Abstract
Drug-loaded erythrocytes have been proposed for the treatment of disease. A common way to load drugs into erythrocytes is to apply osmotic shock. Currently, osmosis-based drug encapsulation is studied mainly experimentally, whereas a related theoretical model is still incomplete. In this study, a set of equations is developed to simulate the osmosis-based drug-encapsulation process. First, the modeling is validated with hemolysis rates and the drug-loaded quantities to be found in the literature. Then, the variation of the erythrocyte volume, formation of the pore on the erythrocyte membrane, and quantities of drug loaded into and hemoglobin released from erythrocytes are studied. Finally, an optimized operating condition for encapsulating drugs is proposed. The results show that the volume of erythrocytes exposed to hypotonic NaCl solution increases first and then abruptly decreases because of the pore formation; afterwards, it again increases and then decreases slowly. In the presence of the pore, the drug is loaded by diffusion, whereas the leak-induced convection goes against the loading. For an allowed 45% hemolysis rate, with a 10% hematocrit, the optimized NaCl concentration is 0.44%, the optimized time for sealing the loaded erythrocytes with hypertonic NaCl solution is at 6.5 s, and the quantity of albumin (drug) loaded is 4.5 mg/ml cells.
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Abbreviations
- \(A\) :
-
Membrane area of erythrocytes, μm2
- \(A_{0}\) :
-
Membrane area of erythrocytes at the isotonic condition, μm2
- \(D\) :
-
Diffusion coefficient, m2/s
- \(H_{\text{ct}}\) :
-
Hematocrit, 0–1
- \(k_{\text{B}}\) :
-
Boltzmann’s constant, J/K
- \(k_{\text{s}}\) :
-
Stretching modulus of the cell membrane, N/m
- \(L_{\text{p}}\) :
-
Hydraulic permeability of the cell membrane, m3/(N s)
- \(m\) :
-
Substance concentration, mol/m3
- \(p\) :
-
Hydraulic pressure, N/m2
- \(R\) :
-
Radius of erythrocytes, μm
- \(R_{\text{g}}\) :
-
Gas constant, J/(mol K)
- \(r\) :
-
Radius of the hemolytic pore, μm
- \(T\) :
-
Absolute temperature, K
- \(t\) :
-
Time, s
- \(t_{\text{ep}}\) :
-
Encapsulation time, s
- \(t_{\text{pc}}\) :
-
Pore opening-closing time, s
- \(t_{\text{st}}\) :
-
Stretching time, s
- \(t_{\text{sw}}\) :
-
Swelling time, s
- \(V\) :
-
Volume of erythrocytes, μm3
- \(V_{0}\) :
-
Volume of erythrocytes at the isotonic condition, μm3
- \(V_{\text{bc}}\) :
-
Osmotically inactive volume of erythrocytes, μm3
- \(v\) :
-
Leak velocity, m/s
- \(\alpha\) :
-
Line tension of the pore, N
- \(\eta\) :
-
Surface viscosity of the cell membrane, N s/m
- \(\mu\) :
-
Cytoplasm viscosity, N s/m2
- \(\sigma\) :
-
Surface tension of the cell membrane, N/m
- 0:
-
Previous time
- 1, 2, 3:
-
Stages of the drug-loading process
- d, h, n:
-
Drug; hemoglobin; NaCl
- i, e:
-
Intracellular; extracellular
- q:
-
d, h or n
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Acknowledgements
This work was supported by the National Natural Science Foundation of China (81571768, 81627806), the Specialized Research Fund for the Doctoral Program of Higher Education of China (20133402120033), and the Fundamental Research Funds for the Central Universities (WK6030000054, WK3490000001).
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Ge, D., Zou, L., Li, C. et al. Simulation of the osmosis-based drug encapsulation in erythrocytes. Eur Biophys J 47, 261–270 (2018). https://doi.org/10.1007/s00249-017-1255-1
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DOI: https://doi.org/10.1007/s00249-017-1255-1