Electroporation technique induced by high-voltage pulses has been successfully used to ablate tumor cells while preserving the function of normal blood vessels. Generally, the tumor blood vessels can provide a pathway to draw nutrients for tumor growth and contribute to invasion and metastasis, which is an obstacle to tumor treatment. The electroporation study of the endothelial cell, which is important in the vasculature microenvironment, is helpful to investigate the influence on both tumor and normal blood vessels. This study built a multicell-layer model of the vascular microenvironment to investigate the discriminative electroporation effect between normal and tumor blood vessels by high-frequency bipolar pulses (HFBPs) and monopolar pulses (MPs). The simulation results showed that both pore number and electroporation region in normal blood vessels are significantly lower than those in tumor blood vessels. The rich vascular smooth muscle cells existed in the normal blood vessels play a protective function for endothelial cells, compared with tumor blood vessels. However, the differences in pore number and electroporation region between normal and tumor blood vessels are gradually smaller with an increased electric field, which demonstrates that the electroporation pulse with higher intensity damages both normal and tumor blood vessels. HFBPs generate a weaker electroporation effect on both normal and tumor blood vessels than traditional MP. However, HFBPs are more suitable to electroporate tumor blood vessels, while preserving the normal blood vessels. Moreover, this study could also provide a multicell-layer model that can be used to analyze the cell electroporation effect in the vascular microenvironment.

Membrane permeabilization is significantly enhanced when a cell is exposed to a high-intensity electric field. This phenomenon is attributed to the nanopores of the cell membrane induced by the high-intensity electric field, which is termed electroporation (EP).1–3 The nanopore reseals after the electric pulse with low intensity ceases, and the cell recovers to its normal state. This phenomenon is called reversible electroporation (RE). Generally, anti-tumor drugs (such as bleomycin or cisplatinum) can easily pass through the cell membrane with the aid of RE to enhance tumor treatment. This method is called electrochemotherapy (ECT).4,5 For electric pulses with higher intensity, the cells succumb to membrane permeabilization induced by electroporation and then are dead after the electric pulse, which is termed irreversible electroporation (IRE). IRE can also be used for tumor treatment without the use of toxic drugs.6,7

Nowadays, ECT and IRE, as two modalities, have been successfully used for clinical tumor treatment. The effectiveness of ECT has been validated on different solid tumor models, particularly in skin cancer (melanoma, basal cell carcinoma, etc.).8–10 Currently, IRE has also been evaluated on multiple cancers in the pancreas, prostate, liver, etc.11–14 The electroporation technique (ECT and IRE) has a unique advantage in that the tumor cells are ablated while the structure of the extracellular matrix (large normal blood vessels, bile ducts, nerves, etc.) is spared. These important tissues remain functional after the treatment. Particularly, this unique feature is very important for IRE treatment with a certain tumor around the large blood vessel that is often unresectable or the treatment fails. Clinical outcomes of IRE tumor treatment adjacent to large blood vessels also validate this unique advantage.15–18 

Although preserving the structure of blood vessels, the electroporation technique still affects the function of blood vessels during the tumor treatment. Generally, the endothelial cells of blood vessels are most important for the main function of normal blood vessels. Markelc et al. reviewed in vitro ECT studies and found that an electric pulse could also electroporate endothelial cells.17 Sersa et al. first showed that ECT could modify the blood flow (the vascular lock effect) in the treated area.19 The vascular lock effect contributes to drug entrapment, which benefits ECT tumor treatment. Moreover, ECT induces endothelial cell death in blood vessels generated by tumors and then blocks tumor blood flow, which also benefits ECT treatment.20 For IRE treatment, Maor et al. found that the vascular smooth muscle cells in normal blood vessels were also ablated. Although fibrosis was observed 35 days after treatment, the structure of vessel integrity remained intact.21,22

The above experimental studies have shown that the endothelial cells can be electroporated in the blood vessel. However, few theoretical studies explore endothelial cell electroporation in the vascular microenvironment. Generally, the structure of normal blood vessels (arteries and veins) is different from the blood vessels generated by tumors. The normal blood vessels mainly consist of three components: endothelial cells (ECs), vascular smooth muscle cells (VSMCs), and connective tissue.23,24 The inner layer in normal blood vessels includes a single layer of ECs surrounded by connective tissue. The middle layer contains rich VSMCs and connective tissue. The outer layer is made of connective tissue. The capillaries only consist of a single layer of ECs surrounded by connective tissue. The tumor vasculatures are mainly similar to those of capillaries. They retain their capillary-like structure, having walls that contain only a single layer of endothelium, but their diameters are much larger than those of normal capillaries.25–30 In order to investigate the cell electroporation effect on both tumor and normal vascular microenvironments, we first built multicell-layer dielectric 2D models of realistic blood vessels31 to study the transmembrane voltage of ECs (the function of ECs is important to blood vessels). The simulation result showed that the transmembrane voltage (TMV) of ECs in normal blood vessels is too low to generate electroporation, which preliminarily provided a conceivable explanation that the function of normal blood vessels is preserved because of the low TMV, compared with tumor blood vessels. Moreover, tumor blood vessels are also more sensitive to an electroporation pulse than normal blood vessels, which benefits the complete tumor ablation.

The ECT and IRE protocols use monopolar pulses to generate an electroporation effect. However, the side effects (muscle contractions and pain sensation) were still observed.5,9,13,32 The side effects, such as muscle contractions, might move the electrodes during treatment, resulting in some possible complications. The high-frequency IRE (H-FIRE) protocol, which uses high-frequency bipolar pulses, has been proposed to reduce muscle contractions.33–36 For ECT treatment, high-frequency bipolar pulses with cisplatin or bleomycin could effectively kill cells in vitro, although higher electric fields were needed.37,38

High-frequency bipolar pulses seem promising for tumor treatment for ECT and IRE protocols. Moreover, the cells in the tissue can also be ablated while preserving the structure of large blood vessels by high-frequency bipolar pulses.39,40 In previous work, we have built multicell-layer dielectric models of blood vessels to study the cell transmembrane voltage (TMV) of ECs in blood vessels.31 In this paper, we further refine the realistic multicell-layer model of normal and tumor blood vessels by considering the Smoluchowski equation. The simulation results showed that the pore number and electroporation region of ECs in normal blood vessels are significantly lower than those in tumor blood vessels, which further validates that the electroporation effect in the tumor blood vessels is stronger than that in normal blood vessels. The high-frequency bipolar pulses generate less electroporation effect of ECs than traditional monopolar pulses on both normal and tumor blood vessels. However, it is worth noting that high-frequency bipolar pulses are more sensitive to tumor blood vessels while preserving normal blood vessels compared with monopolar pulses.

In our previous research, the 2D model has been built in detail.31 In this study, we simply showed a schematic plot of the normal blood vessel model and tumor blood vessel in Fig. 1. The normal blood vessel model (vein) consists of the endothelial cells (ECs) layers, vascular smooth muscle cells (VSMCs) layers, and connective tissue. Endothelial cells are modeled as rectangles with round chamfers. The length and width of a rectangle are 10 and 3 μm, respectively. The radius of a round chamfer is 1 μm. 150 endothelial cells form a circle around the blood with a radius of 300 μm. One side of endothelial cells is surrounded by blood, while the other is surrounded by connective tissue. Generally, the endothelial cells in the intima are tightly connected in the normal blood vessels but loosely connected in tumor blood vessels, resulting from the high vascular permeability.26,27,41 This study mainly investigates the discriminative electroporation effect between tumors and normal blood vessels resulting from the existence of vascular smooth muscle cells. To reduce computational cost and keep the same condition, the distance between the endothelial cells was set to approximately 2.5 μm for stimulation. The distributed impedance boundary condition was also set to model the connective tissue in the inner layer (10 μm thickness) and the outer layer (50 μm). Five layers of VSMCs surrounded by connective tissue form the middle layer. The VSMCs are modeled as ellipses and the major and minor axes of VSMCs are 33 and 3 μm, respectively. The thickness of the normal blood vessel is approximately 113 μm. Figure 1(b) shows the tumor blood vessel, which only consists of an endothelial cells layer and connective tissue. The computational domain is set as a square 2.1 mm in length. The boundaries of the solution domain were defined as electrical insulation. Initial conditions on all boundaries and domains were set to zero. The distance between two electrodes is set to 2 mm. One electrode was assigned an electrical potential with a certain value, and another electrode was assigned a zero potential.

FIG. 1.
Models of normal blood vessels (a) and tumor blood vessels (b).
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Models of normal blood vessels (a) and tumor blood vessels (b).

FIG. 1.
Models of normal blood vessels (a) and tumor blood vessels (b).
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Models of normal blood vessels (a) and tumor blood vessels (b).

Close modal
The electric potential Ψ in the solving domain is governed by the Laplace equation,
(1)
(2)
where ɛ0 is the permittivity of vacuum, ɛr is the relative permittivity, and λ is the conductivity of the solution domain. Ψi(t) is the intracellular potential, and Ψe(t) is the extracellular potential. Vm is the transmembrane potential.
The pores created in the cell membrane could provide new channels for the transmembrane current density. The transmembrane potential was also solved based on the electric current continuity with electroporation, which was modeled by42,
(3)
where λm0 represents the conductivity of the cell membrane and ɛmem represents the relative permittivity of the cell membrane. h (see Table I) represents the membrane thickness. In Eq. (3), the third term represents the electrical current flowing through the pores. De Bruin and Krassowska derived the expression for JEP and modeled it as42 
(4)
where N is the pore number. iEP is the current through a single pore,43 
(5)
where rm (see Table I) is the radius of the pore. A is expressed as
(6)
(7)
TABLE I.

Parameters for model properties.

SymbolTypeValueReference
σ (conductivity) Blood 0.7 S/m 32  
Extravascular tissue 0.0277 S/m 32  
Connective tissue 0.251 S/m 32  
Cytoplasm 0.3 S/m 32  
Membrane 5 × 10−7 S/m 32  
ɛ (relative permittivity) Blood 5.23 × 103 32  
Extravascular tissue 1.51 × 107 32  
Connective tissue 1.99 × 107 32  
Cytoplasm 80 32  
Membrane 8.57 32  
q Pore creation rate 2.46 42  
R Gas constant 8314 42  
F Faraday’s constant 96 500 42  
n Relative entrance length of pore 0.15 42  
Vep (V) Characteristic voltage of electroporation 0.17 42  
T (K) Absolute temperature 295 42  
h (nm) Membrane thickness 5 43  
rm (nm) Pore radius 0.8 43  
N0 (m−2) Pore density when Vm = 0 mV 1.5 × 109 43  
α (m−2 ms−1) Creation rate coefficient 109 43  
SymbolTypeValueReference
σ (conductivity) Blood 0.7 S/m 32  
Extravascular tissue 0.0277 S/m 32  
Connective tissue 0.251 S/m 32  
Cytoplasm 0.3 S/m 32  
Membrane 5 × 10−7 S/m 32  
ɛ (relative permittivity) Blood 5.23 × 103 32  
Extravascular tissue 1.51 × 107 32  
Connective tissue 1.99 × 107 32  
Cytoplasm 80 32  
Membrane 8.57 32  
q Pore creation rate 2.46 42  
R Gas constant 8314 42  
F Faraday’s constant 96 500 42  
n Relative entrance length of pore 0.15 42  
Vep (V) Characteristic voltage of electroporation 0.17 42  
T (K) Absolute temperature 295 42  
h (nm) Membrane thickness 5 43  
rm (nm) Pore radius 0.8 43  
N0 (m−2) Pore density when Vm = 0 mV 1.5 × 109 43  
α (m−2 ms−1) Creation rate coefficient 109 43  
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F, R, and T (see Table I) represent Faraday's constant, the gas constant, and the absolute temperature, respectively. The energy barrier ω0 accounted for the narrowing of the pore as it crosses the lipid bilayer as well as the electrical interactions between the ions and the pore wall. N(t) is given by43 
(8)
where N0 is the pore density at Vm = 0 mV and α, VEP, and q are constants. The model parameter setup is shown in Table I.31,42,43

Three endothelial cells (cells 1–3) and three VSMCs (cells 4–6) at θ = 0°, 45°, and 90° were extracted for analysis [Fig. 2(a)]. θ is the angle between the vessel surface vector and the vector of the electric field direction. The transmembrane voltage (TMV) and pore density at two points in the middle membrane of these cells near the connective tissue and blood were analyzed. Points 1–6 are located in the endothelial cells. Points 7–12 are located in the VSMCs. For monopolar pulses (MP), the simulation time (pulse width) was 100 μs. For high-frequency bipolar pulses (HFBPs), the pulse width was 1 μs. The pulses began with a positive pulse (1 μs), followed by a 1 μs pause, and then a negative pulse (1 μs). This circling was repeated until the energized time was 100 μs, which was the same as the monopolar pulses. The simulation time was 200 μs [Fig. 2(b)]. The voltage of the external pulse is first set to 200 V for simulation. The external electric field is 1 kV/cm.

FIG. 2.
(a) The positions of points 1–12 in the model shown in Fig. 1.31 Points 1–6 are located in the endothelial cells. Points 7–12 are located in the VSMCs. (b) Schematic of monopolar pulses and high-frequency bipolar pulses used for simulation.
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(a) The positions of points 1–12 in the model shown in Fig. 1.31 Points 1–6 are located in the endothelial cells. Points 7–12 are located in the VSMCs. (b) Schematic of monopolar pulses and high-frequency bipolar pulses used for simulation.

FIG. 2.
(a) The positions of points 1–12 in the model shown in Fig. 1.31 Points 1–6 are located in the endothelial cells. Points 7–12 are located in the VSMCs. (b) Schematic of monopolar pulses and high-frequency bipolar pulses used for simulation.
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(a) The positions of points 1–12 in the model shown in Fig. 1.31 Points 1–6 are located in the endothelial cells. Points 7–12 are located in the VSMCs. (b) Schematic of monopolar pulses and high-frequency bipolar pulses used for simulation.

Close modal

The MUMPS solver was performed for the whole-domain calculation with backward differentiation formulas. A free time-stepping algorithm was used during the computation. The minimal and maximal step sizes were 1 and 50 ns, respectively. The fine element size parameter was set to generate a triangular mesh consisting of 415 818 domain elements (different size) and 1 063 615 degrees of freedom. The PC with a 2.9 GHz Intel Core i7 CPU and 16 GB RAM was used for a single simulation.

Figure 3 plots the time evolution of the TMV (transmembrane voltage) and pore density on points 1–6 of the endothelial cell membrane in normal blood vessels by HFBP [(a) and (b)] and MP [(c) and (d)]. For the cell where θ = 90°, the TMV of points 5 and 6 is close to zero. Therefore, no electroporation is generated at points 5 and 6. Figure 3(a) indicates that the TMV at locations near connective tissue (points 1, 3, and 5) is lower than that at locations near blood (points 2, 4, and 6). Therefore, the pore density at locations near connective tissue is also lower than that at locations near blood [Fig. 3(b)]. For instance, the pore density at point 2 is 4.9 × 1014 m−2, which is significantly larger than that at point 1 (3.5 × 109 m−2). The change of pore density by MP is similar to HFBP [Fig. 3(d)]. It is also interesting that the pore density at locations near blood (points 2 and 4) increases more rapidly than that at locations near connective tissue (points 1 and 3). For point 1, the pore density by MP is 3.6 × 1015 m−2, which is significantly larger than that by HFBP.

FIG. 3.
The TMV evolution (with an enlarged view) and pore density on points 1–6 of endothelial cells in the normal blood vessel by high-frequency bipolar pulses (HFBP) [(a) and (b)] and monopolar pulses (MP) [(c) and (d)] during an electric pulse.
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The TMV evolution (with an enlarged view) and pore density on points 1–6 of endothelial cells in the normal blood vessel by high-frequency bipolar pulses (HFBP) [(a) and (b)] and monopolar pulses (MP) [(c) and (d)] during an electric pulse.

FIG. 3.
The TMV evolution (with an enlarged view) and pore density on points 1–6 of endothelial cells in the normal blood vessel by high-frequency bipolar pulses (HFBP) [(a) and (b)] and monopolar pulses (MP) [(c) and (d)] during an electric pulse.
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The TMV evolution (with an enlarged view) and pore density on points 1–6 of endothelial cells in the normal blood vessel by high-frequency bipolar pulses (HFBP) [(a) and (b)] and monopolar pulses (MP) [(c) and (d)] during an electric pulse.

Close modal

Figure 4 plots the time evolution of the TMV (transmembrane voltage) and pore density on points 1–6 of the endothelial cell membrane in tumor blood vessels by HFBP [(a) and (b)] and MP [(c) and (d)]. The TMV of the endothelial cell membrane in tumor blood vessels is similar to that of the normal blood vessels. However, the absolute TMV value of point 2 at the first high-frequency pulse (0.96 V) is obviously higher than the subsequent pulse in the model of the tumor blood vessel. For normal blood vessels, the absolute TMV value of point 2 at the first high-frequency pulse is 0.86 V [Fig. 3(a)], which is also lower than that in the model of tumor blood vessels. For MP, the maximum absolute TMV of point 2 (0.97 V) in the model of the tumor blood vessels is also higher than that in the model of normal blood vessels (0.88 V). Correspondingly, the pore density in the tumor blood vessels is also obviously larger than that in the normal blood vessels for both the stimulations of high-frequency pulses and monopolar pulses.

FIG. 4.
The TMV evolution and pore density of points 1–6 of endothelial cells during the electric pulse in the tumor blood vessel by high-frequency bipolar pulses (HFBP) [(a) and (b)] and monopolar pulses (MP) [(c) and (d)].
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The TMV evolution and pore density of points 1–6 of endothelial cells during the electric pulse in the tumor blood vessel by high-frequency bipolar pulses (HFBP) [(a) and (b)] and monopolar pulses (MP) [(c) and (d)].

FIG. 4.
The TMV evolution and pore density of points 1–6 of endothelial cells during the electric pulse in the tumor blood vessel by high-frequency bipolar pulses (HFBP) [(a) and (b)] and monopolar pulses (MP) [(c) and (d)].
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The TMV evolution and pore density of points 1–6 of endothelial cells during the electric pulse in the tumor blood vessel by high-frequency bipolar pulses (HFBP) [(a) and (b)] and monopolar pulses (MP) [(c) and (d)].

Close modal

Figure 5 plots the time evolution of the TMV and pore density on points 7–12 of the VSMCs in normal blood vessels by HFBP [(a) and (b)] and MP [(c) and (d)]. The pore density on VSMCs by MP is significantly higher than that by HFBP. For instance, at θ = 0°, the pore density of point 7 by MP is 1.9 × 1016 m−2, which is larger than that by HFBP (2.2 × 1010 m−2).

FIG. 5.
The TMV evolution and pore density of points 7–12 of VSMCs during an electric pulse in a normal blood vessel by high-frequency bipolar pulses (HFBPs) [(a) and (b)] and monopolar pulses (MP) [(c) and (d)].
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The TMV evolution and pore density of points 7–12 of VSMCs during an electric pulse in a normal blood vessel by high-frequency bipolar pulses (HFBPs) [(a) and (b)] and monopolar pulses (MP) [(c) and (d)].

FIG. 5.
The TMV evolution and pore density of points 7–12 of VSMCs during an electric pulse in a normal blood vessel by high-frequency bipolar pulses (HFBPs) [(a) and (b)] and monopolar pulses (MP) [(c) and (d)].
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The TMV evolution and pore density of points 7–12 of VSMCs during an electric pulse in a normal blood vessel by high-frequency bipolar pulses (HFBPs) [(a) and (b)] and monopolar pulses (MP) [(c) and (d)].

Close modal

Figure 6 shows the electroporation region distribution in endothelial cells 1–3 for both models of normal blood vessels and tumor blood vessels. One pore is correlated to a pore density of 4.07 × 109 m−2.37 In general, the cells experience different electroporation regions due to the various locations. The electroporation region in tumor blood vessels is significantly larger than that in normal blood vessels by both HFBP and MP. In particular, in the model of normal blood vessels, the electroporation region of cell 1 by HFBP is larger than that by MP. However, for tumor blood vessels, the electroporation region of cell 1 by HFBP is similar to that by MP.

FIG. 6.
The electroporation region distribution of the endothelial cells (cells 1–3) near θ = 0°, 45°, and 90° in normal blood vessels and tumor blood vessels at the end of high-frequency bipolar pulses (HFBP) and monopolar pulses (MP), respectively.
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The electroporation region distribution of the endothelial cells (cells 1–3) near θ = 0°, 45°, and 90° in normal blood vessels and tumor blood vessels at the end of high-frequency bipolar pulses (HFBP) and monopolar pulses (MP), respectively.

FIG. 6.
The electroporation region distribution of the endothelial cells (cells 1–3) near θ = 0°, 45°, and 90° in normal blood vessels and tumor blood vessels at the end of high-frequency bipolar pulses (HFBP) and monopolar pulses (MP), respectively.
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The electroporation region distribution of the endothelial cells (cells 1–3) near θ = 0°, 45°, and 90° in normal blood vessels and tumor blood vessels at the end of high-frequency bipolar pulses (HFBP) and monopolar pulses (MP), respectively.

Close modal

Figures 7(a)–7(d) demonstrate the time evolution of the pore number of the endothelial cells 1–3 by HFBP [(a) and (b)] and MP [(c) and (d)]. For cell 1 (θ = 0°), the total pore number is 1.4 × 106 by HFBP, which is lower than that by MP (2.5 × 107) in the model of normal blood vessels. However, in tumor blood vessels, the total pore number remains similar (1.4 × 108) for both HFBP and MP. For cell 3 (θ = 90°), the total pore number by HFBP is lower than that by MP in the models of both normal blood vessels and tumor blood vessels. For different locations, the endothelial cells experience various pore numbers.

FIG. 7.
The pore number of cells 1–3 during an electric pulse in both normal and tumor blood vessels by high-frequency bipolar pulses (HFBP) [(a) and (b)] and monopolar pulses (MP) [(c) and (d)]. (a) and (c) are for normal blood vessels; (b) and (d) are for tumor blood vessels.
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The pore number of cells 1–3 during an electric pulse in both normal and tumor blood vessels by high-frequency bipolar pulses (HFBP) [(a) and (b)] and monopolar pulses (MP) [(c) and (d)]. (a) and (c) are for normal blood vessels; (b) and (d) are for tumor blood vessels.

FIG. 7.
The pore number of cells 1–3 during an electric pulse in both normal and tumor blood vessels by high-frequency bipolar pulses (HFBP) [(a) and (b)] and monopolar pulses (MP) [(c) and (d)]. (a) and (c) are for normal blood vessels; (b) and (d) are for tumor blood vessels.
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The pore number of cells 1–3 during an electric pulse in both normal and tumor blood vessels by high-frequency bipolar pulses (HFBP) [(a) and (b)] and monopolar pulses (MP) [(c) and (d)]. (a) and (c) are for normal blood vessels; (b) and (d) are for tumor blood vessels.

Close modal

Figure 8(a) shows the electroporation region distribution in cells 4–6 (VSMCs) in the model of normal blood vessels. For cells 4 and 5, the electroporation region by MP is obviously larger than that by HFBP. Figure 8(b) shows the calculated pore number in cells 4–6 by both HFBP and MP. For three cells in different locations, the total pore number by MP is also larger than that by HFBP. For instance, the pore number of cell 4 is 565, which is significantly lower than that of MP (2.5 × 107).

FIG. 8.
The electroporation region distribution (a) and pore number calculation (b) in cells 4–6 in the model of normal blood vessels at the end of high-frequency bipolar pulses (HFBP) and monopolar pulses (MP).
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The electroporation region distribution (a) and pore number calculation (b) in cells 4–6 in the model of normal blood vessels at the end of high-frequency bipolar pulses (HFBP) and monopolar pulses (MP).

FIG. 8.
The electroporation region distribution (a) and pore number calculation (b) in cells 4–6 in the model of normal blood vessels at the end of high-frequency bipolar pulses (HFBP) and monopolar pulses (MP).
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The electroporation region distribution (a) and pore number calculation (b) in cells 4–6 in the model of normal blood vessels at the end of high-frequency bipolar pulses (HFBP) and monopolar pulses (MP).

Close modal

Figures 3–7 show that the endothelial cells in normal blood vessels experience a different electroporation compared with tumor blood vessels for both stimulation of HFBP and MP. In order to overall study the whole pore number and electroporation region of blood vessels by electric pulse, Fig. 9 calculates the whole pore number and electroporation region in both the quarter of normal and tumor blood vessels. Figure 9(a) intuitively shows that the electroporation region in normal blood vessels is larger than that in tumor blood vessels.

FIG. 9.
The electroporation region distribution (a), pore number (b), and pore region (c) of whole ECs in part of normal and tumor blood vessels by high-frequency bipolar pulses (HFBP) and monopolar pulses (MP).
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The electroporation region distribution (a), pore number (b), and pore region (c) of whole ECs in part of normal and tumor blood vessels by high-frequency bipolar pulses (HFBP) and monopolar pulses (MP).

FIG. 9.
The electroporation region distribution (a), pore number (b), and pore region (c) of whole ECs in part of normal and tumor blood vessels by high-frequency bipolar pulses (HFBP) and monopolar pulses (MP).
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The electroporation region distribution (a), pore number (b), and pore region (c) of whole ECs in part of normal and tumor blood vessels by high-frequency bipolar pulses (HFBP) and monopolar pulses (MP).

Close modal

Figure 9(b) calculates the whole pore number in both normal blood vessels and tumor blood vessels. The whole pore number experiences a rapid rise and then moderately increases to a plateau. For HFBP, the whole pore number in normal blood vessels is 1.1 × 108, which is significantly lower than that in tumor blood vessels (1.1 × 1010). For MP, the whole pore number in normal blood vessels is 2.0 × 109, which is also significantly lower than that in tumor blood vessels (1.2 × 1010). For both HFBP and MP, the tumor blood vessels experience a higher electroporation degree compared with normal blood vessels. It is also interesting to find that the pore number by HFBP is similar to that by MP in tumor blood vessels. However, for normal blood vessels, the pore number by HFBP is significantly lower than that by MP. In this study, we use the pore number ratio of tumor/normal blood vessels (PNT/PNN) to express the ability to electroporate tumor blood vessels while preserving normal blood vessels. The PNT/PNN is 100 for HFBP and 6 for MP. This numerical analysis indicates that HFBP is more efficient in electroporating tumor blood vessels while preserving normal blood vessels, compared with MP.

Figure 9(c) calculates the whole percentages of the electroporation regions of endothelial cells in both normal blood vessels and tumor blood vessels. The whole pore region also experiences a rapid rise and then moderately increases to a plateau. Similarly, the pore region in tumor blood vessels is also larger than that in normal blood vessels. For HFBP, the whole pore region in normal blood vessels is 29.1%, which is significantly lower than that in tumor blood vessels (63.4%). For MP, the whole pore number in normal blood vessels is 57.1%, which is significantly lower than that in tumor blood vessels (70.9%). We also use the pore region ratio of tumor/normal blood vessels’ PRT/PRN to express the ability to electroporate tumor blood vessels while preserving normal blood vessels. The PRT/PRN is 2.2 for HFBP and 1.2 for MP. Figure 9 shows that HFBP is more efficient in electroporating tumor blood vessels while preserving normal blood vessels, compared with MP.

Figure 10 shows the pore number (a)–(c) and electroporation region (d)–(f) of endothelial cells in normal blood vessels and tumor blood vessels with various electric fields. The endothelial cells in normal blood vessels experience an electroporation effect when the external electric field is over 0.75 kV/cm. However, the electroporation has already occurred in the membrane of endothelial cells by an electric pulse with 0.5 kV/cm for the model of tumor blood vessels. Electric pulses with higher fields not only increase the pore number but also enlarge the electroporation region. Both the pore number and electroporation area in tumor blood vessels are larger than those in normal blood vessels. This indicates that the tumor blood vessels are larger than those in normal blood vessels. This indicates that the tumor blood vessels suffer a higher electroporation degree than normal blood vessels. Figure 10(c) shows the PNT/PNN with various electric fields. For the external electric field of 0.75 kV/cm, the PNT/PNN by HFBP (213 918) is significantly higher than that by MP (604). For the external electric field of 2.0 kV/cm, the PNT/PNN is 3.2 for HFBP and 2.2 for MP. The difference in PNT/PNN between HFBP and MP is gradually small with the increased electric field. Nevertheless, PNT/PNN by HFBP is obviously larger than that by MP. For the electroporation region, the PRT/PRN by HFBP is also obviously larger than that by MP, with a similar trend in PNT/PNN. For the external electric field of 0.75 kV/cm, the PNT/PNN by HFBP (6.8) is significantly higher than that by MP (3.1). Figure 10 further demonstrates that HFBP is more efficient in electroporating tumor blood vessels while preserving normal blood vessels, compared with MP.

FIG. 10.
The pore number and pore region of whole ECs in both normal and tumor blood vessels by high-frequency bipolar pulses (HFBP) [(a) and (b)] and monopolar pulses (MP) [(c) and (d)]. Pore number ratio of tumor/normal blood vessels PNT/PNN (E) and pore region ratio of tumor/normal blood vessels PRT/PRN (f) by high-frequency bipolar pulses (HFBP) and monopolar pulses (MP).
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The pore number and pore region of whole ECs in both normal and tumor blood vessels by high-frequency bipolar pulses (HFBP) [(a) and (b)] and monopolar pulses (MP) [(c) and (d)]. Pore number ratio of tumor/normal blood vessels PNT/PNN (E) and pore region ratio of tumor/normal blood vessels PRT/PRN (f) by high-frequency bipolar pulses (HFBP) and monopolar pulses (MP).

FIG. 10.
The pore number and pore region of whole ECs in both normal and tumor blood vessels by high-frequency bipolar pulses (HFBP) [(a) and (b)] and monopolar pulses (MP) [(c) and (d)]. Pore number ratio of tumor/normal blood vessels PNT/PNN (E) and pore region ratio of tumor/normal blood vessels PRT/PRN (f) by high-frequency bipolar pulses (HFBP) and monopolar pulses (MP).
View largeDownload slide

The pore number and pore region of whole ECs in both normal and tumor blood vessels by high-frequency bipolar pulses (HFBP) [(a) and (b)] and monopolar pulses (MP) [(c) and (d)]. Pore number ratio of tumor/normal blood vessels PNT/PNN (E) and pore region ratio of tumor/normal blood vessels PRT/PRN (f) by high-frequency bipolar pulses (HFBP) and monopolar pulses (MP).

Close modal

Most experimental studies have shown that the electric pulse could also electroporate cells in the blood vessels. In order to study the discriminative electroporation effect between tumor and normal blood vessels, this paper built a 2D multicell-layer model to simulate the electroporation distribution in both the normal and tumor blood vessels. The function of endothelial cells is important for normal and tumor blood vessels. Therefore, this study mainly studied the electroporation effect on endothelial cells. In the previous study, we preliminarily showed that the endothelial cells in normal blood vessels sustained a lower transmembrane voltage than that in tumor blood vessels. This study further validates that the tumor blood vessels produce a stronger electroporation effect than normal blood vessels, considering the electroporation equation, even for HFBP. However, compared with traditional MP, both the tumor and normal blood vessels experience a different electroporation effect by HFBP.

Figures 3 and 4 show that the electroporation effect varies on the membrane of endothelial cells at different locations of blood vessels. Golberg et al. found that the liver cells around the larger vessel structures appeared less affected by IRE ablation than cells in the tissue parenchyma.44 Through the simulation of electric field distribution, the local electric field increases in the areas around the vessel in the plane perpendicular to the electrodes. However, the local electric field is decreased in the areas around the vessel in a plane-parallel to the electrodes. The experiment also showed that the residual cells after IRE ablation also occurred around the vessel in a plane-parallel to the electrodes due to the relatively weak electric field. This study also found that the electroporation effect of endothelial cells correlates to the areas in the blood vessels. Generally, the occurrence of the electroporation effect depends on the threshold value of TMV. A stronger electroporation effect could occur with higher TMV. For instance, the electroporation on point 2 occurs with higher absolute TMV (0.87 V), compared with point 4 (0.66 V) for MP stimulation. The pore density of point 1 is also higher than that of point 4. The area where the TMV maintain a high value could suffer a stronger electroporation effect. The cell where θ is smaller suffers a stronger electroporation effect on the membrane of endothelial cells of blood vessels in the plane-parallel to the electrodes but a weak electroporation effect on the membrane of endothelial cells of blood vessels in the plane perpendicular to the electrodes.

Generally, the blood vessels generated by tumors can provide a pathway to draw nutrients for tumor growth, which is an obstacle to tumor treatment. Except for direct tumor cell ablation, the electroporation technique (such as ECT) could also disrupt the function of blood vessels (vascular lock effect). The perturbation of tumor blood vessels could contribute to the complete tumor ablation. Sersa et al.20 found that ECT could also make electroporated endothelial cells dead, resulting from the high concentration of bleomycin in tumor blood vessels. Jarm et al.45 reviewed the anti-vascular effects of ECT and found that the tumor vessels were irreversibly disrupted while the normal blood vessels were preserved.

A tumor blood vessel looks more like a capillary in structure. Compared with normal blood vessels (veins), the most obvious difference is that the tumor vasculatures have walls that contain only a single layer of endothelium, but their diameters are much larger than the normal capillaries. Many studies have confirmed that electroporation tumor treatment can preserve the function of large blood vessels (arteries, veins, etc.).11–15 Our previous study46,47 showed that capillary-like structures (sinusoids in the liver) are destroyed while the structure of veins is intact after IRE treatment. It seems that the capillary-like structure is more sensitive to electroporation than veins for electroporation treatment. This study investigated the electroporation effect by building the tumor (capillary-like structure) and normal blood vessels (veins) with a cell structure. Due to this structural difference, the electric pulse could generate a stronger electroporation effect on tumor blood vessels compared with normal blood vessels (veins). The rich vascular smooth muscle cells (VSMCs) could play a protective function for ECs in normal blood vessels, compared with capillary-like vessels.

In general, the existence of VSMCs may distort the local electric field, which may cause a drop in pore number. The TMV value is also positively related to the local electric field.39,40 Figure 11 shows the local electric field at the line of θ = 0 with a distance of 0.5 μm from the ECs in both the normal and tumor blood vessels using both HFBP and MP. For both MP and HFBP stimulation, the local electric field in tumor blood vessels is obviously larger than that in normal blood vessels. Generally, the TMV is positively related to the electroporation degree. A higher TMV could be generated with a larger local electric field. For MP stimulation, the maximum TMV of point 1 in normal blood vessels is 0.87 V but 0.97 V in tumor blood vessels. The pore density of point 1 in normal blood vessels (3.7 × 1015 m−2) is also significantly lower than that in tumor blood vessels (8.3 × 1015 m−2). Figure 9 also shows that the pore number of all ECs in normal blood vessels is lower than that in tumor blood vessels for both HFBP and MP stimulations. The discriminative electroporation effect between tumor and normal blood vessels may result from the distortion of the local electric field with the existence of VSMCs.

FIG. 11.
The local electric field at the line of θ = 0 with a distance of 0.5 μm from the ECs (near point 1) in the normal and tumor blood vessels by MP (a) and HFBP (b).
View largeDownload slide

The local electric field at the line of θ = 0 with a distance of 0.5 μm from the ECs (near point 1) in the normal and tumor blood vessels by MP (a) and HFBP (b).

FIG. 11.
The local electric field at the line of θ = 0 with a distance of 0.5 μm from the ECs (near point 1) in the normal and tumor blood vessels by MP (a) and HFBP (b).
View largeDownload slide

The local electric field at the line of θ = 0 with a distance of 0.5 μm from the ECs (near point 1) in the normal and tumor blood vessels by MP (a) and HFBP (b).

Close modal

Recently, high-frequency bipolar pulses, which replace monopolar pulses, could significantly eliminate muscle contractions during tumor treatment. However, the cell-killing effect of high-frequency bipolar pulses is weaker than that of traditional monopolar pulses with the same electric dose, which has been investigated by many works of the literature.48–50 This paper also simulated the electroporation effect on endothelial cells in both tumor blood vessels and normal blood vessels using high-frequency bipolar pulses. In our previous study, the single-cell simulation and experimental results also showed that the cell electroporation effect by HFBP is weaker than that by MP under the same energized time due to the short pulse.48 Generally, the pore number of the cell membrane is mainly related to the transmembrane voltage (TMV) with enough time, which is shown in Eq. (8). Figures 3 and 4 in the manuscript have shown that the pore density is positively related to the value of TMV. For instance, the peak TMV of point 1 is 0.58 V for HFBP but 0.86 V for MP in normal blood vessels. The pore density of HFBP (3.5 × 109 m−2) is also smaller than that of MP (3.6 × 1015 m−2), although the pore density slightly increases with a high pulse number for HFBP. The TMV can be limited by the short width. Therefore, the weak cell electroporation resulting from HFBP may be attributed to the smaller width and high frequency in normal blood vessels. For tumor blood vessels, the peak TMV of point 1 is 0.94 V for HFBP but 0.97 V for MP in the tumor blood vessels. The pore density of HFBP (7.9 × 1015 m−2) is similar to that of MP (8.3 × 1015 m−2). Due to the lack of VSMCs, the local electric field is less affected compared with the normal blood vessels. Even with a short width, HFBP could generate high TMV for electroporation at the first pulse. Therefore, both HFBP and MP could generate a larger pore number in tumor blood vessels than in normal blood vessels.

Figure 10 shows that the electroporation effect of endothelial cells increases with higher electric field strength using HFBP and MP. Siddiqui et al. found that minor endothelial damage occurred in normal blood vessels that were proximal to electrode insertion, which suffered a stronger electric field.40 Therefore, it is suggested that a stronger electric field could also damage the endothelial cells. Moreover, at a lower electric field, there is a large difference in pore number between the tumor blood vessels and normal blood vessels. This difference is gradually small with the increased electric field, which indicates that the electric field with a higher strength may damage both tumor and normal blood vessels. At a lower external electric field, the TMV cannot reach the threshold value due to the distortion of the local electric field from VSMCs. Therefore, there is a large difference in the electroporation effect between normal and tumor blood vessels. However, with a higher external electric field, even with the existence of VSMCs, the electroporation region is gradually enlarged where the TMV is above the threshold value with a higher external electric field. Therefore, the difference in the electroporation effect between normal and tumor blood vessels gradually becomes smaller. However, the electroporation effect in tumor blood vessels is still larger than that in normal blood vessels. Figures 9 and 10 also validate that the pore number and pore region by the high-frequency bipolar pulses are smaller than those by the monopolar pulses. For 1 kV/cm, the pore number by high-frequency bipolar pulses (1.1 × 108) is smaller than that by monopolar pulses (2.0 × 109) in normal blood vessels. However, with a higher external electric field, the difference in pore number between high-frequency bipolar pulses and monopolar pulses is also gradually small. This phenomenon also occurs in the tumor blood vessel. The simulated result also validates that the electroporation effect on blood vessels by high-frequency bipolar pulses is weak compared with monopolar pulses. However, it is interesting that the difference in electroporation effect between tumor and normal blood vessels by HFBP is larger than that by MP. This simulation result indicates that it is harder for HFBP to electroporate normal blood vessels compared with MP. Figure 11 shows the local electric field at the line of θ = 0 with a distance of 0.5 μm from the ECs (near point 1) in the normal and tumor blood vessels by MP and HFBP. The local electric field by MP is obviously larger than that by HFBP in both normal and tumor blood vessels. Therefore, the electroporation effect by MP is stronger than that by HFBP. The local electric field in normal blood vessels is close to zero (0.14 V/cm) but 137.64 V/cm in tumor blood vessels by HFBP. For MP, the local electric field in normal blood vessels is 201.63 but 349.97 V/cm in tumor blood vessels. The local electric field in normal blood vessels with VSMC is less affected, resulting from the higher frequency and shorter width of HFBP, compared with MP. Moreover, the local electric field may be further decreased due to the capacitive effects of the VSMC with a higher frequency. Baker et al. numerically studied the selective electroporation of tumor cells under radio frequency stimulation and found the demonstration of higher frequencies to induce electroporation in malignant cells, while minimally affecting healthy ones, which suggests the possibility of selective electrical targeting for tumor treatments and protocols.51 This study also found that HFBP causes more targeted damage to the tumor vessels. High frequency may be one of the important factors for selective tumor treatment.

In addition to tumor treatment, the electroporation effect can also be used for blood–brain barrier disruption (BBBD). Due to protection from the blood–brain barrier (BBB), it is hard to accumulate drug concentrations for the treatment of intracranial disorders. The BBB is a highly selective biological barrier mainly resulting from the brain capillary endothelial cells. The electroporation technique has demonstrated the ability to permeate brain capillary endothelial cells and then break the BBB.52,53 Lorenzo et al. found that HFBP can also be used for BBBD with minimal muscle contractions, compared with MP.54 The structure of a capillary, similar to tumor blood vessels, is only made of a single layer of endothelial cells and connective tissue. Figure 10 shows that the HFBP creates a similar pore number and pore region in the capillary model, compared with MP when the external electric field is over 1 kV/cm. Melvin et al. also found that the BBBD was induced with low-magnitude electric fields, and BBBD duration increased with field strength.54  Figure 10 also indicates that the electroporation effect (pore number and pore region) in the capillary (tumor blood vessel model) is enhanced with increased field strength. The blood vessel model built in this study may be useful to study the BBBD by electroporation pulse.

This study studied the electroporation effect, only considering the local electric field. However, the membrane temperature rise may also contribute to the electroporation.55 Christopher et al. found that the lethal threshold with 1–8 μs pulses demonstrates a significant temperature dependence, while the monopolar IRE pulses do not. Milestone et al. proposed a model coupling cell electroporation and thermal effects and concluded that temperature could play a synergistic role in the context of H-FIRE-based tumor protocols.56 This study showed that a monopolar pulse with 100 μs generates a stronger electroporation effect, compared with HFBP under the same energized time. However, this study did not consider the thermal effect by both MP and HFBP. The electroporation process is also obviously affected by temperature rise, particularly on the order of one microsecond. A further numerical study should be conducted by considering the temperature change.

The results obtained in this study are based on the 2D model simulation. Although an obvious structural difference exists (mainly the existence of VSMCs) between normal blood vessels (veins) and tumor blood vessels, the structure model built in this study still needs further improvement. Generally, the diameter of both normal blood vessels with VSMCs and tumor blood vessels varies in mammal tissues for physiological reasons. In order to study the discriminative electroporation effect on both normal blood vessels with VSMCs and tumor blood vessels without VSMCs, this study uses the same inner-diameter model for stimulation. Tumor vessels are known to have high vascular permeability due to the uncontrolled growth rate and loose connection between endothelial cells.27,28 For normal blood vessels, including the capillaries, the endothelial cells are connected relatively tightly. Further structure vessels model should also consider this microscopic difference. The considerable mechanistic difference between tumor and normal blood vessels is not only the structure but also the biology (angiogenic capacity, metabolic differences, etc.) that is susceptible to electroporation. Nevertheless, this study preliminarily showed that tumor blood vessels, without VSMCs, are more sensitive to the electroporation pulses.

This study provides a multi-cell layer model to analyze the electroporation effect (pore number and pore region) of endothelial cells in the vasculature microenvironment. The simulation results showed that the endothelial cells in tumor blood vessels suffer a stronger electroporation effect (pore number and pore region) compared with those in tumor blood vessels. However, the electric field with a higher strength may damage both the tumor and normal blood vessels. High-frequency bipolar pulses are more suitable to electroporate tumor blood vessels, while preserving the normal blood vessels. Furthermore, the model built in this study can be also used to analyze the vasculature electroporation effect for applications of tumor blood disruption, blood–brain barrier disruption, etc.

The authors would like to acknowledge the National Natural Science Foundation of China (NNSFC) (No. 52007172), the China Postdoctoral Science Foundation (No. 2020M672273), and Key Research and Development Special Project of Henan Province (No. 231111211600) for financial support.

The authors have no conflicts to disclose.

Yanpeng Lv: Conceptualization (equal); Investigation (equal); Methodology (equal); Supervision (equal). Shihan Lu: Software (equal); Writing – original draft (equal). Jianhua Zhang: Visualization (equal); Writing – review & editing (equal).

The data that support the findings of this study are available within the article.

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