Technology in Cancer Research & Treatment. Dec/31/2017; 17

Published online Jul/24/2018

PMID: 30045667

PMC: 6071161

doi: 10.1177/1533033818789693

Effect of Tissue Inhomogeneity in Soft Tissue Sarcomas: From Real Cases toNumerical and Experimental Models

Luca Giovanni Campana

Maria Evelina Mognaschi

Abstract

Electrochemotherapy is an established treatment option for patients with superficiallymetastatic tumors, mainly malignant melanoma and breast cancer. Based on preliminaryexperiences, electrochemotherapy has the potential to be translated in the treatment oflarger and deeper neoplasms, such as soft tissue sarcomas. However, soft tissue sarcomasare characterized by tissue inhomogeneity and, consequently, by variable electricalcharacteristic of tumor tissue. The inhomogeneity in conductivity represents the cause oflocal variations in the electric field intensity. Crucially, this fact may hamper theachievement of the electroporation threshold during the electrochemotherapy procedure. Inorder to evaluate the effect of tissue inhomogeneity on the electric field distribution,we first performed ex vivo analysis of some clinical cases to quantifythe inhomogeneity area. Subsequently, we performed some simulations where the electricfield intensity was evaluated by means of finite element analysis. The results of thesimulation models are finally compared to an experimental model based on potato and tissuemimic materials. Tissue mimic materials are materials where the conductivity can besuitably designed. The coupling of computation and experimental results could be helpfulto show the effect of the inhomogeneity in terms of variation in electric fielddistribution and characteristics.

Introduction

Electrochemotherapy (ECT) is a local anticancer therapy that is focused on the treatment ofsmall and superficial tumors. It is based on the combination of short-voltage pulsesdelivered by using needle or plate electrodes and a cytotoxic drug.^1–5 In the standard clinical practice, ECT is applied by means of fixed-geometryelectrodes, 7 needles with a distance of 7.3 mm hexagonally arranged, which apply theelectric field in a volume close to 3 cm3 (depending on the needle length) based on thereference electroporation protocol described by Mir et al and Martyet al.^6,7 During ECT procedure, the operator has arelatively short time interval (after chemotherapy injection) for the application of thevoltage pulses. In particular, the standard operative procedures prescribe the voltage pulseapplication within a 20-minute time interval after chemotherapy administration.^6,7 The drug can be a cheap and nonpermeant one in nonelectropermeabilization conditionswhich, thanks to its short biodisponibility, shows reduced side effects. For this reason,this type of technique shows interesting characteristics for the patient care.

Currently, ECT is applied to treat patients with superficially metastatic melanoma, skintumors, and breast cancer recurrences on the chest wall.^1,2,4,6–8 In recent years, this therapy has been also explored in other types of tumors, suchas liver metastases and soft tissue sarcomas (STS), with promising results.^9–13

The treatment of STS with ECT poses some peculiar challenges, due to their size, anatomicallocation, heterogeneity, and histological characteristics. In fact, patients with STSpresent large and usually deep-seated (eg, intramuscular) tumors and the tumor can arisefrom very different tissues (connective, adipose, muscular, nervous, etc). Finally, eachsingle STS can be highly inhomogeneous from the histological point of view, due to thepresence of different components within it (viable tumor cells [TCs], portions of tumortissue necrosis, myxoid material, etc). Inhomogeneity in the tissue modifies the electricfield distribution. This effect was already shown, for instance, in 2008 by Sersa etal.¹⁴ In particular, they evaluated the effect of vasculature in the electric field distribution.¹⁴

In a previous analysis,¹⁵ the authors found differences in the resistance values evaluated for different needlepairs (needle pair schema in Figure1A) in the same voltage pulse application as shown in Figure 1B. The resistance at each electrode pair wasevaluated following the method used in Ex Vivo Study on Soft Tissue TumoursElectrical Characteristics (ESTTE) protocol.^15–18 This resistance variation could be justified by tissue inhomogeneity.

Figure 1.

A, Schema of the 7-needle electrode and resistance values evaluated applying 8 voltagepulses at each of the 12 pairs. B and C, Resistance values for the cases in Table 1 as function of theenergized pair.

Histopathological analysis has highlighted some interesting cases of inhomogeneity thatoccurs in real tumors. This analysis allowed to isolate some interesting configurations thatwere analyzed by means of finite element analysis (FEM) and experimental models. The finiteelement simulations were used to evaluate the electric field intensity in some simplifiedgeometries. In particular, in order to evaluate the electric field intensity in differentinhomogeneity cases, a 2-needle model, suitably supplied, has been simulated. Simulationresults were compared with experiments on suitable phantoms.

Material and Methods

Histopathological Analysis

The patient data were recorded following the ESTTE protocol described in the study byTosi et al,^15,17,19 evaluating each cases at histological point of view as in those works according tothe World Health Organization classification of tumors of soft tissue and bone.²⁰Table 1 reports the tumor typeand the stroma type. In particular to each specimen, a 7-needle electrode (Figure 2A for an electrode schema) wasimplanted and a sequence of 96 voltage pulses (8 pulses per each of the possible needlepairs), 100 µs long at 5 kHz with amplitude 730 V (needle distance 7.3 mm), was applied.After pulse application, samples were fixed in 10% buffered formalin, embedded inparaffin, and stained with hematoxylin and eosin. For each sample, the average resistanceof the sample and the size of TC and atypical adipocytic component evaluated as in thestudy by Tosi et al^15,17,19 are also reported.

Table 1.

Data of Excised Mass Analyzed Including Type of Tumor and Stroma, Average Size ofCells, and Average Resistivity Evaluated in the study by Campana et al.¹⁵

Patient	Tumor Type	Stroma/Fat Cell	R_av (Ω)	D (µm)	Note
P12	Well-differentiated liposarcoma	Fibrous + fat cells	256.8 ± 40.6 433.5 ± 81.8	AA 89.4 ± 27.6 AA 79.6 ± 21.1	Two electroporation points
P15	Dedifferentiated liposarcoma	Fibrous+ fat cells	101.1 ± 13.8	TC 9.5 ± 3.9	Two histology images
P15	Dedifferentiated liposarcoma	Fibrous + fat cells	101.1 ± 13.8	AA 76.1 ± 24.8
P16	Desmoid-type fibromatosis	Fibrous+ fat cells	120.0 ± 31.7	TC 9.9± 4.1
P18	Myxoid liposarcoma	Myxoid+ fat cells	52.9 ± 11.6	TC 6.3 ± 2.0 AA 18.3 ± 7.3

Abbreviations: AA, atypical adipocytic; TC, tumor cells.

Figure 2.

Electric field distribution in (A) homogeneous model. B and C, Differentconfiguration of the model B in Figure 3. The gray rectangle shows the potato area.

The inhomogeneity analysis has been performed comparing the area of inhomogeneity in realcases and the area covered by the standard 7-needle electrode. In this case, the 7-needleelectrode was superposed to the 1× image according to the image scale and the electrodesizes. An example is in Figure 3.Moreover, for the points from P₁ to P_N, magnified images werecaptured and shown near the 1× image. In the 1× image, the size of the histology sample isreported.

Figure 3.

Example of the inhomogeneity analysis in a real case (undifferentiated epithelioidsarcoma) with magnified images.

Computation Model

A simple parallelepiped model (35 mm × 50 mm × 10 mm) has been used in 3-dimensionalnumerical computations.^21–25 The model includes 2 needles (1.0 cm long, 0.5 mm diameter, and an interneedledistance, d of 7.3 mm, inserted into the parallelepiped), as shown inFigure 4, in accordance withproposed literature models.^26,27 The parallelepiped volume was divided into 2 or 3 subvolumes, each onecharacterized by a different conductivity value. The different subvolumes considered aresketched in Figure 5. Thedifference in conductivity of the subvolumes would mimic the inhomogeneity of the tumortissue as shown in the previous analysis (eg, in Figure 3).

Figure 4.

Three-dimensional numerical model for the 2 needle case²⁶: (A) problem geometry and (B) electric field intensity sampling line.

Figure 5.

Different arrangement of the numerical models with 2 needles considering differentinhomogeneity cases.

The electric field intensity due to the voltage applied between a pair of needles wascomputed using FEM as proposed by more research groups.^25,28–32 The electric field intensity has been computed by means of finite element simulator(COMSOL; https://www.comsol.it/), solving Laplace equation in static condition. Then,an electrical conduction problem on electric scalar potential, V,imposing a constant potential on the needle surfaces^29,33 and considering a conductivity dependent on electric field^29,34–37 σ(E) was solved as follows:1∇⋅σ(E)∇V=0inside the parallepiped.

The potential imposed to the 2 needle surfaces was +730/2 V for electrode 1 in Figure 4 and −730/2 V for electrode 2in Figure 4, according to thestudy by Marty et al and Mir et al.^6,7 Finally, a tangent condition of electric field lines was imposed on the externalboundary of the model as in the study by Ongaro et al^26,27:2∂V∂n=0on external boundary.

The conductivity σ(E) in some cases was posed constant and in othersfollows the nonlinear model proposed by Breton et al³⁵ and used in^36,37:3σ(E)=σ0+σEP−σ02(1+tanh(kv(E−Eth))),

where σ₀ and σ_EP are the conductivity of the nonelectropored andelectropored tissue, respectively, and k_v and E_th are parameters obtained fitting experimental data as in the study by Campanaet al and Dughiero et al.^36,37 For instance, possible parameter values for Equation 3 are σ₀ = 0.04 S/m,σ_EP = 0.12 S/m, k_v = 0.0004 m/V, E_th = 11 500 V/m (potato as in the study by Breton et al³⁵) or σ₀ = 0.2 S/m, σ_EP = 0.8 S/m, k_v = 0.0004 m/V, E_th = 9000 V/m (epidermis as in the study by Pavšelj et al^30,38). The parameters used in this article were evaluated experimentally bymeasurements.

A schematic representation of the models with 2 needles is shown in Figure 5. In these models, σ₁ andσ₂ represent different conductivities suitably designed in order to be loweror comparable to the one of the electroporated potato, according to the combinations ofgel and potato in Table 2. Inparticular, 2 types of gel with different conductivity were used. The electric field hasbeen sampled on the parallelepiped surface (xy layer) and 2-imensionalequilevel maps were shown.^27,28

Table 2.

Setups for Numerical and Experimental Models.

	#1	#2	#3	#4	#5	#6
Geometry	A	B	B	C	C	Figure 4
σ₁	Potato	Potato	Gel	Potato	Gel	Potato
σ₂	Gel	Gel	Potato	Gel	Potato	Gel
Simulation (S)/test (T)	S/T	S/T	S/T	S/T	S	S/T
Gel type	SC1, D2	SC1′, D2′	SC1′, D2′	SC1′, D2′	SC1′, D2′	SC1′, D2′

Tissue Mimic Materials

The gel phantoms, made of tissue mimic materials (TMM), have been produced according to aslightly modified procedure as the one proposed in the study by Mobashsher and Abbosh.³⁹ Gelatin, water, agar, corn flour, glycerin, sodium azide (NaN₃), andsodium chloride (NaCl) were commercially available and used as received. The list andamount of starting ingredients for the production of the phantoms is reported in Table 3.^36,37

The procedure for the preparation of the materials D2 and SC1 follows the procedure inthe study by Campana et al and Dughiero et al,^36,37 whereas the one for the preparation of the modified TMM (D2′ and SC1′) follows thesteps reported below (NaN₃, was substituted by NaCl). First, the corn flour ismixed in a beaker with 20 mL of deionized water and glycerin at room temperature, while ina second beaker other 50 mL of deionized water was used to dissolve the NaCl and thegelatin or agar. The content of the second beaker is heated using a microwave oven (Qlive,700 W microwave) for 30″ (mix final temperature close to 90°C). The 2 mixtures were mixedand heated by means of a microwave oven and stirred vigorously until the whole mixtureturns semisolid (the total heating time depends on the dielectric properties ofmaterials). The TMM is finally cast into boxes with the suitable sizes for experiments. Inthe experiments with potatoes, both the 2 types of gels, D2, SC1, D2′, and SC1′, wereused.

Voltage Pulses

Voltage pulses were applied by means of plate electrode or 2-needle electrode connectedto the generator EPS02 manufactured by Igea S.p.A., Carpi (MO), Italy. At electrodeextremities, 8 rectangular voltage pulses, 100 µs long (duty cycle 50%) at 5 kHz, wereapplied. Voltage amplitude varied according to the electrode distance (eg, from 100 to 700V for plate electrode and 730 V for the 2-needle or 7-needle electrode). The plateelectrode was supplied with voltage pulses applied considering the same polarity for theplates (voltage pulse sequence, VPS8), whereas the 8 pulses of the 2-needle electrode wereapplied changing the polarity of the needles after 4 pulses (VPS4).

Experimental Tests

In experimental tests, a combination of potato samples and TMM was used. In fact, it iswell known that potato became dark few hours after electroporation.^28,40,41 All the samples were preserved covered by plastic film at room temperature andobserved for 24 hours after pulses applications as in the study by Ongaro etal and Campana et al.^28,42

The experimental tests were performed in 2 steps. The aim of the first step (step 1) isthe evaluation of the conductivity of potato and gels obtained following the new procedureand the conductivity of the potato tuber. The experimental setup is illustrated in Figure 6A. In this case, each box ofthe chamber slide was filled by one of the gels or by potato samples. In particular, gelswere cast avoiding air bubbles. For each type of gel, the plate electrode was positionedas in Figure 6A and was suppliedwith 8 pulses following the sequence VPS8. In this case, the voltage amplitude applied togels was 100 and 500 V according to Campana et al and Dughiero etal.^36,37

Figure 6.

Experimental setup for the step 1 (A) and step 2 (B, C).

From voltage V and current I, measured by EPS02, theconductivity σ (in S/m) has been computed from the estimated resistance,R = V/I, of a parallelepiped withsection A (10 mm × 11.3 mm) and a plate distance L of 7 mm (Figure 7A):4σ=R−1LA.

Figure 7.

Images of real specimens (magnification ×1) and zoom of some interesting points interms of inhomogeneity: (A) case P15, (B) case P18, and (C) case P12.

The resistivity ρ (in Ω·m) is the inverse of the conductivity σ, ρ = σ⁻¹.

In the case of the potato samples, the voltage amplitude was varied in the range 100 to700 V in order to evaluate the parameters of Equation 3 according to Campana etal and Dughiero et al.^36,37 The color of potato sample was related to the sample resistivity as in the study byBernardis et al.⁴³ Experiments were repeated at least twice, and the resulting conductivity is theaverage value.

The second step (step 2) helped evaluating the electric field distribution ininhomogeneous cases. In this step, the setup with the 2 needles (Figure 6B) was considered. The cases shown in Figure 6C were analyzed. In theseexperiments, the voltage amplitude was set to 730 V and the electrode was supplied with 8pulses following the sequence VPS4 described at paragraph 2.5. After 24 hours, a picturewas taken.

Results

Histopathological Analysis Results

Figure 7 shows some interestingreal cases in terms of inhomogeneity of the tumor tissues. In some cases, the tissue iscomposed by fat cells close to areas of fibrous tissues. In other cases, theinhomogeneities in adjacent areas are due to differences in cell density.

Moreover, Figure 8 shows that theinhomogeneities areas are macroscopic. In fact, superposing to the histology image withmagnification 1× the area covered by a standard 7-needle electrode (dotted lines in Figure 8), the inhomogeneities betweena needle pair appear to be evident.

Figure 8.

Images of real specimens with the electrode area superposition and zoom of someinteresting points in terms of inhomogeneity. (A) Dedifferentiated liposarcoma (P15different area with respect to Figure5) and (B) desmoid-type fibromatosis (P16).

Experimental Results for Material Characterization

The experiments performed to characterize the electrical conductivity of TMM and potatoesare resumed in Table 3. Potatoconductivity as a function of the applied electric field is represented by a sigmoidfunction as the ones in Equation 3. The parameters of Equation 3 were evaluated by means of a fitof experimental data as in the study by Campana et al and Dughieroet al.^36,37 In particular, there is no relevant variations in the gel conductivities applyingan electric field of 143 V/cm or of 715 V/cm (Table 4), whereas the difference in conductivity isrelevant for potato samples as reported in Tables 4 and 5.

Table 3.

List of Ingredients for the Preparation of Phantom Materials.

	D2 (g)	SC1 (g)	D2′ (g)	SC1′ (g)
Glycerin	2.00	0.90	2.00	0.90
Corn flour	25.0	30.0	25.0	30.0
Gelatin	–	0.60	–	0.60
Agar	1.00	–	1.00	–
Sodium azide	0.80	0.30	–	–
Sodium chloride	0.20	–	1	0.30
Water	Point 1: 20 m L + point 2: 50 mL

Table 4.

Gel and Potato Conductivity at Different Electric Field Intensity.

	ρ (E = 143 V/cm), Ω/m	ρ (E > 700 V/cm)^a, Ω/m	σ (E = 143 V/cm), S/m	σ (E > 700 V/cm)^a, Ω/m
D2	0.78 ± 0.09	0.83 ± 0.03	1.30 ± 0.14	1.20 ± 0.5
SC1	3.38 ± 0.06	3.33 ± 0.2	0.3 ± 0.01	0.3 ± 0.02
D2′	0.64 ± 0.05	0.66 ± 0.02	1.57 ± 0.13	1.52 ± 0.04
SC1′	2.18 ± 0.09	2.16 ± 0.2	0.46 ± 0.02	0.47 ± 0.04
Potato	5.7	1.4	0.18 ± 0.05	0.73 ± 0.17

^a 715 V/cm for SC1′ and D2′ and 1000 V/cm for SC1 and D2.

Table 5.

Potato Resistivity and Conductivity Varying the Applied Electric Field and Parametersof Equation3 Evaluated From Experimental Data.

V (V)	E (V/cm)	ρ (Ω m)	σ (S/m)	V (V)	E (V/cm)	ρ (Ω m)	σ (S/m)
0	0			400	571	1.6	0.63
100	143	5.7	0.18	500	714	1.4	0.73
150	214	3.0	0.33	600	857	1.6	0.63
200	286	1.6	0.62	700	1000	1.2	0.81
E_th	238 V/cm	k_v	0.0184 cm/V	σ₀ (S/m)	0.17	σ_EP (S/m)	0.70

Considering the data reported in Table 5, it appears that, if the applied electric field increases, theresistivity decreases. From 143 to 286 V/cm, the variation in resistivity is larger than40%, whereas for stronger electric field, it is close to 15% to 20%. From data in Table 5, the E_th threshold and k_v values in Equation 3 were evaluated fitting the experimental data by means of the minimumleast square method. In this case, the E_th threshold results equal to 238 V/cm and, considering the conductivity inTable 5, it appears that ifthe falling of the conductivity is close to 45% between 214 and 286 V/m, then it is closeto the electric field at which occurs the half of conductivity gap. This value is coherentto the ones in the literature.^35,40 Finally, the coefficient k_v results equal to 0.0184 cm/V.

Computation Results

Numerical computations were performed on the potato–gel phantom models following setup inTable 3 and consideringconductivity data in Tables 4and 5. Figure 2 reports the simulation results for model Ain Figure 5 and the electric fieldevaluated in a homogeneous model (only potato). Figure 9 shows the electric field distribution inmodel B in Figure 5 and, finally,in Figure 10, and the electricfield distribution in model C in Figure5 is shown.

Figure 9.

Electric field distribution of different configurations of the model B in Figure 3. The gray rectangle showsthe potato area.

Figure 10.

Electric field distribution of different configurations of the model c in Figure 3. The gray rectangle showsthe potato area.

Figure 9 shows that the electricfield distribution is affected by the conductivity of the band inserted into theparallelepiped. In particular, the lower the conductivity of the band, the greater thearea of electroporated tissue (for potato, the electroporated value is considered,ρ(E) > 700 V/cm).

In the cases in Figure 10, theelectric field distribution is affected by the conductivities of the material in thecylinder between the needles. Also in these cases, the cylinder modifies, according to theconductivity, the electric field lines. For instance, electric field intensity has adifferent behavior at the interface with the cylinder, depending on the material, D2 gel,SC1 gel, or potato.

Comparing the electric field distribution in the homogeneous case (Figure 2A) and the ones in the inhomogeneous cases,it is evident that the position of the line at 300 V/cm change considering different gelproperties with respect to homogeneous cases. Its position is modified also in the potatotissue. The same occurs for the cases in Figures 9 and 10. The300 V/cm electric field level is close to the electric field threshold for potatoelectroporation previously identified.^40,41,43

Experimental Results

Figure 11 shows the results ofthe experiments on potatoes. From Figure11A, it appears that the potato piece close to the gel D2 shows an electroporatedarea greater than the potato approached to SC1 gel. The SC1 gel has a lower conductivitythan D2. In the case of the cylinder, the electric field able to electroporate the potatocovers a greater area compared to the case with the D2 gel, according to the computationalresults in Figure 10. The sameaccordance is with the strip geometry with D2 gel, where the electroporated area is largerthan that in the SC1 gel case. This fact is in accordance with the simulation resultswhere the position of the 300 V/cm electric field level was evaluated. Consequently, thearea where the electric field is higher than 300 V/cm could be larger or shorter withrespect to the homogeneous case. This fact is reflected also by the amplitude of the darkarea in experimental results. For instance, if the material of the cylinder (eg, D2) inFigure 10A has a lowerresistivity than the external tissue, the electric field intensity is lower than the oneobtained considering the cylinder made on SC1 (higher resistivity with respect to theexternal tissue in electroporation condition). This fact is reflected also in theintensity of electroporation as evidenced in the experimental results (Figure 11C) where the D2 case shows aless dark intensity than the SC1 case.

Figure 11.

Potato experiments (dark area is electroporated): (A) panel A only potato, panels Band C model A in Figure 3, (B)model B in Figure 3, and (C)model C in Figure 3.

Table 6 reports the amplitudeof the voltage (it is set to 728 V for all cases) and current pulses. It appears thatdifferent experimental setups show different current amplitudes. The current amplitude iscoherent with the inhomogeneity and the distribution of the electric field. For instance,if we consider the 2 models with the cylinder, in the case of the cylinder made of a moreconductive material, for example, D2, the current is higher with respect to the case ofthe homogeneous model (only potato) and the one that considers a less conductive material,SC1, in the cylinder. On the contrary, in the model with the inhomogeneity shaped as astrip, the current value is higher when the material with higher conductivity, D2, isinvolved.

Table 6.

Voltage and Current Amplitude of the Pulses Applied to the Different ExperimentalSetup.^a

Setup	Voltage (V)	Current (A)	Setup	Voltage (V)	Current (A)
Potato	728	4.7	p SC1 p	728	2.7
Potato	728	4.5	p SC1 p	728	2.5
P and D2 cylinder	728	3.8	p D2 p	728	7.0
P and D2 cylinder	728	3.9	p D2 p	728	7.1
P and SC1 cylinder	728	5.4	D2 p D2	728	7.9
P and SC1 cylinder	728	5.3	D2 p D2	728	7.2
			SC1 p SC1	728	3.6
			SC1 p SC1	728	3.7

^a p represents potato tissue.

Discussion

The histological analysis of the presented sarcoma shows that in some cases theinhomogeneity of the tissues could be evident and very different from the electrical pointof view. For instance, this arrangement, as shown in Figures 1 and 8, can generate a different distribution of theelectric field, since the conductivity of fibrous tissue in nonelectroporated conditions isclose to .8 S/m (the fibrous tissue could be considered, eg, approximately similar tocartilage tissue), whereas the conductivity of fat is close to.012 S/m.⁴⁴ Then, in this point, a discontinuity of normal component of the conduction field atthe interface occurs. In fact, if the inhomogeneities of the tissue are macroscopic, asshown in Figure 8, in the areacovered by the standard 7-needle electrode, some needle pairs can be inserted into differenttissue types modifying the electric field distribution.

The effect of inhomogeneity is also evident in the analysis of the resistance related tothe analyzed specimens. In fact, comparing data in Figure 1 and the histological images in Figures 7 and 8, the resistance variability is in accordance with thehomogeneity or inhomogeneity in the tissue. For instance, for the cases P15, P16, and P18,the resistance is under 180 Ω (it varies in a range 40-160 Ω) and it could be noted that thevalue is more constant in case P18 where the tissue is more homogeneous (Figure 7B), whereas in the cases P15 andP16 varies substantially. The same behavior can be observed in the case P12 (2 differentpoints were analyzed), but in this case the variation of the resistance is larger since itvaries between 200 and 550 Ω. In this case, some area of fibrous tissue can be evidenced inthe fatty tissue. The large volume of fat tissue increases the tissue resistivity. Thesedifferences could be due to the tissue inhomogeneity of the electroporated specimen as shownin Figures 7 and 8, since in the more homogeneous sample(P18) these variations are limited in a band of approximately 20 Ω. In fact, in the P12specimen, the fatty component prevails with respect to the fibrous component.

These observations are also evident in the simulations obtained using potato and gelconductivity and in experimental models. In fact, the position of a specified electric fieldlevel is modified in the areas where the electrical conductivity changes. The displacementof the level line with a specified electric field intensity depends on the electricalconductivity. For instance, in the cases in Figure 9, if the strip in the middle has a lower conductivity with respect to theother volumes, panels A and D, electric field line at 300 V/cm (at this electric field levelin potato, the electroporation is occurred^40,45) forms a larger band. For potato, the value of electroporated tissue is consideredsince the electric field in the middle of the 2 needles has an intensity able toelectroporate potato cells.^40,46 On the contrary, in the cases shown in panels B and C, where the strip is moreconductive with respect to the other 2 volumes, the electric field line at 300 V/cm forms anarrow strip. A similar behavior is shown in potato experiments in Figure 11. Considering the models where theinhomogeneity is like a cylinder, the electric field shows a behavior similar to the casethat considers a strip with different electrical conductivities. Moreover, the positions ofthe different electric field levels in the cases of Figure 10 are different from the one obtainedconsidering a homogeneous parallelepiped made only of potato tissue (Figure 2A). For instance, considering the potato withthe cylinder made of SC1, the electric field line at 400 V/cm includes a larger area thanthe case of the cylinder made of D2, which is a more conductive material. Instead, theelectric field line at 300 V/cm covers approximately the same area. This fact is reflectedon the potato experiments where the potato shows a larger electroporated area in the SC1case. The difference in electric field levels is also reflected in the current valuesreported in Table 6. Inparticular, the cylindrical inhomogeneity in the middle of the needle pair modifies thecurrent value in opposite way with respect to the inhomogeneity shaped as a strip. In thecase of the high-conductivity cylinder made of D2, the current is lower than that in thehigh-conductivity cylinder made of SC1.

The TMM and simulations were used by the author as a model to describe the electric fielddistributes in inhomogeneous tissues. In fact, the resistivity of the TMM could be easilydesigned changing the material composition. Consequently, it could be made close to the oneof real tissue. On the other hand, potato tissue is useful to show electroporation effectsince it becomes dark if cell electroporation occurs.⁴⁰ This way simulation and potato with gel experiment appear to be a useful model tocompare experimental data and simulation results, since electrical properties of gel andpotato could be known in an easy way like in the study by Bernardis et al.⁴³

The results showed the effect of the tissue inhomogeneity, opening the question about theeffective distribution of the electric field in inhomogeneous tissues and the effectiveelectroporation of the cells in the area of interest. In tissues, the effectiveelectroporation has to be evaluated by means of suitable experiments. This aspect could bepartially solved by a simulation model where the electric field intensity can be computed inall model area and compared with the known electroporation threshold. In this way, thevoltage can be modified in order to obtain the optimal electric field intensity ininhomogeneous tissues modifying the applied voltage until all the treated area is covered byan electric field larger than the selected threshold. Nevertheless, the electricinhomogeneity is not a well-known parameter without a histological analysis. Consequently,it is not easy to define a formula to guarantee electroporation in this type of tissues. Apossible solution could be increasing the pulse number in order to improve electroporationalso at lower electric field levels.^26,47

Consequently, evaluating the analysis of the results obtained, the average electric fieldcan be considered as a useful prediction of the effective electroporation zone even if onlyin some cases. In fact, it could be a good prediction if the electrical properties ofdifferent areas are close to each other, but it is not if the inhomogeneity areas show verydifferent electrical properties.

Finally, this approach is difficult to apply in practice since it is not possible to knowin advance the real inhomogeneity of the tissue in the treated tumor and the position of theneedles with respect to the inhomogeneity. Nevertheless, this evaluation could show thebehavior of the electric field in some inhomogeneous cases and it could evidence why in somecases the treatment could not be effective.

Conclusions

In this article, the authors showed how the electrical inhomogeneity of the tissues canaffect the electric field applied in standard ECT. The effect of tissue inhomogeneity wasanalyzed using the macroscopic variation of the measured resistance coupled with thehistological evidence of the treated volume. The effect of these differences on the electricfield distribution was studied using some experimental phantoms where the tissue electricalcharacteristics were suitably designed. The experimental results were compared withsimulation results. The effects of the tissue electrical properties on the electric fielddistribution were evidenced. The proposed analytical analysis is able to show the effect ofthe inhomogeneity in the tissues and how they can affect the therapy effectiveness.

Footnotes

Declaration of Conflicting Interests: The author(s) declared no potential conflicts of interest with respect to the research,authorship, and/or publication of this article.

Funding: The author(s) disclosed receipt of the following financial support for the research,authorship, and/or publication of this article: Project granted by CPDA138001 (PaduaUniversity).

ORCID iD: Elisabetta Sieni, PhD http://orcid.org/0000-0001-5297-0576

Acknowledgments

The research was partially made possible thanks to the networking COST TD1104 action(http://www.electroporation.net). The authors are grateful to Igea spa, Carpi(MO), Italy, for the pulse generator loan.

Abbreviations

ECTelectrochemotherapy

ESTTE

Ex Vivo Study on Soft Tissue Tumours Electrical Characteristics

FEMfinite element analysis

STSsoft tissue sarcomas

TCtumor cells

TMMtissue mimic materials

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