Bioelectrochemistry 81 (2011) 10–16

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Bioelectrochemistry

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Optimizing clinical performance and geometrical robustness of a new electrodedevice for intracranial tumor electroporation

Faisal Mahmood, Julie Gehl ⁎Copenhagen University Hospital Herlev, Center for Experimental Drug and Gene Electrotransfer, Department of Oncology, Herlev Ringvej 75, 2730 Herlev, Denmark

⁎ Corresponding author. Tel.: +45 44884488; fax: +E-mail addresses: fama@heh.regionh.dk (F. Mahmood

1567-5394/$ – see front matter © 2011 Elsevier B.V. Adoi:10.1016/j.bioelechem.2010.12.002

a b s t r a c t

a r t i c l e i n f o

Article history:Received 23 August 2010Received in revised form 8 December 2010Accepted 17 December 2010Available online 6 January 2011

Keywords:ElectroporationElectrode deviceOptimizationGeometrical robustnessBrain tumorTreatment planning

Current technology has limited applicability for electroporation based treatment of deep-seated tumors, andis in general, not optimized in terms of compliance with clinically relevant parameters. Here we present anovel electrode device developed for electrotransfer of antineoplastic drugs and genes to intracranial tumorsin humans, and demonstrate a method to optimize the design (i.e. geometry) of the electrode deviceprototype to improve both clinical performance and geometrical tolerance (robustness). We have employed asemiempirical objective function based on constraints similar to those used in radiation oncology. The resultsshow that small geometrical changesmay yield a significant improvement. For example, a 2 mmdisplacementof 6 electrodes yields 14% better compliance with the clinical parameters, compared to the prototype, andadditionally makes the electrode device less sensitive to random geometrical deviations. The method isreadily applicable to other electrode configurations.

45 44883110.), juge@heh.regionh.dk (J. Gehl).

ll rights reserved.

© 2011 Elsevier B.V. All rights reserved.

1. Introduction

When biological tissue is exposed to an excessive electrical forcethe structure of the phospho-lipid bilayer of the plasma membranesmay be changed. This phenomenon is known as electroporation (EP),and when applied efficiently, it induces plasma membrane permea-bilization allowing transport of various exogenous molecules into thecytoplasm [1]. To achieve plasma membrane permeabilization theintensity of the local electric fieldmust surpass a certain tissue specificthreshold Erev. If the applied electric field becomes yet stronger,exceeding a value Eirrev, the structural changes induced in thephospho-lipid layers become more pronounced and the cellseventually die due to prolonged adverse ion concentrations (irre-versible EP) [2].

EP has already demonstrated its potential as a means of cancertherapy, using both genes (gene electrotransfer) [3,4] and anticancerdrugs (electrochemotherapy (ECT)) [5,6]. So far, EP has been used forclinical targets such as cutaneous metastases from disseminatedmalignantmelanoma, breast cancer, and head and neck cancer [7–11].Current technology has limited applicability for deep-seated tumors,mainly due to the difficulties associated with positioning theelectrodes accurately and with little damage to normal tissue duringthe invasive procedure. Another challenge concerns the delivery ofthe intended electric field to the target tissue and at the same timespare normal tissue in its close vicinity. Attempts to overcome these

obstacles are not only advisable [12,13], but also essential for puttingECT forward as a real alternative to e.g. palliative radiation therapy,where patient specific treatment planning has been practiced foryears. Although standard operating procedures are published for EPtreatments [9], they are based on standard electrode devices and assuch do not provide any guidance in individualized treatmentplanning, which should be the next logical step, currently beinginvestigated [14,15].

The purposes of this paper are to 1) introduce a novel clinicalelectroporation device (electrode device) for treatment of deep-seated tumors in soft tissue, in particular brain metastases, and 2)demonstrate a simple numerical optimization of the design (i.e.geometry) of the electrode device using basic principles fromradiation oncology. The objective of the optimization is two-fold: toimprove the clinical performance of the electrode device, and toimprove the geometrical tolerance (robustness) of the device, whichare both critical factors in ensuring the desired level of quality intreatment delivery.

Optimization methods have been presented previously [14,16],however, little attention has been given to the clinical relevance of theoptimization parameters. In this study we formulate five independentclinical parameters to assess the performance of the electrode device:target tissue coverage, homogeneity of the electric field, average of theelectric field intensity, high intensity regions (hot spots) and normaltissue involvement. The optimization is conducted in five steps:1) introduction of incremental geometrical changes to the prototypeof the electrode device to yield alternative geometries, 2) simulationof the corresponding electric field distributions, 3) scoring the clinicalperformance based on the clinical parameters, 4) assessment of the

11F. Mahmood, J. Gehl / Bioelectrochemistry 81 (2011) 10–16

geometrical robustness, and 5) identification of the optimum devicegeometry.

A key feature of this study is thatwe take advantage of the parallelsbetween radiation oncology and ECT. For example the electric fieldintensity in ECT is used analogously to the energy imparted byradiation (absorbed dose) in radiation oncology. We also subdividethe tissue of the treated area into different volumes according to thelevel of involvement and whether it is normal tissue, a subclinicaldisease or a known disease. The concept of applying a geometricaltreatment margin, to account for geometrical uncertainties, is alsoadopted and used to advocate the need for similar quantities in ECT.

2. Methods

2.1. Volume definitions

The proposed volume nomenclature (Fig. 1) is inspired by thedefinition of the International Commission on Radiation Units andMeasurements (ICRU) [17], applied in radiation oncology.

GTV Gross tumor volume (GTV) is the known tumor tissue.CTV Clinical target volume (CTV) includes GTV and volumes withsubclinical disease. We define the CTV as the GTV plus 3 mm margin.PTV Planning target volume (PTV) encloses the CTV and outlines themargins that account for the unintended geometrical variations suchthat CTV is exposed to the prescribed electric field intensity with acertain probability.TEV Total exposed volume (TEV) is defined as the tissue exposed toelectric field intensities exceeding a level that is considered importantfor the normal tissue. We set this level as our threshold value for EP,Erev=350 V/cm.Normal tissue We define normal tissue as the total exposed volume(TEV) minus the clinical target volume (CTV).Hot spot We define hot spots as regions in the entire TEV that areexposed to electric field intensities exceeding Eirrev.

2.2. The electrode device

The electrode device was developed on the basis of the ElectrodeIntroducer Device [18] and the following criteria:

1. CTV should be exposed to electric field intensity between 350 V/cm(Erev) and 1200 V/cm (Eirrev).

2. The electric field distribution in the CTV should have a high degreeof homogeneity.

Fig. 1. Volume designations. The volumes GTV, CTV, PTV are superimposed on the cross-section of the 3D electric field distribution expanded by the prototype. The region inwhich the field intensity is above the threshold level Erev=350 V/cm defines the TEV.

3. CTV sizes up to 30 mm in diameter (spherical volume) should betreatable.

4. The device should have a high degree of flexibility to allowtargeting of different CTV sizes (≤30 mm).

5. Involvement of normal tissue should be as low as possible.6. The device should have an easy-to-use design for clinical

application.

The mentioned threshold values, Erev=350 V/cm and Eirrev=1200 V/cm, are based on the findings of previous studies [19,20].

Fig. 2 shows a drawing of the electrode device prototype. In brief,the device comprises a thin shaft with individual guiding channelsallowing the electrodes to move into predefined positions whendeployed from a retracted position. This principle facilitates theapplication of large electrode geometries using small insertion holes,thus reducing the need for extensive surgical intervention (the keyattribute of the Electrode Introducer Device).

The electrode device consists of 13 cylindrical electrodes, each0.1 mm in radius. 6 electrodes are positioned regularly in the lateralsurface of an imaginary cone with base radius ra and another 6electrodes are positioned regularly in the lateral surface of animaginary cone with base radius rb (bra) (Fig. 3). The two imaginarycone apices are located inside the device tip. One electrode is in thecenter defining the axis of symmetry. The most distal points of theelectrodes are situated in a common base plane (z=0) andcorrespond to radii ra and rb, referred to as ring (a) and ring (b),respectively. The position angles of ring (a) and (b) electrodes have aphase difference of π/6 (Figs. 2 and 3).

2.2.1. The treatment setupIn the treatment situation, the device (with retracted electrodes) is

guided into the brain through a burr hole or after a small craniotomyusing stereotactic equipment. The reference coordinates are acquiredfrom an appropriate imaging modality like magnetic resonanceimaging (MRI). When the electrode device is in place, the electrodesare deployed within the brain penetrating the tumor (Fig. 4). Afterconfirming the position of the device and the individual electrodes(with e.g. fluoroscopy), the voltage is applied (see Section 2.3.1).

2.3. Electric field calculation

The electric field in the tissue volumes was modeled using thecommercially available finite element method software, Comsol

Fig. 2. Electrode device. Electrodes a1–a6 define ring (a), electrodes b1–b6 define ring(b), electrode c is along the z-axis which defines the axis of rotational symmetry. Theposition angles θa, 1 and θb, 2 are also shown.

Fig. 3. Electrode coordinates (mm). Left: the positions of the electrodes of ring (a), andassociated position angles θa,n, n=1,…,6. Right: the position of the electrodes of ring(b) and corresponding position angles θb,n, n=1,…,6. The center electrode (c) isaligned with the z-axis.

12 F. Mahmood, J. Gehl / Bioelectrochemistry 81 (2011) 10–16

Multiphysics 3.5a (Comsol AB, Stockholm, Sweden), installed on a 64-bit Linux platform. The conductive media DC mode was applied usinguniform and constant conductivities for the tissue subdomains (tumorand normal tissue). The dielectric properties of the tissue werediscarded due to low frequency conditions [21].

2.3.1. The pulseThe CTV (30 mmdiameter sphere) is covered using a sequence of 6

voltage configurations. In Fig. 5 the sequence is shown along with theelectric field distribution, displayed as an iso-field plot. The completeECT treatment consists of 8 repetitions of the sequence (8 pulses),delivered at 1 Hz. Overlapping regions receive a suboptimal pulseregime, however, still valid for successful EP [22]. The shown pulsewas chosen among many possible configurations due to its superiormargins and low number of electrode configurations required perpulse (six). It was deduced from systematic testing of the physicallyrelevant combinations using Comsol. The main characteristic of thevoltage configurations is their resemblance to a rotating parallel platecapacitor. The potential difference was kept at 1000 V.

2.4. Optimization

The optimization of the electrode device is carried out bycomparing alternative device geometries that differ incrementallyfrom the prototype following the constraints listed below. Eachgeometry is scored according to its compliance with a set of clinicalparameters (described in Section 2.4.2), assessed in terms of itsgeometrical robustness using the calculated scores, and finally theoptimum geometry is identified.

Fig. 4. Treatment situation. A. The electrode device is guided to the tumor site with the aid ofis delivered to the tumor.

2.4.1. Alternative device geometriesThe incremental geometrical changes (electrode displacements)

were introduced following these constraints:

1. electrode displacement is radial, with a fixed apex2. displacement of the electrodes of ring (a) is synchronous3. displacement of the electrodes of ring (b) is synchronous4. displacements of ring (a) and (b) electrodes are independent and5. the center electrode (c) remains fixed.

Note that the individual displacement of electrodes is discarded.This is valid under symmetrical conditions.

2.4.2. The clinical performanceThe clinical parameter definitions shown here should be regarded

as one possible choice, since the exact relationships for electric fieldeffects on living tissue are not known, and the thresholds Erev and Eirrevare not very well established either.

2.4.2.1. Tumor control. One of the main objectives of cancer treatmentsis to treat sufficiently to prevent proliferation and regrowth. In ECTthis can be facilitated by ensuring "coverage" of the entire CTV. Wedefine a parameter L(Vlow) that accounts for the volume, Vlow, withinthe CTV that is exposed to an electric field with an intensity below thethreshold (Erev=350 V/cm):

L Vlowð Þ = 0 for Vlow N 01 for Vlow = 0

�ð1Þ

L(Vlow) indicates a null-tolerance enforcement, i.e. if any fraction ofthe CTV is undertreated, it will lead to a rejection of the particulargeometry (score=0).

2.4.2.2. Hot spots. At high electric field intensities (ENEirrev), the cellswithin the exposed tissue die. This is an unwanted outcome if theelectrode device is applied in gene electrotransfer where the viabilityof cells is crucial. H(Vhigh) is a parameter that takes into account theextent of Vhigh, the amount of tissue exposed to electric fieldintensities higher than Eirrev=1200 V/cm:

HðVhighÞ = 1−Vhigh

CTVð2Þ

2.4.2.3. Average electric field. Uncertainties associated with thecalculation of the electric field imply that we improve our chance ofstaying inside the limits of reversible EP if the mean electric fieldintensity is close to the interval median (775 V/cm).M(μ) accounts forthe deviation of the mean induced electric field intensity μ from theinterval median:

M μð Þ = 1−

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiμ−775ð Þ2

q425

for Erevbμ bEirrev

0 all other values of μ

8><>: ð3Þ

the stereotactic frame. B. The electrodes are deployed into the tumor. C. The electric field

Fig. 5. Voltage switching. In the upper part of the figure the electrode configurations are illustrated with filled and open circles (∓500 V). The lower part of the figure shows iso-fieldplots at 350 V/cm; a visualization of the points where the electric field intensity is equal to 350 V/cm (Erev). The progression is from left to right, as each iso-field plot is amerger of theprevious plot and the immediate electric field distribution. The dashed circle indicates the position of the CTV.

Fig. 6. Electrode deflection. The electrodes can deflect inwards or outwards dependingon the anisotropy. Two orthogonal linear anisotropies illustrate the possible outcomeunder symmetry conditions. The resultant force F indicating the direction of electrodedeflection and the relative size of the vectors do not necessarily correspond to theactual situation.

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2.4.2.4. Electric field homogeneity. S(λ) is a parameter that takes intoaccount the influence of λ, the average distance from the meanelectric field intensity within CTV (log-transformed). It is defined forλN0:

S λð Þ = 1= λ ð4Þ

S(λ) is normalized to 1.

2.4.2.5. Normal tissue. Finally, we need to address the amount ofnormal tissue exposed to an electric field intensity above Erev andEirrev, respectively. Involvement of normal tissue is only regardedwhen two or more otherwise equally good device geometries arecompared. In such cases the geometry involving the least amount ofnormal tissue is preferred.

Collecting all clinical parameters (L,H,M,S) into one expressionyields the objective function:

A L;H;M; Sð ÞΔa ;Δb= L Vlowð ÞHðVhighÞM μð ÞS λð Þ ð5Þ

where Δa and Δb indicate the geometrical change of ring (a) and (b)electrodes, respectively, relative to the prototype, measured as radialshift of the electrode ends in millimeters (mm). Each clinicalparameter yields a value between 0 and 1. Consequently, A(L,H,M,S)yields a value between 0 and 1, which we define as the score. Themaximum score, for a certain combination of Δa and Δb, gives thegeometry with the best clinical performance:

maxΔa ;Δb

A L;H;M; Sð ÞΔa ;Δbð6Þ

The objective function was evaluated using Matlab R2006a (TheMathworks, Inc., MA, USA) and Comsol. The calculation was based onelectric field data of 16,333 sampling points distributed as vertices of aregular tetrahedral grid in the involved volumes (voxel size=0.87mm3).

2.4.3. Geometrical robustnessTo distinguish between the electrode displacements related to the

optimization procedure (Section 2.4.1) and the unwanted radialmovement of the electrodes in a treatment situation, we denote thelatter electrode deflection.

Geometrical errors follow the normal distributionwith amean anda standard deviation, and typically divided into systematic errors(arise in the treatment preparation stage) and random errors (onlyrelevant for fractionized treatments). Correction procedures canreduce errors but not eliminate them. Therefore, geometrical margins,based on a predefined level of tumor control in a predefined

percentage of patients, should be applied when planning thetreatment [23,24].

Here we address two independent geometrical margins. One isrelated to the inaccuracy in positioning the electrode device itself,termed CTV margin (the CTV margin is the expansion of the CTV toyield the PTV). The other is related to the deflection of the electrodesduring deployment in the tissue, termed deflection margin. Thesemargins are not known since the uncertainties of the treatmentprocedure have not been investigated. The tumor control probabilitiesfor different electric field intensities are unknown as well. Instead wereport the CTV tolerance and the deflection tolerance, which are definedas the allowed geometrical errors and collectively referred to as thegeometrical robustness of the electrode device.

2.4.3.1. Deflection tolerance. We define the deflection tolerance as thelargest deflection of the electrodes of ring (a) and (b), respectively,that does not compromise coverage of the 30 mm spherical CTV.Electrode deflection can occur in anisotropic target tissue (e.g.tumors). Fig. 6 illustrates the mechanical force exerted on theelectrodes in anisotropic tissue. In one case the electrodes experiencean inward force and in the other situation the force is directedoutward, causing a reduction and an increase of the electrode ringradii, respectively. Perfectly homogenous tissue will only exert a forceexactly opposing the movement of the electrodes with no lateral forcecomponents and we would expect no deflection. The deflectiontolerance should be at least the size of the deflection margin.

Table 1Top 5 scoring electrode geometries.

Δa Δb L H M S Score Tolerances (mm) Normal tissue

Deflection a, b CTV rev irrev

1 2 1 0.95 0.96 0.81 0.74 4, 2 0.5 0.560 0.0440 3 1 0.95 0.96 0.81 0.74 5, 1 0.5 0.559 0.0460 4 1 0.95 0.92 0.84 0.73 4, 0 0.5 0.565 0.046⋆0 2 1 0.94 0.98 0.79 0.73 5, 2 0.5 0.552 0.0452 4 1 0.96 0.84 0.87 0.70 2, 0 0.5 0.585 0.042

0 0 1 0.93 0.96 0.73 0.65 1, 1 0.5 0.532 0.045

‘Tolerances (mm)’ indicate the allowed deflections (in mm) of the electrodes and theallowed positional error of the entire device. ‘Normal tissue’ shows normal tissueinvolvement in fractions of TEV: ‘rev’ is the fraction exposed to electric field intensitiesfrom Erev to Eirrev, and ‘irrev’ is the fraction exposed to electric field intensities aboveEirrev. The star indicates the geometry with the highest level of robustness. Theprototype score is shown in the bottom line.

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2.4.3.2. CTV tolerance. We define the CTV tolerance as the expansion ofthe 30 mm spherical CTV to the maximum size of a spherical volumethat can be covered by the 350 V/cm iso-field (Fig. 5). The CTVtolerance is found by incremental enlargement of the sphericalvolume (using Matlab scripting with Comsol). Ideally, the CTVtolerance and CTV margin should be equal, to achieve the predefinedtumor control probability and secure normal tissue sparing.

3. Results

3.1. Clinical performance

The objective function A(L,H,M,S) is calculated for all combinationsof the displacements Δa={−6,−5,−4,−3,−2,−1,0,1,2,3,4,5,6}and Δb={−2,−1,0,1,2,3,4,5,6} and the scores are illustrated inFig. 7. In particular (Δa=0,Δb=0) means zero displacement, whichcorresponds to theelectrodedeviceprototype.Negative valuesofΔa andΔb, respectively, are equivalent to an inward displacement of theelectrodes and positive values are equivalent to an outward displace-ment of the electrodes relative to the prototype, measured inmillimeters at the electrode ends. A quick visual inspection identifiesseveral combinations ofΔa andΔb as high scoring geometries (Fig. 7). InTable 1 the clinical parameters of the objective function are specified forthe top 5 scoring device geometries and compared to the prototype. Themaximum score is 0.74 found at (Δa=1,Δb=2) and (Δa=0,Δb=3),suggesting a displacement of the electrodes of ring (a) by 1 mm and0 mmoutwards, respectively, and displacement of the electrodes of ring(b) by 2 mmand 3 mmoutwards, respectively. The amount of involvednormal tissue is practically equal for these geometries.

3.2. Geometrical robustness

Table 1 shows deflection tolerances of ring (a) and (b) electrodesof the 5 geometries with the best clinical performance and theprototype. For example, for geometry (Δa=1,Δb=2) a 4 mm inwardor outward deflection of ring (a) electrodes is tolerated, and only a2 mm inward or outward deflection of ring (b) electrodes is tolerated.In other words, the electrodes of ring (a) can travel up to 4 mm andstill cover the CTV sufficiently, whereas the ring (b) electrodes cantravel only 2 mm. Equivalently, using the scoremap in Fig. 7, we couldread off the distance from the point representing the particulargeometry to the beginning of the area with score zero. We see forexample that for the geometry (Δa=0,Δb=2) the ring (b) electrodes

Fig. 7. Electrode device score. The small circle at (Δa=0,Δb=0) indicates the positionof the prototype and the star at (Δa=0,Δb=2) indicates the position of the optimumgeometry. The large dashed circle shows the actual deflection tolerance in comparisonto the independent deflection tolerances of ring (a) and (b) electrodes. Neighboringgeometries are connected using linear interpolation.

can travel a small distance only (2 mm) before going into the areawith score zero, whereas the ring (a) electrodes of the same geometrycan travel much longer (5 mm), i.e. the deflection tolerance of ring (a)electrodes is much larger.

The tabulated data (Table 1) also show the tolerance of thepositioning of the electrode device (CTV tolerance). For example, thelargest spherical CTV that can be covered by the 350 V/cm iso-fieldexpanded by the (Δa=0,Δb=2) geometry has a radius of 15.5 mm,i.e. 0.5 mm larger than the CTV used in the optimization process. Thisimplies a 0.5 mm CTV tolerance of this geometry, meaning that thePTV has 0.5 mm margin to the CTV. The data also show that the CTVtolerance is independent of the device geometry since the CTVtolerance levels are equal.

3.3. The optimum geometry

The clinical performance (score including normal tissue involve-ment) of the top 5 geometries is almost the same. The geometricalrobustness, however, is quite different. This suggests that in practicethe geometry with the largest deflection tolerance should be selectedas the optimum device geometry.

The device geometry (Δa=0,Δb=2)qualifies as the onewith the bestgeometrical robustness; ring (a) exhibits 5 mm tolerance, both inwardsand outwards, and ring (b) exhibits 2 mm tolerance, both inwards andoutwards (Fig. 7). This is an approximation since the deflection tolerancesof ring (a) and ring (b) are not completely independent, and the actualdeflection tolerance might be slightly smaller.

4. Discussion

We have made a number of assumptions and simplifications in thepresented optimization method. For example, a more advancedelectric field model would have included e.g. the non-linear dynamicsdue to the electric field dependent conductivity, σ(E) [19,25,26].Literature suggests that the electric fields modeled using fielddependent conductivities encloses a slightly larger volume for typicalpulse durations and field intensities [16,19,27]. The main reason forthis shortcoming is the limitation of the electrical property data onbrain tissue in particular. However, a possible improvement of theelectric field model would be to analyze its sensitivity, byimplementing different functional expressions for σ(E) into thesimulations. The sensitivity of the clinical performance to the EPthreshold can also be analyzed with the implementation ofdifferent EP threshold levels. Including the macroscopic heteroge-neity of the target volume in the electric field model would alsoprovide a better estimate of the electric field intensities, sincetissue heterogeneity often indicates non-uniform conductivity andpermittivity [28]. However, these extensions to the model are not

15F. Mahmood, J. Gehl / Bioelectrochemistry 81 (2011) 10–16

considered important for demonstrating the general feasibility ofthe method.

In the present work, the EP threshold levels, Erev and Eirrev, for brainmetastases were extracted from results of our preclinical studies andreported values from other tissues [19,20]. Better estimates of theclinical performance expressions L, H, M, S demand better under-standing of electric field induced tissue reactions and betterdetermination of the threshold levels.

Other optimization methods are possible, e.g. genetic algorithms[29,30] or Theil's inequality coefficient [14,31]. These have beenavoided since genetic algorithms requires long calculation time whenmore than a few parameters are used and Theil's inequality is verysensitive to additive transformation [31], which becomes an issue iffor example the EP thresholds are uncertain. An advantage of ourmethod is the ease with which one can access values of the individualclinical parameters and decide which geometry is optimal in eachcase. For example, normal tissue involvement sometimes constitutes aseriousmatter and other times it is of less concern, if it is a non-criticalstructure or necrotic tissue. In radiation oncology the conformityindex is sometimes applied as a tool for attributing a score to atreatment plan and comparing several treatment plans for the samepatient [32], very similar to the scoring we present. The morecommonly used dose–volume histograms provide statistical informa-tion about absorbed dose distribution in the treated tissue but do notprovide a good indication of conformity. Still, similar histograms couldserve as a complementary tool in ECT if we substitute the absorbeddose with for example the electric field intensity.

The results showed that several alternatives to the prototypecomply better with the treatment criteria and also exhibit greatergeometrical robustness. The optimization shows small differences inthe overall scores, even between quite different device geometries,and normal tissue involvement is also quite comparable betweengeometries. Most critical is the fraction of irreversibly electroporatednormal tissue that only amounts to about 0.045 of the TEV. Again, thisnumber is uncertain because it is dependent on the accuracy of thethreshold level for irreversible EP. The largest differences are seen inthe deflection tolerances (Table 1). It is not possible to state therequired level of deflection tolerance since the deflectionmargin is yetto be assessed from clinical trials and tests, but since the clinicalperformances were very similar, the device geometry with the largestdeflection tolerance should be preferred for clinical use. The CTVtolerance is found to be 0.5 mm, which is unrealistically small inpractice. Correction procedures (e.g. fluoroscopy) may reduce theuncertainty due to the stereotactic frame, which normally can beconsidered to be 1–2 mm. The uncertainties due to imaging in theplanning stage of the treatment and morphological/translationalchanges of the GTV in the time after the imaging (which can be severaldays) are also reduced by the correction procedure. However, thetarget volume delineation error, the calculation error will remain,demanding a certain CTVmargin. A realistic guess of the CTVmargin is1–2 mm when correction procedures are applied and about thedouble (4–5 mm) when no correction procedures are used. Thissuggests that the maximum treatable CTV should be reduced from30 mm to around 26–28 mm in diameter, when correction proceduresare applied.

In this paper we have only addressed the maximum size of thetarget volume (30 mm). In light of the advances towards treatmentplanning of ECT [15], it must be required that the electrode devices areadjustable so that different volumes can be targeted withoutcompromising normal tissue safety. The electrode device presentedin this paper has a feature, referred to as flexible deployment, toaccommodate the variation in the metastasis sizes. Flexible deploy-ment allows electrode deployment in different depths. The electricfield distribution can be scaled accordingly by adjusting the appliedpotential difference relative to the new deployment depth. Optimi-zation of other CTV diameters will therefore, to a good approximation,

yield the same result (clinical performances and relative geometricalrobustness) as shown in this paper.

5. Conclusion

We have demonstrated a simple method to incorporate a set ofclinical parameters into a geometry optimization task. The methodwas applied to a novel electrode device prototype designed toelectroporate deep-seated tumors, primarily intracranial metastases.Since electroporation based treatments face challenges similar tothose in radiation oncology, generally concerned with the spatialspecificity, we adopted some of the same ideas and terminology.Another novelty of the optimization method was its emphasis onclinically important parameters, in terms of tumor control, hot spots,average electric field intensity, electric field distribution and normaltissue involvement. Geometrical uncertainties related to the EPtreatment, using our electrode device, have also been addressed. Wecan conclude that the geometrical robustness of the electrode deviceis improved with small adjustments of the prototype. The positioningtolerance (CTV tolerance) of the device indicates that the largesttreatable CTV is smaller than anticipated. In conclusion, based on ourempirical electroporation thresholds and mathematical formulationof the clinical parameters, we have successfully proposed betterperforming alternatives to the prototype.

Despite the fact that the electric field model employed in this workis very simple, we have demonstrated the overall feasibility of themethod. A secondary purpose of this work was to draw attention tothe importance of quantitative approaches in clinical electroporation,which is a rapidly growing technology and should be delivered in themost advantageous way. Such a goal is only achievable if differentstrategies are tested.

Acknowledgments

This work was supported by grants from the Danish NationalAdvanced Technology Foundation. Thanks to our colleagues for theinspiring discussions and proofreading, especially J.M. Edmund, M.Linnert and T.H. Sørensen.

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Faisal Mahmood received his B.Sc. and M.Sc. degree inbiophysics from the Niels Bohr Institute, University ofCopenhagen. He has completed a postgraduate specializa-tion in both nuclear medicine physics and radiationtherapy physics. Currently he is pursuing a Ph.D. degreeat the University of Copenhagen, Herlev Hospital. His main

research interests are radiation therapy, diagnostic ima-ging, numerical electric field models and magnetic reso-nance imaging for verification of in vivo electroporation.

Julie Gehl is an MD and Oncologist. The focus of interest inresearch is cell electroporation to enhance uptake of drugsand genes. She defended her doctorate thesis at theUniversity of Copenhagen on this topic and continued toform the Center for Experimental Drug and Gene Electro-transfer (C*EDGE), which is a multidisciplinary group

working with in vitro, in vivo and clinical studies on theoptimization of drug and gene delivery by electrotransfer.She is a Clinical Associate Research Professor at theUniversity of Copenhagen and a research fellow of theRoyal Swedish Academy of Sciences, supported by the ActaOncologica Foundation.