Membrane permeability characteristics of bovine oocytes and development of a step-wise cryoprotectant adding and diluting protocol

Effect of the flow-force relationships used in two parameter modelling of freezing and vitrification protocols for bovine embryos

Cells may become damaged by strong volume changes and related intracellular changes during slow freezing or vitrification. These osmotic events can be modelled mathematically, using descriptions of transmembrane flow of solute and water. We compared different variants of an often used 2-parameter (2P) formalism in fitting of an empirical shrink-swell curve of a bovine embryo in 5 vol% glycerol, and in simulations of CPA loading and removal in a vitrification protocol. In its original form, the 2P model uses a flow-force relationship for the flux of CPA that is not analogous to that for water (asymmetrical), but in the other variants used, the flow-force relationships for water and CPA are analogous to each other (symmetrical). The effect of used model on estimated values for Lp and Ps in 5 vol% glycerol was small. Also the effect on shrinking and swelling in vitrification media was small, but the original 2P model predicted stronger swelling of embryos during one-step CPA removal. One variant that we compared simply assumes Raoult's law, i.e. M = m, even in very concentrated solutions We conclude that this simple model is easy and appropriate for simulating osmotic events of embryos. But if a method for correcting for the deviation from Raoult's law is used, a symmetrical model seems more appropriate than the original (asymmetrical) 2P model.

Use of membrane transport models to design cryopreservation procedures for oocytes

Oocyte cryopreservation is increasingly being used in reproductive technologies for conservation and breeding purposes. Further development of oocyte cryopreservation techniques requires interdisciplinary insights in the underlying principles of cryopreservation. This review aims to serve this purpose by: (1) highlighting that preservation strategies can be rationally designed, (2) presenting mechanistic insights in volume and osmotic stress responses associated with CPA loading strategies and cooling, and (3) giving a comprehensive listing of oocyte specific biophysical membrane characteristics and commonly used permeation model equations. It is shown how transport models can be used to simulate the behavior of oocytes during cryopreservation processing steps, i.e., during loading of cryoprotective agents (CPAs), cooling with freezing as well as vitrification, warming and CPA unloading. More specifically, using defined cellular and membrane characteristics, the responses of oocytes during CPA (un)loading were simulated in terms of temperature- and CPA type-and-concentration-dependent changes in cell volume and intracellular solute concentration. In addition, in order to determine the optimal cooling rate for slow programmable cooling cryopreservation, the freezing-induced cell volume response was simulated at various cooling rates to estimate rates with tolerable limits. For vitrification, special emphasis was on prediction of the timing of reaching osmotic tolerance limits during CPA exposure, and the need to use step-wise CPA addition/removal protocols. In conclusion, we present simulations and schematic illustrations that explain the timing of events during slow cooling cryopreservation as well as vitrification, important for rationally designing protocols taking into account how different CPA types, concentrations and temperatures affect the oocyte.

Effect of cryoprotectant concentration on bovine oocyte permeability and comparison of two membrane permeability modelling approaches

The plasma membrane permeability to water and cryoprotectant (CPA) significantly impacts vitrification efficiency of bovine oocytes. Our study was designed to determine the concentration-dependent permeability characteristics for immature (GV) and mature (MII) bovine oocytes in the presence of ethylene glycol (EG) and dimethyl sulphoxide (Me₂SO), and to compare two different modeling approaches: the two parameter (2P) model and a nondilute transport model. Membrane permeability parameters were determined by consecutively exposing oocytes to increasing concentrations of Me₂SO or EG. Higher water permeability was observed for MII oocytes than GV oocytes in the presence of both Me₂SO and EG, and in all cases the water permeability was observed to decrease as CPA concentration increased. At high CPA concentrations, the CPA permeability was similar for Me₂SO and EG, for both MII and GV oocytes, but at low concentrations the EG permeability of GV oocytes was substantially higher. Predictions of cell volume changes during CPA addition and removal indicate that accounting for the concentration dependence of permeability only has a modest effect, but there were substantial differences between the 2P model and the nondilute model during CPA removal, which may have implications for design of improved methods for bovine oocyte vitrification.

Natural honey acts as a nonpermeating cryoprotectant for promoting bovine oocyte vitrification

Sugars are commonly supplemented into vitrification solution to dehydrate cells in order to reduce the formation of fatal intracellular ice crystals. Natural honey is a mixture of 25 sugars (mainly fructose and glucose) that have different biological and pharmacological benefits. The present study was designed to determine if honey can be used as a nonpermeating cryoprotectant in vitrification of bovine oocytes. In the first experiment, denuded-MII oocytes were exposed to 0.25, 0.5, 1.0, 1.5 or 2.0 M of honey or sucrose. Natural honey and sucrose caused similar ooplasm dehydration. A significant relationship existed between time and ooplasm volume change (P < 0.05), during dehydration and rehydration phases, in both honey and sucrose solutions. In the second experiment, the immature cumulus-oocyte complexes (COCs) were vitrified in an EG/DMSO-based vitrification solution containing honey (0.5, 1 or 1.5 M) or sucrose (0.5 M) as a gold standard. The vitrified-warmed COCs were matured in vitro and evaluated for nuclear maturation. The maturation (MII) rate was greater in nonvitrified control (81%) than vitrified groups (54%, P < 0.05). In the third experiment, COCs were either remained nonvitrified (control) or vitrified in 1.0 M honey or 0.5 M sucrose, followed by IVM, IVF and IVC (for 9 days). Cleavage rate was greater in control (74%) than in vitrified groups (47%, P < 0.05), without significant difference between sugars. Blastocyst rate was 34, 13 and 3% in control, honey and sucrose groups respectively (P < 0.05). In conclusion, natural honey acted as a nonpermeating cryoprotectant in vitrification solution and improved the embryonic development in vitrified bovine COCs.

Vitrification of in vitro-derived bovine embryos: targeting enhancement of quality by refining technology and standardising procedures

Bovine invitro fertilisation technology has been widely exploited in commercial settings. The majority of invitro-derived cattle embryos are transferred into recipient cows as recently collected (i.e. 'fresh') embryos due to the lack of a reliable cryopreservation method that results in favourable pregnancy rates following transfer of thawed embryos. This is a primary reason for the poor industry uptake of this extreme temperature freezing process. Numerous investigations into vitrification have revealed the importance of rapid cooling and warming rates, enhancing embryo viability after cryopreservation compared with conventional slow freezing. Those studies spawned a considerable assortment of cryovessels and diversity of procedures, delivering variable rates of success, which makes performing vitrification consistently a practical challenge. Hence, further research is required in order to both optimise and standardise vitrification methodology and to design a cryovessel that enables direct transfer of vitrified embryos to recipients after warming. In parallel with improvements in vitrification, it is important to continue to raise the quality of invitro-derived cattle embryos through modifications in laboratory culture techniques. The twin goals of methodology refinement and standardisation, leading to embryo quality enhancement, are each imperative if invitro fertilisation technology is to be adopted in the field.

Microfluidic method reduces osmotic stress injury to oocytes during cryoprotectant addition and removal processes in porcine oocytes

Oocyte cryopreservation is an important technology in assisted reproduction and fertility preservation. However, the developmental potential of cryopreserved oocyte remains poor. Osmotic stress injury (OSI) during cryoprotectants (CPAs) loading and unloading steps has critical impact on successful cryopreservation. In order to minimize OSI to oocytes, a microfluidic device was designed and fabricated to achieve continuous CPA concentration change. MII porcine oocytes were loaded and unloaded CPAs with step-wise and microfluidic methods, oocyte volume changes were recorded and compared, loading and unloading duration of microfluidic methods were optimized. The survival and developmental rate of treated oocytes in step-wise and microfluidic linear methods were also evaluated. The results showed that oocyte volume changes with microfluidic method were obviously less than step-wise method, and the survival, cleavage and blastocyst rate of oocytes were 95.3%, 64.4%, and 19.4%, respectively, which were significantly higher than the traditional step-wise method (79.4%, 43.6%, and 9.7%) (p < 0.05). In conclusion, microfluidic device can effectively reduce the osmotic damage to oocytes and improve the survival rate and developmental rate of oocytes, which may provide a new path for oocyte cryopreservation.

A microfluidic platform with cell-scale precise temperature control for simultaneous investigation of the osmotic responses of multiple oocytes

The temperature-dependent oocyte membrane permeability plays a significant role in oocyte cryopreservation, such as optimizing the addition/removal of cryoprotective agents and the rate of cooling/rewarming. However, the systems for studying the temperature dependence of oocyte membrane permeability are either too complicated or unable to achieve wide-range precise temperature control. In addition, these systems cannot achieve the simultaneous observation of multiple oocytes. Here, we report a novel microfluidic platform that combines a precise local temperature heater/detector and a simple global water bath to achieve wide-range accurate temperature control without increasing the difficulty of fabrication, and it also realizes non-interfering, position-controllable and non-missing capture of multiple oocytes for parallel experiments to increase throughput. The permeability coefficients (L_p, P_s) of the mouse oocyte membrane exposed to cryoprotective agents (1.5 M EG and 1.5 M PG) at four temperatures (4, 15, 25 and 37 °C) are consistent with those reported in previous works, which proves the feasibility and practicality of the microfluidic platform in this study.

Chilling sensitivity of Steindachneridion parahybae (Siluriformes: Pimelodidae) oocytes in different cryoprotectants

The viability of post-thaw fish oocytes can be affected by different stages of the freezing process, such as cryoprotectant toxicity, cold sensitivity, freezing curves and thawing. Therefore, these steps need to be investigated for the development of a protocol. In the present study, the aim was to investigate chilling sensitivity at different oocyte stages of Steindachneridion parahybae. Immature and mature oocytes were incubated in Hanks' or 90% L15 solutions containing different CPAs (cryoprotectant solutions) per experiment: (1) 0.1-0.4 M sucrose + 1-2 M methanol and (2) 1-4 M methanol X 1-4 M propylene glycol X 1-4 M DMSO for mature oocytes; (3) 0.5 M sucrose or fructose + 2 M methanol or PG or DMSO and (4) 0.25-1 M fructose + 1-4 M DMSO for immature oocytes. All treatments were kept for 120 min at -5.9 ± 2.8°C. For the control treatment, only Hanks' or 90% L15 solutions were carried out. Evaluations were made by viability tests: membrane integrity staining in 0.4% Trypan blue (TB) and fertilization rate (%F) sole for mature oocytes. Results presented that mature oocytes were the most sensitive to lower temperatures, because there was no %F. All cryoprotectants tested in the different concentrations can be used for immature oocytes, however the statistically superior cryoprotectant was CPA with fructose and DMSO, with the low concentration of this CPA being was the best statistically. This may indicate that for this species the immature stages have presented a lower chilling sensitivity than the mature stages.

Cell membrane permeability coefficients determined by single-step osmotic shift are not applicable for optimization of multi-step addition of cryoprotective agents: As revealed by HepG2 cells

HepG2 cells have a number of research applications and cryopreservation of these cells would improve supply and thus facilitate the study. Development of effective cryopreservation protocols relies on knowledges of the fundamental mass transport characteristics of HepG2 cell membrane. Currently, the permeability parameters estimated from single-step addition are routinely used to predict the osmotic responses of the cells in multistep protocols, as well as used for prediction of optimal cooling rates. However, the reasonability of this approach has not been rigorously studied. Here we measured the hydraulic conductivity (L_p) and the permeability coefficient (P_s) of HepG2 cells in the absence/presence of dimethyl sulfoxide (Me₂SO) at various temperatures with single and multistep addition of Me₂SO. We found that the permeability yielded via one-step addition of the Me₂SO cannot exactly predict the volume change of the cells when the CPA was added in multiple steps.

Osmotic behaviour of human mesenchymal stem cells: Implications for cryopreservation

Aimed at providing a contribution to the optimization of cryopreservation processes, the present work focuses on the osmotic behavior of human mesenchymal stem cells (hMSCs). Once isolated from the umbilical cord blood (UCB) of three different donors, hMSCs were characterized in terms of size distribution and their osmotic properties suitably evaluated through the exposure to hypertonic and isotonic aqueous solutions at three different temperatures. More specifically, inactive cell volume and cell permeability to water and di-methyl sulfoxide (DMSO) were measured, being cell size determined using impedance measurements under both equilibrium and dynamic conditions. Experimental findings indicate that positive cell volume excursions are limited by the apparent increase of inactive volume, which occurs during both the shrink-swell process following DMSO addition and the subsequent restoration of isotonic conditions in the presence of hypertonic solutions of impermeant or permeant solutes. Based on this evidence, hMSCs must be regarded as imperfect osmometers, and their osmotic behavior described within a scenario no longer compatible with the simple two-parameter model usually utilized in the literature. In this respect, the activation of mechano-sensitive ion-channels seemingly represents a reasonable hypothesis for rationalizing the observed osmotic behavior of hMSCs from UCB.

A microfluidic perfusion approach for on-chip characterization of the transport properties of human oocytes

Accurate characterization of the cell membrane transport properties of human oocytes is of great significance to reproductive pharmacology, fertility preservation, and assisted reproduction. However, the commonly used manual method for quantifying the transport properties is associated with uncontrolled operator-to-operator and run-to-run variability. Here, we report a novel sandwich structured microfluidic device that can be readily fabricated for characterizing oocyte membrane transport properties. Owing to its capacity for excellent control of both solution replacement and temperature in the microchannel, the temperature-dependent permeability of the oocyte membrane can be precisely characterized. Furthermore, the fertilization and developmental competence analysis post perfusion indicate that our approach does not compromise the physiological function of in vitro matured human oocytes. Collectively, we present the development of a novel sandwich structured microfluidic device based approach that allows on-chip characterization of the transport properties of human oocytes under innocuous osmotic shock or injury to the cells.

Ovarian tissue transport to expand access to fertility preservation: from animals to clinical practice

Primordial follicles dictate a female's reproductive life span and therefore are central to fertility preservation for both endangered species and individuals with fertility-threatening conditions. Ovarian tissue containing primordial follicles can be cryopreserved and later thawed and transplanted back into individuals to restore both endocrine function and fertility. Importantly, increasing numbers of human live births have been reported following ovarian tissue cryopreservation and transplantation. A current limitation of this technology is patient access to sites that are approved or equipped to process and cryopreserve ovarian tissue - especially in larger countries or low resource settings. Here, we review empirical evidence from both animal models and human studies that suggest that ovarian tissue can be transported at cold temperatures for several hours while still maintaining the integrity and reproductive potential of the primordial follicles within the tissue. In fact, several human live births have been reported in European countries using tissue that was transported at cold temperatures for up to 20 h before cryopreservation and transplantation. Ovarian tissue transport, if implemented widely in clinical practice, could therefore expand both patient and provider access to emerging fertility preservation options.

Live-cell quantification and comparison of mammalian oocyte cytosolic lipid content between species, during development, and in relation to body composition using nonlinear vibrational microscopy

Cytosolic lipids participate in the growth, development, and overall health of mammalian oocytes including many roles in cellular homeostasis. Significant emphasis has been placed on the study of lipids as a dynamic organelle, which in turn requires the development of tools and techniques to quantitate and compare how lipid content relates to cellular structure, function, and normalcy. Objectives of this study were to determine if nonlinear vibrational microscopy (e.g., coherent anti-Stokes Raman scattering or CARS microscopy) could be used for live-cell imaging to quantify and compare lipid content in mammalian oocytes during development and in relation to body composition; and compare its efficacy to methods involving cellular fixation and staining protocols. Results of this study demonstrate that CARS is able to identify lipids in live mammalian oocytes, and there exists quantifiable and consistent differences in percent lipid composition across ooctyes of different species, developmental stages, and in relation to body composition. Such a method of live-cell lipid quantification has (i) experimental power in basic cell biology, (ii) practical utility for identifying developmental predictive biomarkers while advancing biology-based oocyte/embryo selection, and (iii) ability to yield rationally supporting technology for decision-making in rodents, domestic species, and human assisted reproduction and/or fertility preservation.

The effects of permeating cryoprotectants on intracellular free-calcium concentrations and developmental potential of in vitro-matured feline oocytes

Embryos produced from vitrified feline oocytes have resulted in pregnancies, but the efficiency of oocyte vitrification in cats is still low. Our objectives were to evaluate the effects of exposing feline oocytes to ethylene glycol (EG), propanediol (PrOH) and dimethyl sulfoxide (DMSO) on changes in intracellular free-calcium concentrations ([Ca2+]i), the time needed for enzymatic digestion of the zona pellucida (ZP), the incidence of parthenogenetic activation and degeneration and embryonic development following in vitro fertilisation (IVF). All of the chemicals tested altered [Ca2+]i, but changes in [Ca2+]i, resistance of the ZP to enzymatic digestion and the incidence of parthenogenetic activation (<5% for all treatments) were not affected (P > 0.05) by extracellular Ca2+. Exposure to EG (>44.1%) and DMSO (19.7%) increased (P < 0.05) oocyte degeneration compared with control oocytes and oocytes exposed to PrOH (≤2.5%). Following exposure to a combination of PrOH and DMSO (10% v/v each), blastocyst development (per cleaved embryo; 52.1%) was similar (P > 0.05) to control oocytes (64.4%). When oocytes were vitrified with PrOH and DMSO, 28.3% of surviving (intact plasma membrane) oocytes cleaved following IVF, but no blastocyst developed. When a non-permeating cryoprotectant (galactose, 0.25 M) was added to the vitrification medium, 47.7% of surviving oocytes cleaved and 14.3% developed to the blastocyst stage.

An efficient method for the sanitary vitrification of bovine oocytes in straws

Background

At present, vitrification has been widely applied to humans, mice and farm animals. To improve the efficiency of vitrification in straw, bovine oocytes were used to test a new two-step vitrification method in this study.

Results

When in vitro matured oocytes were exposed to 20% ethylene glycol (EG20) for 5 min and 40% ethylene glycol (EG40) for 30 s, followed by treatment with 30% glycerol (Gly30), Gly40 or Gly50, a volume expansion was observed in Gly30 and Gly40 but not Gly50. This indicates that the intracellular osmotic pressure after a 30 s differs between EG40 and ranged between Gly40 (approximately 5.6 mol/L) and Gly50 (approximately 7.0 mol/L). Since oocytes are in EG40 just for only a short period of time (30 s) and at a lower temperature (4°C), we hypothesize that the main function of this step in to induce dehydration. Based on these results, we omitted the EG40 step, before oocytes were pretreated in EG20 for 5 min, exposed to pre-cooled (4°C) Gly50, for 30 s, and then dipped into liquid nitrogen. After warming, 81.1% of the oocytes survived, and the surviving oocytes developed into cleavage stage embryos (63.5%) or blastocysts (20.0%) after parthenogenetic activation.

Conclusions

These results demonstrate that in a two-step vitrification procedure, the permeability effect in the second step is not necessary. It is possible that the second step is only required to provide adequate osmotic pressure to condense the intracellular concentration of CPAs to a level required for successful vitrification.

Recent progress in cryopreservation of bovine oocytes

Principle of oocyte cryoinjury is first overviewed and then research history of cryopreservation using bovine oocytes is summarized for the last two decades with a few special references to recent progresses. Various types of cryodevices have been developed to accelerate the cooling rate and applied to the oocytes from large domestic species enriched with cytoplasmic lipid droplets. Two recent approaches include the qualitative improvement of IVM oocytes prior to the vitrification and the short-term recovery culture of vitrified-warmed oocytes prior to the subsequent IVF. Supplementation of L-carnitine to IVM medium of bovine oocytes has been reported to reduce the amount of cytoplasmic lipid droplets and improve the cryotolerance of the oocytes, but it is still controversial whether the positive effect of L-carnitine is reproducible. Incidence of multiple aster formation, a possible cause for low developmental potential of vitrified-warmed bovine oocytes, was inhibited by a short-term culture of the postwarm oocytes in the presence of Rho-associated coiled-coil kinase (ROCK) inhibitor. Use of an antioxidant α-tocopherol, instead of the ROCK inhibitor, also supported the revivability of the postwarm bovine oocytes. Further improvements of the vitrification procedure, combined with pre- and postvitrification chemical treatment, would overcome the high sensitivity of bovine oocytes to cryopreservation.

Is it best to cryopreserve human cumulus-free immature oocytes before or after in vitro maturation?

Freezing unfertilized oocytes is an option for females without a partner, either to preserve their fertility prior to sterilizing cancer treatment or for social reasons. Our study considered whether it is best to freeze immature human oocytes at the germinal vesicle (GV) stage, prior to in vitro maturation (IVM) or at metaphase-II (M-II), after IVM. Sibling GV-stage oocytes from stimulated ICSI cycles were allocated to freezing either prior to (n=109) or after (n=107) IVM. Cumulus-free oocytes were cryopreserved using a choline-substituted slow-freezing protocol and matured in a defined medium, with analysis of chromatin, microtubules, and microfilaments by three-dimensional imaging. Cryopreserved oocytes were compared with oocytes matured in vitro but never frozen (n=114). Survival was similar between oocytes frozen before or after IVM (69.7% vs. 70.5%). Polar body extrusion after IVM was lower in oocytes frozen at the GV stage versus those matured and then frozen (51.3% vs. 75.7%) or not frozen (75.4%). Stratification by patient age (<36 and ⩾36year) showed no difference in oocyte survival or maturation. Oocytes frozen as GVs showed elevated proportions of spontaneous activation (with or without polar body), an effect augmented by patient age. Spindle and chromosome configurations were disrupted to similar extents in both groups of frozen oocytes, with no further detrimental effect of patient age. The length, width, and volume of bipolar M-II spindles were comparable in all three groups. When frozen as GVs, oocytes exhibited decreased maturation and increased spontaneous activation, suggesting that it is best to freeze oocytes at M-II.

Some comments on recent discussion of the Boyle van't Hoff relationship

The estimation of several cellular biophysical parameters must be made in order to mathematically predict optimal cryopreservation protocols. These parameters include total cell volume, osmotically inactive volume, cell surface area, and relative water and solute permeabilities. Recent attention has been paid to the determination of the osmotically inactive volume and, specifically, an argument was made suggesting that this volume was incorrectly determined in the literature [4]. Here we show that this assertion is false.

Maturation outcomes are improved following Cryoleaf vitrification of immature human oocytes when compared to choline-based slow-freezing

PURPOSE

The cryopreservation of immature oocytes permits oocyte banking for patients at risk of losing their fertility. However, the optimum protocol for such fertility preservation remains uncertain.

METHODS

The present study investigated the survival, maturation, cytoskeletal and chromosome organization of sibling immature oocytes leftover from controlled ovarian stimulation cycles, that were either slow-frozen (with choline-substitution) or vitrified. A comparison group included oocytes that were never cryopreserved.

RESULTS

Among the three groups, comparable rates were observed for both survival (67-70%) and polar body extrusion (59-79%). Significantly more oocytes underwent spontaneous activation after IVM following slow-freezing compared with either vitrification or no cryopreservation. Likewise, the incidence of spindle abnormalities was greatest in the slow-frozen group, with no differences in spindle morphometrics or chromosome organization.

CONCLUSIONS

While the overall incidence of mature oocytes with normal bipolar spindles from warmed immature oocytes was low, the yield using Cryoleaf vitrification was slightly superior to choline-based slow-freezing.

Amicus Plato, sed magis amica veritas: plots must obey the laws they refer to and models shall describe biophysical reality!

In the companion paper, we discussed in details proper linearization, calculation of the inactive osmotic volume, and analysis of the results on the Boyle-vant' Hoff plots. In this Letter, we briefly address some common errors and misconceptions in osmotic modeling and propose some approaches, namely: (1) inapplicability of the Kedem-Katchalsky formalism model in regards to the cryobiophysical reality, (2) calculation of the membrane hydraulic conductivity L(p) in the presence of permeable solutes, (3) proper linearization of the Arrhenius plots for the solute membrane permeability, (4) erroneous use of the term "toxicity" for the cryoprotective agents, and (5) advantages of the relativistic permeability approach (RP) developed by us vs. traditional ("classic") 2-parameter model.

On proper linearization, construction and analysis of the Boyle-van't Hoff plots and correct calculation of the osmotically inactive volume

The Boyle-van't Hoff (BVH) law of physics has been widely used in cryobiology for calculation of the key osmotic parameters of cells and optimization of cryo-protocols. The proper use of linearization of the Boyle-vant'Hoff relationship for the osmotically inactive volume (v(b)) has been discussed in a rigorous way in (Katkov, Cryobiology, 2008, 57:142-149). Nevertheless, scientists in the field have been continuing to use inappropriate methods of linearization (and curve fitting) of the BVH data, plotting the BVH line and calculation of v(b). Here, we discuss the sources of incorrect linearization of the BVH relationship using concrete examples of recent publications, analyze the properties of the correct BVH line (which is unique for a given v(b)), provide appropriate statistical formulas for calculation of v(b) from the experimental data, and propose simplistic instructions (standard operation procedure, SOP) for proper normalization of the data, appropriate linearization and construction of the BVH plots, and correct calculation of v(b). The possible sources of non-linear behavior or poor fit of the data to the proper BVH line such as active water and/or solute transports, which can result in large discrepancy between the hyperosmotic and hypoosmotic parts of the BVH plot, are also discussed.