Cryopreservation of rat pancreatic islets: effect of ethylene glycol on islet function and cellular composition

Supplementary cryoprotective effect of carboxylated ε-poly-l-lysine during vitrification of rat pancreatic islets

This study was designed to investigate whether cryosurvival of rat pancreatic islets can be improved by carboxylated ε-poly-l-lysine (CPLL). Islets isolated from Wistar × Brown-Norway F1 rats (101-200 μm in diameter) were cryopreserved in three vitrification solutions containing ethylene glycol (EG; 30%, v/v) and CPLL (0%, 10%, or 20%, v/v) by Cryotop^® protocol (10 islets per device). The post-warm survival rate of the islets vitrified in the presence of 20% CPLL (74%), assessed by FDA/PI double staining, was higher than those in 0% and 10% CPLL (65% and 66%, respectively). Decreased EG concentrations (10% and 20%) in the presence of 20% CPLL resulted in impaired post-warm islet survival rates (50% and 64%, respectively). Value of stimulus index (SI) for 20 mM/3 mM glucose-stimulated insulin secretion was 4.1 in islets vitrified-warmed in the presence of 30% EG and 20% CPLL, which was comparable with those in fresh control islets and vitrified islets in 30% EG alone (4.1 and 4.4, respectively). A large number of islets (50 islets per device) could be cryopreserved in the presence of 30% EG and 20% CPLL by using nylon mesh as the device, without considerable loss of post-warm survival (68%) and SI value (3.7). In conclusion, supplementation of antifreeze 20% CPLL was effective in improving the post-warm survival of isolated rat pancreatic islets when vitrification solution containing 30% EG was used.

Polyvinyl Pyrrolidone: A Novel Cryoprotectant in Islet Cell Cryopreservation

The present study was performed on the basis of the hypothesis that the low molecular weight (MW) compounds, DMSO and glycerol, permeate the cell and interact hydrophobically with intracellular proteins, thereby perturbing the cytoskeletal architecture of frozen cells and diminishing islet cell integrity and function. Isolated rat islets were cultured overnight (18–24 h) at 37°C in RPMI medium supplemented with 10% fetal calf serum and 1% mixture of penicillin/streptomycin. Using a programmable temperature controller, samples of precounted islets were then frozen under liquid nitrogen, in the presence of either 2 M DMSO (MW = 0.078 kDa), 3 M glycerol (MW = 0.092 kDa), 5% polyethylene glycol (PEG, MW = 20 kDa), or 10% polyvinylpyrrolidone (PVP, MW = 40 kDa), and stored at −80°C for 1 week. Following thawing and overnight (18–24 h) culture, intact islet recovery was determined by islet counting after dithizone staining. Islet function was assessed by determination of glucose-stimulated insulin secretion in perifusion experiments with Krebs-Ringer bicarbonate buffer, pH 7.4, containing either basal (3.3 mM) or high (16.7 mM) glucose concentrations. The assessment of islet recovery and function of all cryopreserved samples was performed only after thawing and overnight culture (18–24 h) of islets. The mean ± SEM percent intact islet recovery was higher with PVP compared with DMSO (82 ± 4.6 vs. 62.7 ± 3.1%, respectively, p < 0.005, n = 9). Furthermore, the glucose stimulation index of insulin secretion by islets taken from samples frozen with PEG and PVP, after thawing and overnight culture, was comparable to that of freshly isolated islets, in contrast to DMSO and glycerol. There was no significant difference in intact islet recovery and function between samples frozen with PVP and those frozen with PEG. Samples frozen with DMSO and glycerol had similar results in islet recovery and function. These data show that PVP is a new and potent cryoprotectant for islet cell freezing.

Long-term cryopreservation of reaggregated pancreatic islets resulting in successful transplantation in rats

Preservation of pancreatic islets for long-term storage of islets used for transplantation or research has long been a goal. Unfortunately, few studies on long-term islet cryopreservation (1 month and longer) have reported positive outcomes in terms of islet yield, survival and function. In general, single cells have been shown to tolerate the cryopreservation procedure better than tissues/multicellular structures like islets. Thus, we optimized a method to cryopreserve single islet cells and, after thawing, reaggregated them into islet spheroids. Cryopreserved (CP) single human islet cells formed spheroids efficiently within 3-5 days after thawing. Approximately 79% of islet cells were recovered following the single-cell cryopreservation protocol. Viability after long-term cryopreservation (4 weeks or more) was significantly higher in the CP islet cell spheroids (97.4 ± 0.4%) compared to CP native islets (14.6 ± 0.4%). Moreover, CP islet cell spheroids had excellent viability even after weeks in culture (88.5 ± 1.6%). Metabolic activity was 4-5 times higher in CP islet cell spheroids than CP native islets at 24 and 48 h after thawing. Diabetic rats transplanted with CP islet cell spheroids were normoglycemic for 10 months, identical to diabetic rats transplanted with fresh islets. However, the animals receiving fresh islets required a higher volume of transplanted tissue to achieve normoglycemia compared to those transplanted with CP islet cell spheroids. By cryopreserving single cells instead of intact islets, we achieved highly viable and functional islets after thawing that required lower tissue volumes to reverse diabetes in rats.

Cryopreservation of rat islets of Langerhans by vitrification

Cryopreservation could be a possible means of addressing the shortage of islets of Langerhans. We investigated the effects of EDT324 solution on the vitrification of isolated rat islets of Langerhans. Rat pancreatic islets were cryopreserved in 10% DMSO by a slow-rate freezing method or were cryopreserved in EDT324 solution by vitrification. The cryopreserved islets were compared in terms of viability, stimulation index and metabolic function after transplantation. After cryopreservation, the viability and stimulation of islets stored in EDT324 were 92.4% and 6.4, respectively, and were higher than islets stored by slow freezing (72.5% and 1.5, respectively). Streptozotocin-induced diabetic rats were transplanted with islets cryopreserved in EDT324, which corrected diabetes and achieved euglycemia within 2 days after transplantation. These results indicate that EDT324 allows successful cryopreservation of rat islets for long-term storage as an alternative solution to traditionally used solutions, such as 10% DMSO. Transplantation of cryopreserved islets into diabetic rats can achieve euglycemia.

Mammalian cell-based sensor system

Use of living cells or cellular components in biosensors is receiving increased attention and opens a whole new area of functional diagnostics. The term "mammalian cell-based biosensor" is designated to biosensors utilizing mammalian cells as the biorecognition element. Cell-based assays, such as high-throughput screening (HTS) or cytotoxicity testing, have already emerged as dependable and promising approaches to measure the functionality or toxicity of a compound (in case of HTS); or to probe the presence of pathogenic or toxigenic entities in clinical, environmental, or food samples. External stimuli or changes in cellular microenvironment sometimes perturb the "normal" physiological activities of mammalian cells, thus allowing CBBs to screen, monitor, and measure the analyte-induced changes. The advantage of CBBs is that they can report the presence or absence of active components, such as live pathogens or active toxins. In some cases, mammalian cells or plasma membranes are used as electrical capacitors and cell-cell and cell-substrate contact is measured via conductivity or electrical impedance. In addition, cytopathogenicity or cytotoxicity induced by pathogens or toxins resulting in apoptosis or necrosis could be measured via optical devices using fluorescence or luminescence. This chapter focuses mainly on the type and applications of different mammalian cell-based sensor systems.

Bioartificial Organ Grafts: A View at the Beginning of the Third Millennium

An immunoisolated collection of cells, which communicate and exchange essential factors, co-stimulatory hormones, as well as providing immunoprotection and immunomodulation, can be prepared, given existing scientific and medical know-how, within two decades. These "Bioartificial Organ Grafts" have advantages relative to isolated cell therapies, including beta-cell encapsulation for diabetes treatment, and xenotransplantation, which has a de facto moratorium. This paper documents that the majority of the research for the bioartificial organ grafts has been concluded, with the remaining hurdles minimum in comparison. The use of co-encapsulation and the induction of local immune-privilege will provide a more sensitive humoral hormonal response and graft survival, without systemic immunosuppression. A call for the staged implementation of bioartificial organ grafts, based on the best available medical practice, materials, tissue and technology available, is advocated. The implementation of bioartificial organ grafts can begin within the next two years, based on allografts succeeded by genetically modified human tissue, without the need to pass through a xenograft stage.

Cryopreservation of Human Pancreatic Islets from Non-Heart-Beating Donors Using Hydroxyethyl Starch and Dimethyl Sulfoxide as Cryoprotectants

Although widely used, DMSO is toxic for pancreatic islets. We combined hydroxyethyl starch (HES) with DMSO to simplify the procedure of freezing and thawing, and to decrease the toxicity of DMSO. A preclinical study was performed using islets from beagle dogs. After storage for 4 weeks, the islets were thawed and examined. The islet structure was well maintained after thawing. Although the number of the islets decreased to 71.2 ± 20.1%, the function of the islets was evaluated by static incubation after thawing and showed a 1.80 ± 0.78 stimulation index. We have introduced this technique for the cryopreservation of human islets from non-heart-beating donors. Twelve cases of human islet cryopreservation were performed. The sample tube of each human cryopreservation was thawed to evaluate the morphology, contamination, and endocrine function. Although fragmentation was observed in five samples (41.6%), the other seven (58.4%) showed a normal structure when evaluated by microscopic and electron microscopic study. The stimulation index (SI) of static incubation deteriorated from 3.37 ± 3.02 to 1.34 ± 0.28 after thawing. We divided the thawed islets into two groups: group 1 (n = 8), SI >1.2; group 2 (n = 4), SI <1.2. The group 1 islets showed a higher rate of normal structure (87%) than did group 2 (25%). Moreover, the SI before cryopreservation was 4.01 ± 3.57 in group 1, which was higher than the SI of 2.11 ± 0.72 in group 2. Based on the good results from the preclinical study using a large-animal model, this method was introduced for clinical application. Even from the pancreata of non-heart-beating donors, a successful islet cryopreservation was achieved. However, the isolated islets with poor function should not be cryopreserved for transplantation.

Cryopreservation of Freshly Isolated Porcine Islet Cells

INTRODUCTION

The use of xenogenic islet cells may be a possibility to overcome the shortage of human donor organs to treat diabetes. Microencapsulation seems to be a promising method for immunoprotection. Since isolation, purification, encapsulation, and transplantation of islet cells are labor intensive, cryopreservation has emerged as an attractive system of islet banking. The aim of this study was to determine the influence of three different freezing media (FM) on viability of freshly isolated porcine islet cells (FIPIC).

METHODS

FIPIC were isolated using a modified Ricordi method and purification performed using a Lymphoprep density gradient. Viability of FIPIC prior to freezing and after thawing was determined using the MTT-based Cell Growth Determination Kit. Insulin production was detected using enzyme-linked immunosorbent assay. Three different FM containing dimethylsulfoxide (DMSO) or glycerol and sucrose were used for cryoprotection of FIPIC.

RESULTS

Isolation and purification of FIPIC resulted in 95% +/- 1.3% viability and 97% +/- 1.4% purity. Cryopreservation with FM I (containing DMEM, FCS, DMSO) yielded 98.4% and FM III (containing DMEM, FCS, glycerol) 93.1% viability, whereas only 85.6% were alive when cryoprotection is performed with FM II (containing DMSO, BM). Glucose stimulation revealed a loss of 2.8% and 1.9% of insulin secretion per microgram DNA when working with FM I and FM III, but a decrease in glucose-dependent insulin secretion of 7.8% (P < .05) when FIPIC were stored in FM II.

DISCUSSION

Low concentrations of DMSO or the use of glycerol and sucrose seem to be equivalent to cryopreserve FIPIC.

Cryopreservation of Insulin-Producing Cells Microencapsulated in Sodium Cellulose Sulfate

INTRODUCTION

Diabetes mellitus may be treated with pancreatic islet cell transplantation. The use of xenogenic islet cells may overcome the shortage of human donor organs. Microencapsulation seems to be a promising method for immunoprotection. Since isolation, purification, encapsulation, and transplantation of islet cells are labor-intensive, cryopreservation has emerged as an attractive system for islet banking. In this study sodium cellulose sulfate (NaCS), a novel method for microencapsulation of islet cells, was tested for its capability to protect cells during cryopreservation.

METHODS

HIT-T15 cells were microencapsulated in NaCS. Cells were frozen and thawed using three different media containing varying amounts of dimethylsulfoxide (DMSO) and glycerol. Cell viability and cell growth were monitored using 3-(-4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide before freezing and 1 week after thawing.

RESULTS

NaCS did not show any negative impact on the growth rates of encapsulated HIT-T15 cells compared with nonencapsulated controls. Nonencapsulated cells were adequately cryopreserved by both DMSO- and glycerol-containing freezing media. DMSO was not suitable for cryopreservation of encapsulated HIT-T15 cells, whereas glycerol seemed to produce no considerable cell loss during freezing and thawing.

DISCUSSION

Islet banking of cells encapsulated in NaCS was feasible. Microencapsulation did not harm islet cell recovery. As NaCS is less immunogenic and more biocompatible than other materials used for microencapsulation, it may be a promising method for immunoisolation of islet cells to replace the endocrine pancreas in a physiological way.

Maintenance of stimulus-secretion coupling and single beta-cell function in cryopreserved-thawed human islets of Langerhans

Studies of stimulus-secretion coupling in human beta-cells have been hampered by poor availability of tissue due to variability of the supply of cadaver pancreati and in the adequacy of enzymatic liberation of islets as well as by the shunting of isolates into transplant trials. Here we establish that aliquots of islets, several from high-quality but low-yield islet isolates (50,000-100,000 islets), cryopreserved and then thawed as needed, respond to glucose in a calcium- and metabolic-dependent fashion. Insulin secretion is modulated by blockers of voltage-dependent Na+ and Ca2+ channels, and paracrine hormones (glucagon and somatostatin) in manners indistinguishable from fresh tissue preparations. Using single-cell electrophysiological and electrochemical assays we demonstrate that single beta-cells from cryopreserved islets display (1) stimulus-depolarization coupling based on rapid closure of K+ (ATP) channels; (2) action potential electrogenesis with upstrokes based on voltage-dependent Na and Ca currents; and (3) Ca2+ entry-mediated depolarization-exocytosis coupling sustained over multiple bouts of stimulation and modulated by paracrine hormones. All of these features are indistinguishable from those seen in single cells from freshly harvested islets. These results support the utility of cryopreservation, even of low-yield but functional isolates, as a means of ensuring a steady source of repeatedly accessible tissue for research on normal and diabetic islets.

PVA hydrogel sheet macroencapsulation for the bioartificial pancreas

We newly developed a sheet-type macroencapsulation device entrapping rat islets from 3% polyvinyl alcohol (PVA) dissolved in Euro-Collins solution containing 10% fetal bovine serum and 5% dimethyl sulfoxide (PVA + EC) using a freezing/thawing technique. The same encapsulation technique but with 3% PVA dissolved only in double-distilled water (PVA) and a culture of free islets were served as controls. After 14-day culture in the CMRL-1066 medium, the islet recovery rate, morphological changes, insulin content, and insulin secretion were evaluated in vitro to prove the feasibility of this method of encapsulation. We also xenotransplanted the device into the peritoneal cavity of diabetic C57BL/6 mice to check its function in vivo. After 1-day culture, the islet recovery rate and insulin content in the PVA group were significantly lower than that in the PVA + EC and free islet groups. After 14-day culture, only the islets in the PVA+EC group maintained a normal morphology and effective insulin secretory response to high glucose while the response was not observed in the PVA group after 1-day culture and no longer observed in the free islets after 7-day culture. After transplantation of rat islets encapsulated in the PVA + EC device to diabetic C57BL/6 mice, nonfasting blood glucose levels showed a rapid decrease from high glucose levels of pre-transplantation, maintaining significantly lower glucose levels during the whole course of study in comparison with the sham-operated group. Our results indicated that this freezing/thawing macroencapsulation technique using 3% PVA + EC was effective for xenotransplantation of islet cells.

Rabbit and pig ear skin sample cryobanking: effects of storage time and temperature of the whole ear extirpated immediately after death

The post-mortem temporal and thermal limits within which there will be ample guarantees of rescuing living skin cells from dead specimens of two species, rabbit and pig, were studied. Post-mortem extirpated whole ears were stored (in non-aseptic conditions) either at 4 degrees C or at room temperature (from 22 to 25 degrees C) or at 35 degrees C for different time lapses after animal death. In both species, the post-mortem maximum time lapses where cell viability was not significantly reduced were 240, 72, and 24 h post-mortem (hpm) for 4, 22-25 and 35 degrees C, respectively. Once the post-mortem temporal limits for each tested thermal level at which cells from skin samples are able to grow in culture were defined, the survival ability of skin samples submitted to these temporal limits and cryopreserved were tested. In the pig, skin samples stored at the three tested thermal levels survived after vitrification-warming, reaching confluence in culture. In rabbit, only tissue samples from ears stored at 35 degrees C for 24 hpm did not survive after vitrification-warming. In conclusion, we should remark that cell survival rates obtained according to the assayed post-mortem time lapses and thermal levels are sufficient to collect and to cryopreserve skin samples from the majority of dead specimens.

Novel approaches to cryopreservation of human pancreatic islets

BACKGROUND

Optimized conditions for survival and function of human islets must be defined if sufficient islets are to be recovered from a single human donor pancreas to reverse type-1 diabetes after isolation, cryopreservation, and transplantation. The objective of this study was to compare the cryoprotective effect of ethylene glycol (EG) with the standard cryoprotectant, dimethyl sulfoxide (DMSO), on isolated human islet survival and function. Furthermore, the effect of different addition protocols and equilibrium concentrations of the cryoprotectants were studied.

METHODS

Islets were isolated from human pancreata by using standard techniques of collagenase digestion and discontinuous Ficoll gradient purification. Aliquots of freshly isolated human islets were cryopreserved in six groups by using DMSO or EG. Cryoprotectants were added stepwise to produce a final concentration of 1.5 or 2.0 M, or added in a single step to a concentration of 1.5 M. Islets were cryopreserved by using established protocols and cultured for 48 hr at 37 degrees C before assessment of percentage of recovery and in vitro viability.

RESULTS

After cryopreservation, percentage of recovery of islets was significantly higher in the group treated with 1.5 M of DMSO added in a stepwise protocol (74+/-3%, mean+/-SEM) compared with the standard 2.0 M of DMSO (62+/-4%) (P<0.05, unpaired t test, n=6). There was no difference between the recovery of islets cryopreserved with either 1.5 M of DMSO stepwise (74+/-3%) or 1.5 M of DMSO one-step (69+/-3%). Islet recovery was higher in groups treated with DMSO compared with EG, regardless of concentration of cryoprotectant or addition protocol, although the difference was significant only when comparing DMSO and EG 1.5 M one-step. Furthermore, islets treated with 1.5 M of DMSO, added either stepwise (6.0+/-0.4) or in one-step (6.5+/-0.8), had significantly higher stimulation indices compared with islets treated with the standard cryoprotectant for human islets, 2.0 M of DMSO (4.5+/-0.5) (P<0.05).

CONCLUSIONS

These results demonstrate that a lower concentration of DMSO (1.5 M) allows for the cryopreservation of human islets with superior survival and preservation of function post-culture compared with 2.0 M of DMSO and various concentrations of EG.

Human islet cell transplantation--future prospects

BACKGROUND

Islet transplantation has the potential to cure diabetes mellitus. Nevertheless despite successful reversal of diabetes in many small animal models, the clinical situation has been far more challenging. The aim of this review is to discuss why insulin-independence after islet allotransplantation has been so difficult to achieve.

METHODS

A literature review was undertaken using Medline from 1975 to July 2000. Results reported to the International Islet Transplant Registry (ITR) up to December 1998 were also analysed.

RESULTS

Up to December 1998, 405 islet allotransplants have been reported the ITR. Of those accurately documented between 1990 and 1998 (n = 267) only 12% have achieved insulin-independence (greater than 7 days). However with refined peri-transplant protocols insulin independence at 1 year can reach 20%.

CONCLUSIONS

There are many factors which can explain the failure of achieving insulin-independence after islet allotransplantation. These include the use of diabetogenic immunosuppressive agents to abrogate both islet allo-immunity and auto-immunity, the critical islet mass to achieve insulin-independence and the detrimental effects of transplanting islets in an ectopic site. However recent evidence most notably from the Edmonton group demonstrates that islet allotransplantation still has great potential to become an established treatment option for diabetic patients.

The effects of microencapsulation on pancreatic islet osmotically induced volumetric response

Microencapsulation of pancreatic islets has been proposed as a means to prevent allograft rejection and to protect islets during cryopreservation. The aim of this study was to investigate: 1) the effects of the cryoprotectants (CPAs) dimethyl sulfoxide (DMSO) and ethylene glycol (EG) on the volume of Ca2+ alginate microcapsules, and 2) the effects of microencapsulation on the volumetric response of human and canine pancreatic islets during CPA equilibration. Stock sodium alginate with a high mannuronic acid content (HM) or a high guluronic acid content (HG) was used to generate empty capsules (mean diameter 200 microm) with an electrostatic generator. The capsules were held in place by a holding pipette system and videotaped during the addition of 2 or 3 M CPA at 22 degrees C. Islets (isolated from human cadaveric donors and mongrel dogs and then cultured overnight at 37 degrees C) were encapsulated in alginate (HM), loaded into a microperfusion chamber, and the change in islet volume was videotaped after exposure to the same CPAs and concentrations. These were compared to the volume responses of nonencapsulated islets. Images were analyzed using a computerized image analysis system and the data were analyzed using ANOVA. HG microcapsules showed a significant (p < 0.05) increase in volume following exposure to EG but not to DMSO. HM microcapsule volume did not change significantly following exposure to either EG or DMSO and was therefore chosen as the substrate for islet encapsulation. Free, nonencapsulated canine and human islets responded to the osmotic challenge of the 2 M DMSO by shrinking to 70.00 +/- 1.04% (mean +/- SEM) and 70.11 +/- 1.05%, and in 2 M EG to 72.89 +/- 1.93% and 69.33 +/- 1.38%, respectively, of the isotonic volume before returning to the original cell volume. Exposure to 3 M DMSO or EG resulted in a further dehydration to 65.89 +/- 0.91% and 67.67 +/- 1.91% for canine and 62.22 +/- 0.66.% or 65.89 +/- 1.30% for human islets. Minimum volumes were reached within 30-40 s after exposure to the cryoprotectant. Encapsulated human islets reached 86.88 +/- 1.47% of their original volume in 2 M and 80.33 +/- 0.89% in 3 M DMSO, and 87.33 +/- 1.86% in 2 M and 82.80 +/- 1.57% in 3 M EG. This volume change was significantly less (p < 0.01) than that observed in corresponding free islets. Encapsulated canine islets reached 83.67 +/- 2.13% of their original volume in 2 M and 78.22 +/- 0.95% in 3 M DMSO, and 85.44 +/- 1.92% in 2 M and 78.11 +/- 2.01% in 3 M EG. As with human islets, this was significantly different than free islets (p < 0.01). These minimal volumes were reached within 30-50 s. These results demonstrate that there are cryoprotectant and alginate-specific interactions and that microencapsulation modulates the degree of osmotically induced shrinkage of islets. The development or modification of existing cryopreservation protocols to improve postcryopreservation recovery or function must account for these factors.

Water and cryoprotectant permeability characteristics of isolated human and canine pancreatic islets

Cryopreservation allows accumulation of the necessary islet transplantable mass as well as adequate time for tissue typing and infectious disease screening. Cryopreservation protocols may be optimized by modeling the osmotically induced volume excursions that occur during the addition and removal of cryoprotective agents (CPAs). To that end, three transport parameters were measured at 22 degrees C in canine and human islets isolated by collagenase digestion and euroficoll purification: (i) the apparent hydraulic conductivity (Lp), (ii) the permeability coefficient of the CPA (Ps), and (iii) the associated reflection coefficient (sigma). The parameters were determined by volumetric analysis of islets upon abrupt exposure to 1, 2, and 3 M dimethyl sulfoxide (DMSO), ethylene glycol (EG), glycerol (GLY), and propylene glycol (PG). The parameters were calculated using the Kedem-Katchalsky theory to describe islet volume excursion kinetics (assuming islets to be single equivalent osmotic units with the same volume and surface area of the actual islet) and a three-parameter curve fit was performed using the Marquardt-Levenberg method. It was determined that the permeability characteristics of pancreatic islets are species specific, and based upon the measured parameters, the highest Ps values for canine islets were observed following exposure to 2 M EG, and the highest Ps values for human islets were observed following exposure to 2 M PG. The permeability parameters were analyzed adjusting for islet radius using ANCOVA procedures to acquire least square means. For canine islets exposed to 2 M EG these values were determined to be 0.936 microm/min/atm, 2.47 microm/s, and 0.90 (for Lp, Ps, and phi, respectively) and for human islets exposed to 2 M PG the values were determined to be 1.56 microm/min/atm, 3.48 microm/s, and 0.85 (for Lp, Ps, and sigma, respectively). These parameters were used in a model to calculate osmotically induced islet volumetric response upon addition/dilution of the optimum CPAs, taking into consideration critical volume excursion limits at which irreversible damage occurs.