C.E. Huggins

A membrane model describing the effect of temperature on the water conductivity of erythrocyte membranes at subzero temperatures.

Thermodynamic models show that the loss of intracellular water from human erythrocytes during freezing depends heavily upon the water conductivity of the erythrocyte membrane. These calculations, which are based on the simple extrapolation of ambient conductivity data to subzero temperatures, show that more than 95% of cell water is transferable during freezing, whereas experiments show that at least 20% of cell water is retained. A study of the effects of different published values for the membrane water conductivity on cell water retained during freezing shows that this discrepancy may be a consequence of the simple extrapolation procedure. For a homogeneous membrane system, absolute reaction rate theory was used to develop a surface-limited permeation model that includes the resistance to the flow of water not only through the interior region of the membrane but also across possible rate-limiting barriers at the solution-membrane interfaces. The model shows that it is unlikely that a single rate-limiting process dominates water transport in the red cell as it is being cooled from ambient to subzero temperatures. The effective membrane conductivity at subzero temperatures could possible be much lower than a simple extrapolation of existing data would predict. With the aid of this model analytical predictions of intracellular water during freezing are more consistent with experimental observations.

An experimental comparison of intracellular ice formation and freeze-thaw survival of hela S-3 cells

Abstract A small-volume fluorescent dye viability assay has been successfully applied to a conduction cryomicroscope freezing-thawing stage as a means of determining post-thaw survival of the nucleated mammalian cell HeLa S-3. The survival signature for HeLa S-3 cells has been determined, revealing an optimum cooling rate of −30 °C/min where the maximum survival is 30%. No cells survive for cooling rates greater than −128 °C/min and the decreased survival at supraoptimal cooling rates coincides with a linear increase in the percentage of cells containing intracellular ice from 0% at −16 °C/min to 100% at −128 °C/min. Although no data were taken to identify increased salt concentration as the mechanism responsible for cell injury at suboptimal cooling rates, the post-thaw leakage of intracellular fluorescent dye at these rates takes approximately 4–10 min as opposed to instantaneous release of dye for cells which contain ice at the high cooling rates. This indicates two modes of damage. Cell number density has been identified as an important parameter in freezing studies since survival can be enhanced at slow rates by packing cells together in groups. Packing also causes a greater fraction of the cells in a sample to have intracellular ice present, thus decreasing survival at the faster rates. These responses can be explained by assuming that the outer cells in a group protect the inner ones from solution damage at slow rates, yet restrict water flux from the inner cells at faster rates, causing an increased likelihood of intracellular ice formation. Both of these results are consistent with the dual-mechanism freezing damage theory proposed by Mazur.

Intracellular freezing in biomaterials.

Abstract The present paper reviews previous work related to the intracellular freezing of biological cells and discusses some general conclusions which can be drawn from this work. Topics considered include definition of the physiochemical conditions requisite for the formation of intracellular ice, methods of detecting the presence of ice inside of frozen cells, theories of freezing injury attributable to intracellular ice, mechanisms of cryophylactic protection, and envisioned future trends in intracellular freezing research. New experimental data are also presented which describe the frequency of intracellular ice formation in frozen human erythrocytes as a function of the cooling rate. It is demonstrated that the probability of intracellular freezing is zero at cooling rates less than −6 °C/min, 100% at cooling rates greater than −17 °C/min, and varies proportionately with the cooling rate in the intermediate range. These data are discussed in light of previous analytical and experimental work.

Water transport in a cluster of closely packed erythrocytes at subzero temperatures.

Abstract A one-dimensional model has been developed to describe the kinetics of water transport in a cluster of closely packed cells. For the case of human red blood cells, the intracellular medium has been treated as an ideal, hydrated, nondilute multicomponent electrolyte solution. Results show that the volume flux of water out of the interior cells of the cluster lags behind that of the exterior cells. At any given temperature (or time), the amount of water retained within a cluster of closely packed cells of a given type exceeds (on an overall percentage basis) the amount of water retained within a single isolated cell of the same type. For a given cooling rate the probability of intracellular ice nucleation at any given temperature will therefore be greater for cells in the interior of a cluster, and the survival signature for a cell cluster should peak at a cooling rate which is less than the corresponding optimal value for a single, isolated cell. These results are consistent with experimental observations.

An analysis of the heat and solute transport during solidification of an aqueous binary solution—I. basal plane region

Abstract A mathematical analysis of the steady, dendritic solidification of an aqueous binary solution has been developed. The energy and solute transport equations were solved using a simple “two-zone” technique. In this procedure, the coupled energy and solute equations are solved first in a zone near the basal plane, and then independently solved in a zone near the dendrite tips, to obtain families of temperature, concentration and dendrite shape profiles in each region. Geometric and thermodynamic matching criteria are employed to determine the specific temperature, concentration and dendrite shape profile in each region that is mutually compatible and satisfies the overall boundary conditions. Heat and mass transport phenomena near the basal plane are analyzed in the present work, while the tip region analysis and matching procedure will be accomplished in an accompanying paper. The results of the basal region analysis indicate that solidification at a higher rate (larger basal heat flux) produces shorter dendrites that are more blunt. A non-dimensional axial similarity variable was found which describes the temperatures and concentration fields independent of the rate of freezing.

Investigation of the effects of cryophylactic agents on the isolated rat heart at 37°C

Summary In order to investigate the effects of cryophylactie agents and subzero cooling in rat hearts, an isolated perfusion system was modified from that originally described by Langendorff. The heart was suspended in a bath of perfusate, and the temperature, perfusion, flow rates, and pressures could be varied or maintained constant. The function of the heart was assessed by measuring pulse rate, electrocardiogram, the pressure within the right ventricle, and release of lactie dehydrogenase and glutamic oxaloacetic transaminase enzymes into the effluent. Finally, the perfused hearts were examined histologically. Using this technique, more than 100 hearts from 400-g albino Sprague Dawley rats were perfused at 37°C using flow rates of 6 ml per min. A satisfactory perfusate, which allowed 6 hrs of acceptable function, was found to be Tis-U-Sol to which were added 380 mg per liter of calcium chloride dihydrate, and the concentration of magnesium ions was increased from the standard level of 1.6 to 7.7 mEq per liter. At 37°C, dimethyl sulfoxide and glycerol were found to be more damaging to the myocardium than was ethylene glycol; when the latter was used at 3 m concentration, it could be perfused through the heart for 30 min and removed, with subsequent restoration of function.

Effect of solution non-ideality on erythrocyte volume regulation

A non-ideal, hydrated, non-dilute pseudo-binary salt-protein-water solution model of the erythrocyte intracellular solution is presented to describe the osmotic behavior of human erythrocytes. Existing experimental activity data for salts and proteins in aqueous solutions are used to formulate van Laar type expressions for the solvent and solute activity coefficients. Reasonable estimates can therefore be made of the non-ideality of the erythrocyte intracellular solution over a wide range of osmolalities. Solution non-ideality is shown to affect significantly the degree of solute polarization within the erythrocyte intracellular solution during freezing. However, the non-ideality has very little effect upon the amount of water retained within erythrocytes cooled at sub-zero temperatures.

Advances in Blood Preservation

The changes which occur in human erythrocytes and plasma in long-term preservation of blood for transfusion have long presented a problem. A system has now been developed employing an endocellular cryophylactic agent to protect the cells and arrest their aging during freezing, storage and thawing. Thawed cells are washed by dilution with sugar solution and reversible agglomeration, which removes extraneous substances.Low titers of anti-A and anti-B antibodies in the resuspended frozen blood make it possible to use specially selected group 0 blood for all recipients.The concept of specific donor selection by statistical need may modify or replace the generally accepted practice of random collection for random need.

The concentration polarization effect in a multicomponent electrolyte solution--the human erythrocyte.

Abstract A thermodynamic model describing the concentration polarization of solutes within cells during osmotic experiments is presented. The intracellular RBC solution is modeled as an ideal, hydrated and non-dilute salt-protein-water electrolyte solution in which the various solute species are allowed to diffuse independently. Application of this model to the case of human erythrocytes being cooled at subzero temperatures indicates that at the optimum cooling rate for the cryopreservation of RBCs a significant amount of solute polarization occurs within the intracellular solution, resulting in the temporary spatial separation of the salt and protein components. The concentration polarization process also significantly affects the transport of water out of RBCs during the cooling process. On the basis of these results, we believe that the concentration polarization phenomenon plays a significant role in determining the survival probability of cells at both high and low cooling rates.

An analysis of the heat and solute transport during solidification of an aqueous binary solution—II. Dendrite tip region

Abstract An analysis of energy and mass transport near the tips of steadily advancing dendrites has been developed. Transport equations have been derived and have been solved using the method of variable transformation to a 1-dim. system. Geometric and thermodynamic matching criteria were employed to ensure that the tip region transport fields were compatible with those obtained previously in the basal plane region. The overall results indicate that the higher the free field temperature the shorter and more blunt are the dendrites. Similarly increasing the free-field concentration at constant free-field superheat drastically reduces the dendrite length. Dendrite length was also found to be inversely proportional to the rate of freezing.