This study develops a macroscopic model of mass transport in electroporated biological tissue in order to predict the cellular drug uptake. The change in the macroscopic mass transport coefficient is related to the increase in electrical conductivity resulting from the applied electric field. Additionally, the model considers the influences of both irreversible electroporation (IRE) and the transient resealing of the cell membrane associated with reversible electroporation. Two case studies are conducted to illustrate the applicability of this model by comparing transport associated with two electrode arrangements: side-by-side arrangement and the clamp arrangement. The results show increased drug transmission to viable cells is possible using the clamp arrangement due to the more uniform electric field.

References

1.
Alberts
,
B.
,
2004
,
Essential Cell Biology
,
Garland Science
,
New York
.
2.
Krassowska
,
W.
, and
Filev
,
P. D.
,
2007
, “
Modeling Electroporation in a Single Cell
,”
Biophys. J.
,
92
(
2
), pp.
404
417
.
3.
Teissie
,
J.
,
Golzio
,
M.
, and
Rols
,
M. P.
,
2005
, “
Mechanisms of Cell Membrane Electropermeabilization: A Minireview of Our Present (lack of?) Knowledge
,”
Biochim. Biophys. Acta
,
1724
(
3
), pp.
270
280
.
4.
Weaver
,
J. C.
, and
Chizmadzhev
,
Y. A.
,
1996
, “
Theory of Electroporation: A Review
,”
Bioelectrochem. Bioenergetics
,
41
(
2
), pp.
135
160
.
5.
Weaver
,
J. C.
,
2003
, “
Electroporation of Biological Membranes From Multicellular to Nano Scales
,”
IEEE Trans. Dielectr. Electr. Insul.
,
10
(
5
), pp.
754
768
.
6.
Pavlin
,
M.
,
Leben
,
V.
, and
Miklavčič
,
D.
,
2007
, “
Electroporation in Dense Cell Suspension—Theoretical and Experimental Analysis of Ion Diffusion and Cell Permeabilization
,”
Biochim. Biophys. Acta
,
1770
(
1
), pp.
12
23
.
7.
Pavlin
,
M.
, and
Miklavčič
,
D.
,
2008
, “
Theoretical and Experimental Analysis of Conductivity, Ion Diffusion and Molecular Transport During Cell Electroporation—Relation Between Short-Lived and Long-Lived Pores
,”
Bioelectrochemistry
,
74
(
1
), pp.
38
46
.
8.
Delemotte
,
L.
, and
Tarek
,
M.
,
2012
, “
Molecular Dynamics Simulations of Lipid Membrane Electroporation
,”
J. Membr. Biol.
,
245
(
9
), pp.
531
543
.
9.
Tarek
,
M.
,
2005
, “
Membrane Electroporation: A Molecular Dynamics Simulation
,”
Biophys. J.
,
88
(
6
), pp.
4045
4053
.
10.
Tieleman
,
D. P.
,
2004
, “
The Molecular Basis of Electroporation
,”
BMC Biochem.
,
5
(
1
), pp.
10
22
.
11.
Puc
,
M.
,
Kotnik
,
T.
,
Mir
,
L. M.
, and
Miklavčič
,
D.
,
2003
, “
Quantitative Model of Small Molecules Uptake After In Vitro Cell Electropermeabilization
,”
Bioelectrochemistry
,
60
(
1–2
), pp.
1
10
.
12.
Pavselj
,
N.
,
Bregar
,
Z.
,
Cukjati
,
D.
,
Batiuskaite
,
D.
,
Mir
,
L. M.
, and
Miklavčič
,
D.
,
2005
, “
The Course of Tissue Permeabilization Studied on a Mathematical Model of a Subcutaneous Tumor in Small Animals
,”
IEEE Trans. Biomed. Eng.
,
52
(
8
), pp.
1373
1381
.
13.
Rubinsky
,
B.
,
2009
,
Irreversible Electroporation
,
Springer
,
Dordrecht, The Netherlands
.
14.
Golberg
,
A.
, and
Yarmush
,
M. L.
,
2013
, “
Nonthermal Irreversible Electroporation: Fundamentals, Applications, and Challenges
,”
IEEE Trans. Biomed. Eng.
,
60
(
3
), pp.
707
714
.
15.
Rols
,
M. P.
, and
Teissié
,
J.
,
1990
, “
Electropermeabilization of Mammalian Cells. Quantitative Analysis of the Phenomenon
,”
Biophys. J.
,
58
(
5
), pp.
1089
1098
.
16.
Sel
,
D.
,
Cukjati
,
D.
,
Batiuskaite
,
D.
,
Slivnik
,
T.
,
Mir
,
L. M.
, and
Miklavčič
,
D.
,
2005
, “
Sequential Finite Element Model of Tissue Electropermeabilization
,”
IEEE Trans. Biomed. Eng.
,
52
(
5
), pp.
816
827
.
17.
Davalos
,
R. V.
,
Rubinsky
,
B.
, and
Otten
,
D. M.
,
2002
, “
A Feasibility Study for Electrical Impedance Tomography as a Means to Monitor Tissue Electroporation for Molecular Medicine
,”
IEEE Trans. Biomed. Eng.
,
49
(
4
), pp.
400
403
.
18.
Pavlin
,
M.
, and
Miklavčič
,
D.
,
2003
, “
Effective Conductivity of a Suspension of Permeabilized Cells: A Theoretical Analysis
,”
Biophys. J.
,
85
(
2
), pp.
719
729
.
19.
Pavlin
,
M.
,
Kandušer
,
M.
,
Reberšek
,
M.
,
Pucihar
,
G.
,
Hart
,
F. X.
,
Magjarevićcacute
,
R.
, and
Miklavčič
,
D.
,
2005
, “
Effect of Cell Electroporation on the Conductivity of a Cell Suspension
,”
Biophys. J.
,
88
(
6
), pp.
4378
4390
.
20.
Čorović
,
S.
,
Mir
,
L. M.
, and
Miklavčič
,
D.
,
2012
, “
In Vivo Muscle Electroporation Threshold Determination: Realistic Numerical Models and in vivo Experiments
,”
J. Membr. Biol.
,
245
(
9
), pp.
509
520
.
21.
Pavšelj
,
N.
,
Préat
,
V.
, and
Miklavčič
,
D.
,
2007
, “
A Numerical Model of Skin Electropermeabilization Based on In Vivo Experiments
,”
Ann. Biomed. Eng.
,
35
(
12
), pp.
2138
2144
.
22.
Lacković
,
I.
,
Magjarević
,
R.
, and
Miklavčič
,
D.
,
2010
,
Incorporating Electroporation-Related Conductivity Changes Into Models for the Calculation of the Electric Field Distribution in Tissue
,
Springer
,
Berlin, Germany
, pp.
695
698
.
23.
Corovic
,
S.
,
Lackovic
,
I.
,
Sustaric
,
P.
,
Sustar
,
T.
,
Rodic
,
T.
, and
Miklavčič
,
D.
,
2013
, “
Modeling of Electric Field Distribution in Tissues During Electroporation
,”
Biomed. Eng. Online
,
12
(
1
), pp.
16
42
.
24.
Granot
,
Y.
, and
Rubinsky
,
B.
,
2008
, “
Mass Transfer Model for Drug Delivery in Tissue Cells With Reversible Electroporation
,”
Int. J. Heat Mass Transfer
,
51
(
23
), pp.
5610
5616
.
25.
Mahnic-Kalamiza
,
S.
,
Miklavcic
,
D.
, and
Vorobiev
,
E.
,
2014
, “
Dual-Porosity Model of Solute Diffusion in Biological Tissue Modified by Electroporation
,”
Biochim. Biophys. Acta
,
1838
(
7
), pp.
1950
1966
.
26.
Glaser
,
R. W.
,
Leikin
,
S. L.
,
Chernomordik
,
L. V.
,
Pastushenko
,
V. F.
, and
Sokirko
,
A. I.
,
1988
, “
Reversible Electrical Breakdown of Lipid Bilayers: Formation and Evolution of Pores
,”
Biochim. Biophys. Acta
,
940
(
2
), pp.
275
287
.
27.
Klenchin
,
V. A.
,
Sukharev
,
S. I.
,
Serov
,
S. M.
,
Chernomordik
,
L. V.
, and
YuA
,
C.
,
1991
, “
Electrically Induced DNA Uptake by Cells is a Fast Process Involving DNA Electrophoresis
,”
Biophys. J.
,
60
(
4
), pp.
804
811
.
28.
Weaver
,
J. C.
,
1993
, “
Electroporation: A General Phenomenon for Manipulating Cells and Tissues
,”
J. Cell. Biochem.
,
51
(
4
), pp.
426
435
.
29.
Tekle
,
E.
,
Astumian
,
R. D.
, and
Chock
,
P. B.
,
1994
, “
Selective and Asymmetric Molecular Transport Across Electroporated Cell Membranes
,”
Proc. Natl. Acad. Sci. U. S. A.
,
91
(
24
), pp.
11512
11516
.
30.
Rols
,
M.-P.
, and
Teissié
,
J.
,
1998
, “
Electropermeabilization of Mammalian Cells to Macromolecules: Control by Pulse Duration
,”
Biophys. J.
,
75
(
3
), pp.
1415
1423
.
31.
Neumann
,
E.
,
Kakorin
,
S.
, and
Tœnsing
,
K.
,
1999
,
Fundamentals of Electroporative Delivery of Drugs and Genes
,
Elsevier S.A
,
Lausanne, Switzerland
, pp.
3
16
.
32.
Kotnik
,
T.
,
Mir
,
L. M.
,
Flisar
,
K.
,
Puc
,
M.
, and
Miklavčič
,
D.
,
2001
, “
Cell Membrane Electropermeabilization by Symmetrical Bipolar Rectangular Pulses: Part I. Increased Efficiency of Permeabilization
,”
Bioelectrochemistry
,
54
(
1
), pp.
83
90
.
33.
Tien
,
H. T.
, and
Ottova
,
A.
,
2003
, “
The Bilayer Lipid Membrane (BLM) Under Electrical Fields
,”
IEEE Trans. Dielectr. Electr. Insul.
,
10
(
5
), pp.
717
727
.
34.
Davalos
,
R. V.
,
Mir
,
L. M.
, and
Rubinsky
,
B.
,
2005
, “
Tissue Ablation With Irreversible Electroporation
,”
Ann. Biomed. Eng.
,
33
(
2
), pp.
223
231
.
35.
Chen
,
C.
,
Smye
,
S. W.
,
Robinson
,
M. P.
, and
Evans
,
J. A.
,
2006
, “
Membrane Electroporation Theories: A Review
,”
Med. Biol. Eng. Comput.
,
44
(
1
), pp.
5
14
.
36.
Lee
,
R. C.
,
2006
, “
Cell Injury by Electric Forces
,”
Ann. N. Y. Acad. Sci.
,
1066
(
1
), pp.
85
91
.
37.
Esser
,
A. T.
,
Smith
,
K. C.
,
Gowrishankar
,
T. R.
, and
Weaver
,
J. C.
,
2007
, “
Towards Solid Tumor Treatment by Irreversible Electroporation: Intrinsic Redistribution of Fields and Currents in Tissue
,”
Technol. Cancer Res. Treat.
,
6
(
4
), pp.
261
273
.
38.
Ivorra
,
A.
,
Al-Sakere
,
B.
,
Rubinsky
,
B.
, and
Mir
,
L. M.
,
2009
, “
In Vivo Electrical Conductivity Measurements During and After Tumor Electroporation: Conductivity Changes Reflect the Treatment Outcome
,”
Phys. Med. Biol.
,
54
(
19
), pp.
5949
5963
.
39.
Neal Ii
,
R. E.
, and
Davalos
,
R. V.
,
2009
, “
The Feasibility of Irreversible Electroporation for the Treatment of Breast Cancer and Other Heterogeneous Systems
,”
Ann. Biomed. Eng.
,
37
(
12
), pp.
2615
2625
.
40.
Lee
,
E. W.
,
Wong
,
D.
,
Prikhodko
,
S. V.
,
Perez
,
A.
,
Tran
,
C.
,
Loh
,
C. T.
, and
Kee
,
S. T.
,
2012
, “
Electron Microscopic Demonstration and Evaluation of Irreversible Electroporation-Induced Nanopores on Hepatocyte Membranes
,”
J. Vasc. Interventional Radiol.
,
23
(
1
), pp.
107
113
.
41.
Saulis
,
G.
, and
Saule
,
R.
,
2012
, “
Size of the Pores Created by an Electric Pulse: Microsecond vs Millisecond Pulses
,”
Biochim. Biophys. Acta
,
1818
(
12
), pp.
3032
3039
.
42.
Meir
,
A.
, and
Rubinsky
,
B.
,
2014
, “
Electrical Impedance Tomographic Imaging of a Single Cell Electroporation
,”
Biomed. Microdev.
,
16
(
3
), pp.
427
437
.
43.
Neal
,
R. E.
,
Garcia
,
P. A.
,
Kavnoudias
,
H.
,
Rosenfeldt
,
F.
,
McLean
,
C. A.
,
Earl
,
V.
,
Bergman
,
J.
,
Davalos
,
R. V.
, and
Thomson
,
K. R.
,
2015
, “
In Vivo Irreversible Electroporation Kidney Ablation: Experimentally Correlated Numerical Models
,”
IEEE Trans. Biomed. Eng.
,
62
(
2
), pp.
561
569
.
44.
Miklavčič
,
D.
,
Šemrov
,
D.
,
Mekid
,
H.
, and
Mir
,
L. M.
,
2000
, “
A Validated Model of In Vivo Electric Field Distribution in Tissues for Electrochemotherapy and for DNA Electrotransfer for Gene Therapy
,”
Biochim. Biophys. Acta
,
1523
(
1
), pp.
73
83
.
45.
Djuzenova
,
C. S.
,
Zimmermann
,
U.
,
Frank
,
H.
,
Sukhorukov
,
V. L.
,
Richter
,
E.
, and
Fuhr
,
G.
,
1996
, “
Effect of Medium Conductivity and Composition on the Uptake of Propidium Iodide Into Electropermeabilized Myeloma Cells
,”
Biochim. Biophys. Acta
,
1284
(
2
), pp.
143
152
.
46.
Neumann
,
E.
,
Kakorin
,
S.
, and
Toensing
,
K.
,
1999
, “
Fundamentals of Electroporative Delivery of Drugs and Genes
,”
Bioelectrochem. Bioenergetics
,
48
(
1
), pp.
3
16
.
47.
Swartz
,
M. A.
, and
Fleury
,
M. E.
,
2007
, “
Interstitial Flow and Its Effects in Soft Tissues
,”
Annu. Rev. Biomed. Eng.
,
9
(
1
), pp.
229
256
.
48.
Becker
,
S.
, and
Kuznetsov
,
A. V.
,
2013
,
Transport in Biological Media
,
Elsevier
,
Amsterdam, The Netherlands
/Academic Press, Boston, MA.
49.
Hrabe
,
J.
,
Hrabĕtová
,
S.
, and
Segeth
,
K.
,
2004
, “
A Model of Effective Diffusion and Tortuosity in the Extracellular Space of the Brain
,”
Biophys. J.
,
87
(
3
), pp.
1606
1617
.
50.
Young
,
D. M.
,
1971
,
Iterative Solution of Large Linear Systems
,
Academic Press
,
New York
.
51.
Patankar
,
S. V.
,
1980
,
Numerical Heat Transfer and Fluid Flow
,
Hemisphere Publishing
,
Washington, DC/New York
.
52.
Prausnitz
,
M. R.
,
Lee
,
C. S.
,
Liu
,
C. H.
,
Pang
,
J. C.
,
Singh
,
T.-P.
,
Langer
,
R.
, and
Weaver
,
J. C.
,
1996
, “
Transdermal Transport Efficiency During Skin Electroporation and Iontophoresis
,”
J. Controlled Release
,
38
(
2
), pp.
205
217
.
53.
Cussler
,
E. L.
,
2009
,
Diffusion: Mass Transfer in Fluid Systems
,
Cambridge University Press
,
New York/Cambridge, UK
.
54.
Magzoub
,
M.
,
Zhang
,
H.
,
Dix
,
J. A.
, and
Verkman
,
A. S.
,
2009
, “
Extracellular Space Volume Measured by Two-Color Pulsed Dye Infusion With Microfiberoptic Fluorescence Photodetection
,”
Biophys. J.
,
96
(
6
), pp.
2382
2390
.
55.
Becker
,
S.
,
Zorec
,
B.
,
Miklavcic
,
D.
, and
Pavselj
,
N.
,
2014
, “
Transdermal Transport Pathway Creation: Electroporation Pulse Order
,”
Math. Biosci.
,
257
, pp.
60
68
.
56.
Lodish
,
H. F.
,
2008
,
Molecular Cell Biology
,
W.H. Freeman
,
New York
.
57.
Dechadilok
,
P.
, and
Deen
,
W. M.
,
2006
, “
Hindrance Factors for Diffusion and Convection in Pores
,”
Ind. Eng. Chem. Res.
,
45
(
21
), pp.
6953
6959
.
58.
Myers
,
G. E.
,
1971
,
Analytical Methods in Conduction Heat Transfer
,
McGraw-Hill
,
New York
.
59.
Goresky
,
C. A.
, and
Nadeau
,
B. E.
,
1974
, “
Uptake of Materials by the Intact Liver. The Exchange of Glucose Across the Cell Membranes
,”
J. Clin. Invest.
,
53
(
2
), pp.
634
646
.
You do not currently have access to this content.