation time. The microscopic separation between the dilute and concentrated phases induced at the freezing step was proposed as the physical process to interpret the viscoelastic data.

Habitable Snowballs: Temperate Land Conditions, Liquid Water, and Implications for CO2 Weathering

AbstractHabitable planets are commonly imagined to be temperate planets like Earth, with areas of open ocean and warm land. In contrast, planets in snowball states, where oceans are entirely ice covered, are believed to be inhospitable. However, we show using a general circulation model that terrestrial planets in the inner habitable zone are able to support large unfrozen areas of land while in a snowball state. Due to their lower albedo, these unfrozen regions reach summer temperatures in excess of 10 °C. Such conditions permit CO2 weathering, suggesting that continental weathering can provide a mechanism for trapping planets in stable snowball states. The presence of land areas with warm temperatures and liquid surface water motivates a more‐nuanced understanding of habitability during these snowball events.

A study of heat transfer during cryosurgery of lung cancer.

In this study, a mathematical model describing two-dimensional bio-heat transfer during cryosurgery of lung cancer is developed. The lung tissue is cooled by a cryoprobe by imposing its surface at a constant temperature or a constant heat flux or a constant heat transfer coefficient. The freezing starts and the domain is distributed into three stages namely: unfrozen, mushy and frozen regions. In stage I where the only unfrozen region is formed, our problem is an initial-boundary value problem of the hyperbolic partial differential equation. In stage II where mushy and unfrozen regions are formed, our problem is a moving boundary value problem of parabolic partial differential equations and in stage III where frozen, mushy, and unfrozen regions are formed, our problem is a moving boundary value problem of parabolic partial differential equations. The solution consists of the three-step procedure: (i) transformation of problem in non-dimensional form, (ii) by using finite differences, the problem converted into ordinary matrix differential equation and moving boundary problem of ordinary matrix differential equations, (iii) applying Legendre wavelet Galerkin method the problem is transferred into the generalized system of Sylvester equations which are solved by applying Bartels-Stewart algorithm of generalized inverse. The complete analysis is presented in the non-dimensional form. The consequence of the imposition of boundary conditions on moving layer thickness and temperature distribution are studied in detail. The consequence of Stefan number, Kirchoff number and Biot number on moving layer thickness are also studied in specific.

Comparative study of relating equations in coupled thermal-hydraulic finite element analyses

The generalized Clapeyron equation, the experimental curve of the water content and the porosity constraint condition are relating equations for coupled thermal-hydraulic analyses (THA). Based on a literature review and numerical case studies, the applicability of each of these relating equations is discussed for the THA of high-speed railway subgrades in cold regions. The efficiency of each relating equation is assessed through a series of numerical case studies and comparisons with experimental results. Based on the heat transport and water migration equations, the results indicate that the generalized Clapeyron equation and the experimental curve of the liquid water content can effectively reproduce the temperature variation, water migration and phase transition in a single one-way freezing process with the sufficient replenishment of water in unfrozen regions. Furthermore, the porosity constraint condition is applicable as a relating equation for freezing unsaturated soils with vapours and saturated soils with little water migration.

Seasonal dynamics and controls of deep soil water infiltration in the seasonally-frozen region of the Qinghai-Tibet plateau

Deep soil water infiltration is a key hydrological process in seasonally frozen regions, and displays a distinct behavior from that in other unfrozen regions; however, the seasonal dynamics and key controls of deep soil water infiltration in the seasonally frozen region of the Qinghai-Tibet plateau (QTP) are still poorly understood. In this study, we examine the seasonal dynamics of deep soil water infiltration, and attempt to quantitatively assess the relative influences of several driving factors by applying a random forests statistical analysis. The following key results were obtained. Deep soil water infiltration shows marked seasonal variation. Rainfall intensity exerts little effect on the seasonal dynamics of deep soil water infiltration as almost all rainfall returns to the atmosphere via evapotranspiration. No infiltration occurred when the depth of lower layer frozen soil reached 29 cm, whereas deep infiltration increased during the thawing of soil frost, suggesting that deep infiltration is impeded by soil freezing. Overall, the observed seasonal dynamics of deep soil water infiltration and volumetric soil moisture content were similar during the freeze-thaw process. Furthermore, deep soil water infiltration was more strongly influenced by deep volumetric soil moisture than by shallower volumetric soil moisture. Our results suggest that the topsoil Mattic Epipedon, soil organic matter content, and root systems’ role in vertical moisture movement should be taken into consideration when modeling hydrological processes in alpine meadows.

Numerical simulation on freezing phase change heat transfer in cryosurgery with two cryoprobes

AbstractA mathematical model for phase change heat transfer in biological tissue (including tumor and normal tissue) embedded with two cryoprobes was established. In this model, the vascular architecture was described as a tree‐like branched fractal network, and the effective thermal conductivity and flow rate of blood were presented based on this fractal structure. Occurrence of three regions including frozen, phase‐changing, and unfrozen regions in biological tissue during the freezing process was also considered. The numerical studies on temperature distribution and ice crystal growth process in biological tissue embedded with two cryoprobes were performed. The results showed that the growth rate of ice crystal is more rapid in the initial freezing stage and becomes slower later. So it is unreasonable to prolong freezing time merely without other assisting measures for enlarging the freezing region in the late freezing stage. Furthermore, the placement distance of the two cryoprobes plays a significant role in the growth of ice crystal in the initial freezing stage, and the influence of different distances between two probes on ice crystal growth becomes less profound with an increasing of freezing time. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/htj.20332

Freezing of blood perfused tissue: An improved quasi-steady solution

An approximate analytic solution is obtained for the temperature distribution and freezing front propagation in tissue. The solution accounts for blood perfusion and metabolic heat generation. The method of solution is based on the introduction of assumed temperature profiles in the frozen and unfrozen regions. The assumed profiles satisfy all boundary conditions as well as the governing heat equations at the moving interface. In addition, the steady state interface location is identically satisfied. Two cases are considered: freezing of a semi-infinite blood perfused tissue over a planar probe and around a spherical probe. The accuracy of the solution is verified in two test cases with known exact solutions: the limiting case of Neumann’s problem and a numerical solution to tissue freezing around a spherical probe. The present theory represents a significant improvement over the quasi-steady model.

One‐dimensional analysis of a poroelastic medium during freezing

AbstractA solution to the problem of freezing of a poroelastic material is derived and analysed in the case of one‐dimensional deformation. The solution is sought within the framework of thermo‐poroelasticity, with specific account of the behaviour of freezing materials. The governing equations of the problem can be combined into a pair of coupled partial differential equations for the temperature and the fluid pressure, with particular forms in the freezing and the unfrozen regions. In the freezing region, the equations are highly non‐linear, partly due to the dependence of thermal and hydraulic properties on water saturation, which varies with temperature. Consequently, the solution is obtained through numerical methods, with special attention to the propagation of the freezing front boundary. The response to one‐dimensional freezing is illustrated for the case of cement paste. Finally, the influence on the solution of varying selected parameters is analysed, such as the temperature boundary conditions, the parameters characterizing the geometry of the porous system, the ratio of fluid and thermal diffusivities, and the rate of cooling applied at the freezing end. Copyright © 2008 John Wiley &amp; Sons, Ltd.

Suppression of high-density artefacts in x-ray CT imagesusing temporal digital subtraction with application tocryotherapy

Image guidance in cryotherapy is usually performed using ultrasound. Althoughnot currently in routine clinical use, x-ray CT imaging is an alternativemeans of guidance that can display the full 3D structure of the iceball,including frozen and unfrozen regions. However, the quality of x-ray CT imagesis compromised by the presence of high-density streak artefacts. To suppressthese artefacts we applied temporal digital subtraction (TDS). This TDS methodhas the added advantage of improving the grey-scale contrast between frozenand unfrozen tissue in the CT images. Two sets of CT images were taken of aphantom material, cryoprobes and a urethral warmer (UW) before and during thecryoprobe freeze cycle. The high-density artefacts persisted in both imagesets. TDS was performed on these two image sets using the corresponding maskimage of unfrozen material and the same geometrical configuration of thecryoprobes and the UW. The resultant difference image had a significantlyreduced artefact content. Thus TDS can be used to significantly suppress oreliminate high-density CT streak artefacts without reducing the metalliccontent of the cryoprobes. In vivo study needs to be conducted toestablish the utility of this TDS procedure for CT assisted prostate or livercryotherapy. Applying TDS in x-ray CT guided cryotherapy will facilitateestimation of the number and location of all frozen and unfrozen regions,potentially making cryotherapy safer and less operator dependent.

In Vivo Results with a New Device for Ultrasonic Monitoring of Pig Skin Cryosurgery: The Echographic Cryoprobe

One of the main difficulties encountered in cryosurgery is the uncertainty in the extent and depth of the tissue effectively treated during the freezing process. The objective of this study was to evaluate in vivo ultrasonic control of skin cryosurgery using a new echographic cryoprobe. An echographic cryoprobe, developed specifically for dermatology applications, combines a high-frequency (20 MHz) miniature ultrasonic transducer and a N2O-driven closed cryoprobe. Knowledge of the ultrasound velocity of frozen skin is a prerequisite for monitoring the iceball formation kinetics. Therefore, in a first study, we estimated the ultrasound velocity of frozen skin specimens. In a second step, the operation of the echographic cryoprobe was assessed, under in vivo conditions similar to those used in human therapeutics, on normal skin of three female "Large-White" pigs under anesthesia. The mean value of ultrasound velocity of frozen skin obtained by pooling the data from all the skin specimens included in this study was 2865 +/- 170 m per s. The average rates of growth (10(-2) mm per s) of the iceballs were found to be 12.2 +/- 1.0 (pig 1), 9.0 +/- 1.0 (pig 2), and 8.4 +/- 0.9 (pig 3). The echographic cryoprobe had a built-in high-frequency ultrasonic transducer that served two functions. It enabled in vivo real-time monitoring of depth penetration of the iceball and it gave important feedback to the operator or to the console relating to the rate of growth of the iceball. Automatic (i.e., operator-independent) detection of the echo signal from the freezing front and calculation of the depth penetration of the iceball was possible.

Heat transfer during immersion frying of frozen foods

A model was developed to predict heat transfer during frying of foods that are initially in a frozen state. The model involves two moving boundaries, one between frozen and unfrozen regions, and the other between the dry crust and the moist core region. Heat transfer within the crust region was predicted by Fourier's law, while heat transfer within the core region was formulated with the enthalpy method. Food composition and thermophysical properties were used to predict heat transfer within the food. The predicted results were experimentally validated.

ZF and low-LF μSR in spin-glassy icosahedral Al-Mn-Si quasicrystal

ZF-μSR measurements in icosahedral Al73Mn21Si6, which has a spin glass freezing temperature of 6.4K, show that the spin-freezing process in this quasicrystal is very similar to that observed in crystalline dilute Cu(Mn), but that the temperature range of partial freezing (coexisting frozen and unfrozen regions) is much wider in the quasicrystal. Low-LF spectra confirm that a substantial volume remains unfrozen down to Tg/2 at least. Whether this is more consistent with macroscopic inhomogeneous freezing or any more homogeneous model, such as fractal clusters, depends on resolving and understanding the T≪Tg static limit.

MRI-monitored cryosurgery in the rabbit brain

The inability to observe the transient, irregular shape of the frozen region that develops during cryosurgery has inhibited the application of this surgical technique to the treatment of tumors in the brain and deep in visceral organs. We used proton NMR spin-echo and spoiled gradient-echo imaging to monitor the development of frozen lesions during cryosurgery in the rabbit brain and the resulting postervosurgical changes up to 4 hr after freezing. Spoiled gradient-echo images (TE = 14 ms; TR = 50 ms) were acquired during freezing and thawing at a rate of 15 s/slice. Although the frozen region itself is invisible in MR images, its presence is distinguished easily from the surrounding unfrozen soft tissue because of the large contrast difference between frozen and unfrozen regions. T 2-weighted spin-echo images (TE = 100 ms, TR = 2 s) obtained after thawing suggest that edema forms first at the margin of the region that was frozen (cryolesion) and then moves into the region's core. Histological examination showed complete necrosis in the cryolesion and a sharp transition to undamaged tissue at the margin of the lesion and its image. Blood-brain barrier (BBB) damage was investigated using gadolinium-DTPA. The region of edema in the T 2-weighted spin-echo images was coincident with the area of BBB damage in the Gd-DTPA-enhanced T 1-weighted spin-echo images (TE = 33 ms, TR = 400 ms) and both were distinguishable as areas of high signal relative to the surrounding normal tissue. The results of these experiments indicate that MR can both effectively monitor the cryosurgical freezing and thawing cycle and characterize the postcryosurgical changes in tissue during follow-up.

Discrete ice lens theory for frost heave beneath pipelines

The discrete ice lens theory of frost heave in one-dimensional soil columns was developed to provide a better physical basis for engineering predictions of frost heave in soils. The theory has now been extended to the two-dimensional heat- and mass-flow situation beneath a buried chilled pipeline. Although the frozen and unfrozen soil regions beneath a buried cold pipeline are two dimensional, and the temperature and water-flow fields are potentially complex, considerable simplifications can be made by invoking the so-called quasi-static approach for estimating temperature fields around the buried pipeline. It is proposed that the curved, quasi-static temperature profiles available from published relationships are appropriate for frost-heave predictions in the two-dimensional region beneath a pipeline. Using these curved temperature profiles in the same program and solution procedure developed previously for one-dimensional soil columns allows frost-heave predictions for a buried pipeline to be carried out with a minimum of computational effort. Therefore, the lengthy and tedious numerical procedures that have been a feature of previous attempts to model heat and mass flow and the resulting frost heave in two dimensions can be avoided. The procedure has been used to predict the frost depth and heave beneath two well-documented pipeline test sections at Calgary, Alta., and Caen, France, with very good agreement between prediction and observation. Some predictions for a practical field situation indicate the initial ground temperature plays an important role in frost heave, frost penetration, and the time at which the final ice lens forms in the freezing soil. Key words : frost heave, discrete ice lens, pipeline, segregation potential, hydraulic conductivity of frozen soil.

Salt redistribution during freezing of saline sand columns at constant rates

Columns of sand with grain sizes from about 250 to 600 μm were saturated with a sodium chloride solution with a concentration of 35 parts per thousand (ppt) and frozen at constant rates ranging from 1 to 20 mm d−1. Electrical conductivity of the soil solution, water content, and temperature were measured during the experiments. The interface between the frozen and unfrozen regions was sharply defined and mechanically hard with no evidence for a soft, ice‐bearing transition region thicker than a millimeter. Ice content near the interface was less than 50%. Substantial salt redistribution occurred with downward freezing but not with upward freezing. For downward freezing, the amount of salt rejected near the interface decreased with increasing freezing rate and increased with the salinity of the soil solution in the unfrozen region. Salt redistribution consisted of salt rejection and brine drainage from an extended partially frozen region just above the interface. Brine drained from this partially frozen region until the ice content reached about 900–950 ppt. Brine drained through the interface and mixed rapidly in the unfrozen region, apparently by salt fingering. No evidence could be found for a salt‐enriched layer just below the interface. There was a layer just above the interface, moving with it, which was undersaturated at low and oversaturated at high freezing rates. An effective distribution coefficient may be useful in describing salt redistribution during freezing of saline sands.

Prediction of the freezing characteristics of spherical-shaped food products

An analysis of the freezing characteristics of spherical shaped food products with time dependent surface-temperature variation is presented. The one dimensional heat conduction equations in spherical coordinates for the frozen and unfrozen regions are solved simultaneously by a suitable transformation to obtain an equivalent slab. Goodman's integral method is applied to obtain the solution in terms of four dimensionless parameters. The results are presented for an exponential variation of the surface temperature for parameter values covering the ranges of the thermophysical properties and processing conditions encountered in food freezing practice. A correlation for facilitating the estimation of the freezing time is also given.