원심법에 의한 얇은 아가로스 마이그로비즈의 인슐린에 의한 글루코스 응답곡선 평가를 위한 확산모델

화학공학의 이론과 응용 제8권 제1호 2002년

Theories and Applications of Chem. Eng., 2002, Vol. 8, No. 1

박영건

전남대학교 의학연구소

Diffusion model for assessing the performance of thin agarose microbeads

bioartificial pancreases using centrifugation

Youeng Guen Park

Research Institute of Medical Sciences, Chonnam National University,

INTRODUCTION

For a bioartificial pancreas (BAP), islets of Langerhans (islets) are enclosed in a semipermeable polymer membrane which protect the islets from immunorejection after transplantation [1]. Recently, many studies have been performed to enclose biological cells into synthetic membranes. To provide biocompatibility and permit retrieval of appropriately designed implants, the membrane is permeable to small molecules such as oxygen, nutrients, glucose, and insulin, but totally impermeable to large molecules such as immunoglobulins and complement protein. The islets which are immuno-isolated from the host by a semipermeable membrane are free from rejection and are anticipated to control glucose metabolism for a long period. Another advantage of immunoisolation is that it may solve the donor shortage problem because not only allogeneic but also xenogeneic islet transplantation would become feasible. One promising immunoisolating approach is the microencapsulation of individual islets. The success of a microencapsulation procedure depends on the capsule size which influences the graft volume and the diffusion of oxygen, nutrients, glucose and insulin across the membrane.

The secretion of insulin from islets is of a typical pattern. It includes a first phase, which is so rapid, is four times higher than basal insulin secretion level, and the longer second phase is appeared. For normal glucose homeostasis of the BAP, the first phase which is equivalent to the insulin response to glucose is to be appeared. In this study, the perifusion analysis using compartment model was carried out to predict the dynamic behavior of glucose-induced insulin secretion. The model will be better understanding the performance of a bioartificial pancreas so as to serve as a guide in designing a function of the BAP.

MATERIALS AND METHOD

Islet isolation: Islets were isolated from hamster donors by the collagenase digestion method with our own modification [2]. The pancreas was excised and placed into a plastic Petri dish. The pancreatic tissue of 3 hamsters was chopped to about 1 min in size and mixed with collagenase in HEPES (800 mg/dl). The tissue was vigorously shaken for 5 min at 37℃. Islets from digested tissue were separated in a 3-step gradient of dextran solutions by centrifugation at 800g for 20 min. The islets from the interfaces between densities of 1.072 and 1.095 g/cm3 were separated and then washed several times with HEPES solution.

Thin encapsulated islets with 5-10 □m in coating thickness: Dextran was dissolved in HEPES buffered saline to prepare 7 wt% dextran solutions. Two thousand of islets were suspended in 0.4 ml solution of 5 wt% agarose. It was overlayered on the top of a 3 ml layer of 7% of dextran (density; 1.032 g/ml, 0℃) in a glass test tube. After the addition of the islets suspension, the tube was centrifuged at 440g (g=980 cm2/min) for 10 min to settle down the islets to the bottom of the tube. Agarose gel was formed on the surface of the islets by passing through the 7% dextran solution layer. After centrifugation, the test tube was immersed in an icy water to induce the agarose solution layer on the bead surface to form gel better. The microencapsulated islets were cultured in Petri dishes with MEM supplemented with 5% FCS (Fetal calf serum) and 50 mg/L gentamycin at 37℃ in the mixture of 5% CO2  and 95% air for a certain period before in vitro experiment.

KINETIC MODELING OF A BAP WITH COMPARTMENT MODEL

1) Mass transfer of glucose: The in vitro perifusion system for glucose shown in Fig. 1 (A) is composed of a series of perfusate and islets chambers. The change of glucose concentration, Cg1 and Cg2 in the perifusate and the islet compartments, respectively, under a complete mixing condition can be represented as:

(1)

(2)

where V1 and V2 are the volumes of the perifusate and the islet compartments, respectively, Ac is the membrane surface area, Kg is the overall mass transfer coefficient of glucose through the membrane, and Q is the flow rate of the perifusate in the fluidized chamber. If the change of glucose concentration in the perfusate, Cg1 is assumed to be zero, the glucose stimulation in the islet compartment:

(3)

2) Modelling of insulin generation by the BAP: Glucose diffuses through the agaross hydrogel, reaches the surface of islets and stimulates insulin secretion. To describe the insulin release mode from islets we adopted the model of Normuras numerical expression [3, 4]. Insulin secretion i(t) in Fig. 1(B), can be cataloged into 2 components: 1) a static contribution proportional to the blood glucose concentration (Cg2), and 2) a dynamic contribution in response to the rate of change of glucose concentration (dCg2/dt). The model of the system, in which the stepwise input of glucose concentration (Cg2(t)) and biphasic response of insulin secretion, I(t) can be depicted as follows.

(4)

(5)

(6)

where T1 and T2 are the first order delays in response, Kp and Td are coefficients for proportional action and derivative action, respectively, and I is the amount of insulin produced in the islet compartment. Substituting Eq. (3) into Eqs. (4) and (5) yields.

(7)

3) The mass transfer of insulin: The secreted insulin in respone to glucose concentration change in the islet compartment is released through the membrane into the perfusate (Fig. 1 (C)). The concentrations in the perfusate (Ci1) and the islet (Ci2) compartments are given as:

(8)

(9)

where N is the number of islets in the islet compartment and KiAc is the mass flow rate of insulin through the membrane. In this work, N was 70 microencapsulated or naked islets. Initial conditions at time zero for Ci1 and Ci2 are:

(10)

After substituting Eq. (7) into Eq. (9), and solving Eqs. (8) and (9) to obtain the insulin release in the perfusate compartment under initial conditions yields:

(11)

where B1, B2, B3, B4 and B5 are constants. Eq. (11) slows that it is considered of exponential functions of m, n, z, □, and □. But when the plateau level is achieved at steady state, the concentration of insulin release in the perfusate compartment from Eq. (11) is

(12)

RESULTS AND DISSCUSSION

For the BAP, the glucose in the perfusate compartment passes across the membrane by diffusion into the islet compartment and stimulates the islets to secrete insulin, and the insulin in the islet compartment passes across the membrane by diffusion back to the perfusate compartment. The membrane thickness is critical factor to control the insulin secretion concentration within the BAP. The mass transfer rate of insulin has a greater influence than that of glucose due to high molecular weight. The effect of the membrane thickness on the insulin secretion in response to glucose stimulation at concentrations from 0 mg/dl to 160 mg/dl is investigated. The BAP with the thinner membrane keeps the insulin behavior without delay in response to glucose stimulation, while that with thicker membrane lose the first phase response. The decrease in the membrane thickness led to significantly improve the kinetics in insulin. However, the insulin concentrations at the steady state was independent of the membrane thickness.

The change of insulin secretion in response to glucose stimulation for microencapsulated islets depend on the exponential terms of m, n, z, □ and □. □ and □, and z in Eq. 12 are the functions of mass transfer coefficients of insulin and glucose, respectively. The behavior of insulin release is influenced by the membrane thickness due to  □, □, and z terms. In case of □Ｂ□, Exp[-□t] approaches zero rapidly with time, while Exp[-□t] has influence on the behavior of insulin secretion in the BAP for a long time. The influence of Exp[-□t] on the time to reach the plateau level has greater than that of Exp[-zt] due to smaller molecular weight of glucose. On the other hand, m and n, which are related to the intrinsic properties of insulin secretion in response to glucose stimulation by islets, don't have influence on the insulin release with increasing membrane thickness. When 5% agarose solution was used, the time to reach the plateau level for m and n are 56 and 9 mins, respectively, regardless of the membrane thickness. After all, the behavior of insulin concentration was influenced by the coefficient for proportional action, the glucose stimulation concentration, the number of islet and the perfusate flow rate after the plateau level reached.

70 microencapsulated islets with thin agarose walls were placed in the fluidized chamber to compare a perifusion model with experiment data the. The glucose concentration in the perfusate compartment was raised from 80 to 160 mg/dl after the circulation of glucose solution for 60 min. For perifusion model, Ci1 and Ci2 as the initial conditions were 32.7 and 49.7 □U/70 islets, respectively and the time was set 0 at the moment. It was biphasic responses of insulin release with important features of the first and second phases of insulin release. The perifusion model of insulin release represents our data well.

CONCLUSION

In order to predict the insulin release in response to glucose stimulation, the perifusion model was developed. The model shows that the production of insulin from islets is sensitive to glucose stimulation. The dependency of the behavior of insulin concentration can be cataloged as the first order delays in response of glucose concentration and the rate of change of glucose concentration, and the mass flow rates of glucose and insulin across the membrane. When the microencapsulated islets are used, the properties of hydrogel membrane gave a duller response of insulin to glucose with increasing the membrane thickness. However, after the plateau level is reached, the insulin concentration released from microencapsulated islets depends on the coefficient of proportional action, glucose stimulation concentration, and perfusate flow rate, independent of the membrane properties. Therefore, this model will be better understand the performance of a bioartificial pancreas so as to serve as a guide in designing a function of a BAP.

REFERENCES

1. G.F. Klomp et al., J. Biomed. Mat. Res. 17 (1983) 865

2. P.E. Lacy, M. Kostianovsky, Diabetes 16 (1967) 35

3. M. Normura,  Iyoudennshi to Seitaikougaku 19 (1981) 203

4. K. Ryuzo et al., Acta Endocrinologica 87 (1978) 339