TRITA-KET R115 ISSN 1104-3466 ISRN KTH/KET/R-115-SE

MMOODDEELLLLIINNGG OOFF TTHHEE EELLEECCTTRROOCCHHEEMMIICCAALL TTRREEAATTMMEENNTT OOFF TTUUMMOOUURRSS

EVA NILSSON

DOCTORAL THESIS

Department of Chemical Engineering and Technology Applied Electrochemistry Royal Institute of Technology Stockholm 2000 AKADEMISK AVHANDLING som med tillstånd av Kungliga Tekniska Högskolan i Stockholm, framlägges till offentlig granskning för avläggande av teknisk doktorsexamen fredagen den 10 mars 2000 kl. 13.00 i Kollegiesalen, Valhallavägen 79, Kungliga Tekniska Högskolan, Stockholm. ABSTRACT

The electrochemical treatment (EChT) of tumours entails that tumour tissue is treated with a continuous direct current through two or more electrodes placed in or near the tumour. Promising results have been reported from clinical trials in China, where more than ten thousand patients have been treated with EChT during the past ten years. Before clinical trials can be conducted outside of China, the underlying destruction mechanism behind EChT must be clarified and a reliable dose-planning strategy has to be developed. One approach in achieving this is through mathematical modelling. Mathematical models, describing the physicochemical reaction and transport processes of species dissolved in tissue surrounding platinum anodes and cathodes, during EChT, are developed and visualised in this thesis. The considered electrochemical reactions are oxygen and chlorine evolution, at the anode, and hydrogen evolution at the cathode. Concentration profiles of substances dissolved in tissue, and the potential profile within the tissue itself, are simulated as functions of time. In addition to the modelling work, the thesis includes an experimental EChT study on healthy mammary tissue in rats. The results from the experimental study enable an investigation of the validity of the mathematical models, as well as of their applicability for dose planning. The studies presented in this thesis have given a strong indication of the destruction mechanism involved in EChT. It is shown by the modelling work, in combination with the experiments, that the most probable cause of tissue destruction is acidification at the anode and alkalisation at the cathode. The pH profiles obtained from the theoretical models have shown good correlation with the experimentally measured destruction zones, assuming that a pH above and below certain values cause tissue destruction. This implies that the models presented in this thesis could be of use in predicting the tumour destruction produced through EChT, and thereby provide a basis for a systematic dose planning of clinical treatments. Moreover, the models can serve as valuable tools in optimising the operating conditions of EChT. Modelling work of the anode processes has explained the role of chlorine in the underlying destruction mechanism behind EChT. It is found that the reactions of chlorine with tissue play important roles as generators of hydrogen ions. The contribution of these reactions to the acidification of tissue, surrounding the anode, is strongly dependent on the applied current density and increases with decreasing current density. Key words: cancer, direct current, dose planning, electrochemical treatment (EChT), electrotherapy, mathematical modelling, tumour. THESIS CONTENTS

This thesis is a summary and discussion of the following papers:

I. H. von Euler, E. Nilsson, A.-S. Lagerstedt and J.M. Olsson, Development of a dose-planning method for electrochemical treatment of tumors: A study on mammary tissue in healthy female CD rats, Electro. Magnetobiol. 18 (1999) 93-104. II. E. Nilsson, J. Berendson and E. Fontes, Electrochemical treatment of tumours: a simplified mathematical model, J. Electroanal. Chem. 460 (1999) 88-99. III. E. Nilsson, J. Berendson and E. Fontes, Development of a dosage method for electrochemical treatment of tumours: a simplified mathematical model, Bioelectrochem. Bioenerg. 47 (1998) 11-18. IV. E. Nilsson, J. Berendson and E. Fontes, Impact of chlorine and acidification in the electrochemical treatment of tumours, accepted for publication, J. Appl. Electrochem. (1999). V. E. Nilsson and E. Fontes, Mathematical modelling of physico- chemical reaction and transport processes occurring around a platinum cathode during the electrochemical treatment of tumours, submitted for publication, Bioelectrochemistry (2000). VI. E. Nilsson, H. von Euler, J. Berendson, A. Thörne, P. Wersäll, I. Näslund, A.-S. Lagerstedt, K. Narfström and J.M. Olsson, Electrochemical treatment of tumours, in press, Bioelectrochemistry. ACKNOWLEDGEMENTS

Many people have contributed to the contents of this thesis, and I would like to take this opportunity to thank: Jaak Berendson, my supervisor and friend, for your confidence and support in all situations. You have been the best supervisor I can imagine. Ed, my fiancé and in-house supervisor in electrochemistry, downhill skiing and driving, for the coaching, your positive thinking and for picking up the pieces during the hard times. Philip Byrne for being a friend and for your valuable opinions on the summary and papers included in this thesis. "Fikarumsgänget" at IMT, Sundsvall, for the unforgettable parties and for advising me in stock trading, driving and gambling. Torbjörn Carlberg, thank you for receiving me at Mitthögskolan. Kjersti Bergström-Boucht for everything ranging from the administrative services to the stimulating discussions about horseback riding, interior design and art. The late Daniel Simonsson, for supporting the project and for the encouragement in the beginning of my doctoral studies. The TEKTIB group, including members from Radiumhemmet, The Swedish University of Agricultural Sciences and Huddinge University Hospital, is acknowledged for their co-operation and valuable discussions. Cancerfonden, KTH, and Stiftelsen för Strategisk Forskning are acknowledged for the financial support and Permascand for supplying the electrodes. I would also like to thank the people at Applied Electrochemistry and KEP, Sundsvall, for creating a friendly and inspiring atmosphere. Finally, I would like to thank my family, Lars, Vivi-Anne and Anders for always being there for me.

CONTENTS

1. INTRODUCTION 1

1.1. Experiences from the electrochemical treatment of tumours 1 1.2. Destruction mechanisms 7 1.3. Dose planning 9 1.4. Objectives of this thesis 10

2. EXPERIMENTAL 11

3. MATHEMATICAL MODELLING 13

3.1. General problem definition 13 3.2. Anode modelling 15 3.3. Cathode modelling 17 3.4. Model equations 19 3.5. Input data and numerical implementation 21

4. RESULTS AND DISCUSSION 23

4.1. Experiments in rat mammary tissue 23 4.2. Anode modelling 25 4.3. Cathode modelling 35

5. CONCLUSIONS 42

6. REFERENCES 44

APPENDIX

Paper I Paper II Paper III Paper IV Paper V Paper VI

1. INTRODUCTION

Electrochemical treatment (EChT) of tumours is a therapy in which tumour tissue is treated with a continuous direct current. Several factors contribute to the tumour destruction caused by EChT, although their respective roles in producing the anti-tumour effect are not yet fully understood. These uncertainties regarding the destruction mechanisms bring about the lack of a reliable dose planning methodology. In this introduction, the experimental and clinical experiences of the electrochemical treatment of tumours are reviewed. The current knowledge of the destruction mechanism underlying EChT is presented along with different attempts towards dose planning. Finally, the objective of this thesis is formulated. A short review on the application of direct current in the treatment of tumours was presented by Watson in 1991 [1]. Since then, many interesting studies have been published and for that reason a second review of the same subject was written by the present author and co-workers, see Paper VI. Sections 1.1-1.3 are based on the material presented in Paper VI, in which further details of the respective aspects can be found.

1.1. Experiences from the electrochemical treatment of tumours Reports on the anti-tumour effect of low-level direct current date back to the end of the nineteenth century [2]. However, interest in its underlying mechanisms and possible therapeutic use waned until 1959 when Humphrey and Seal reported encouraging results from its application to sarcoma tumours in mice [3]. Following this, a number of workers applied EChT in both animal tumour models and in clinical trials.

Pioneering clinical studies by Nordenström Björn Nordenström, a Swedish professor in radiology, is considered to be a pioneer in the treatment of tumours with direct electric current and combination therapies in patients. In the late seventies, Nordenström started to treat primary lung cancers by applying current between two platinum wire electrodes. The anode was placed centrally in the tumour and the cathode approximately twice the tumour diameter away from the anode. The applied voltage was about 10 V. The patients were treated under local anaesthesia and were seldom uncomfortable during the treatment. A preliminary trial in five patients was published in 1978 [4], and, in his book written in 1983 [5], Nordenström reported results from the treatment of 26 lung tumours in 20 patients. Many of these patients were, for various

1 reasons, unsuitable for surgical, radiotherapeutic or chemotherapeutic treatment. The average delivered coulomb dosage (current multiplied by time) was 80 C/cm of tumour diameter. Regression was obtained in 12 out of 26 tumours and no signs of re-growth were detected after a 2-5 year follow-up period. Among the side effects, Nordenström noticed slight fevers and local pain during the treatment. Nordenström pointed out that most tumours possess an excess of fixed electronegative charges on their surfaces and, therefore, only the anode should be placed inside the tumour so as to prevent the spreading of micro- metastases during treatment [6]. However, Nordenström obtained positive results, in a later work [7], when he placed the cathode in the tumour. Nordenström, together with his colleagues, investigated the effects of a combined, simultaneous therapy of EChT and the chemotherapeutic agent, adriamycin [8, 9]. Beneficial effects were obtained in a preliminary study of 14 patients with large lung cancers, incurable by conventional methods [8]. One of the latest articles by Nordenström and his colleagues reports positive results from the electrochemical treatment of a patient with breast cancer [10]. The authors also proposed a combination therapy between an extensive electrochemical pre-treatment and a restricted surgical operation. Ideally, the electrochemical treatment would kill undetected tumour foci so that post-operative recurrence would be avoided.

Clinical trials in China An EChT project, based on the experiences of Nordenström and supported by the Chinese government, was initiated in China in 1987. Experimental and clinical data were rapidly gathered for two years and in 1989, the electrochemical treatment of tumours was approved by a committee of experts, organised by the Ministry of Public Health in China, to be used throughout the entire country [11, 12]. Professor Xin Yu-Ling and co- workers, at The China-Japan Friendship Hospital in Beijing, were assigned to organise postgraduate courses and up to 1998, more than 2000 physicians had been trained in EChT. The clinical experiences of EChT in China was internationally presented at the First Conference of the International Association for Biologically Closed Electric Circuits in Medicine and Biology held in Stockholm, Sweden, in 1993. A large amount of clinical material, covering more than 2000 cases of various benign and malignant tumour types, treated during a period between 1987 and 1992, was discussed at this conference and subsequently published [13]. During this period, Xin and his collaborators modified Nordenström’s electrode placement methodology. Instead of placing an anode in the tumour and a cathode far away from it, they inserted a number

2 of anodes into the centre of the tumour and the same number of cathodes just outside its periphery. The number of publications found in international journals, concerning the clinical results from China, are currently quite limited. However, a recent report [14] suggests that EChT provides a safe, simple and effective complementary treatment for patients with lung neoplasms, who are neither suitable for surgery nor responsive to chemotherapy or radiotherapy. In this study, Xin et al. had again modified their electrode placement technique and the anodes and cathodes were placed inside the tumours, with the anodes in the centre and cathodes at the periphery. This modification not only protected the normal tissue from destruction, but was also shown to enhance the therapeutic effect. A second international symposium in 1998 on the electrochemical treatment of cancer, was held in Beijing, China, where it was reported that the treatment had been established in 1260 hospitals throughout China. Furthermore, more than ten thousand patients, with various kind of tumours, were said to have been treated during the previous ten years, indicating a tremendous clinical experience of the method [12]. Xin and his collaborators had once again modified the electrode placement technique. Anodes and cathodes were placed alternately, at 2 cm intervals, throughout the tumour volume. Typical electrical treatment parameters were 6-8 V and 50-80 mA. Different coulomb dosages were given depending on the type of tumour. For example, solid malignant tumours were given a dosage of 80- 100 C/cm of tumour diameter while benign hemangioma, which is rich in electrolytes, was treated with 30-40 C/cm of tumour diameter. It was concluded from this conference that patients with malignant tumours of less than 8-10 cm diameter, who were unsuitable for surgery or were non- responsive to radio/chemotherapy, and patients with benign tumours would benefit from EChT. However, it was clearly pointed out that EChT was a local therapy, and that it should be combined with surgery, radio-, chemo- and/or immuno-therapy. In the cases of lung, liver and eosophageal cancer, the presented results indicated substantially lower mortality rates compared to those presented in the statistics available in occidental countries [15]. The 5-year survival rate for lung cancer treated with EChT was 39%, while the western figure is 14%. The corresponding values for liver cancer are 15% and 5%. Moreover, patients with non-curative esophageal cancer, treated with EChT, demonstrated a 5-year survival rate of 13%, which is similar to corresponding data reflecting the survival rate in all patients suffering from this neoplasm in western countries. However, randomised and controlled clinical trials are yet to be performed in China, and the characterisation and follow-up rate of patients, as well as the classification of the tumours, are only sparingly presented in the available reports [12]. These circumstances must be taken into consideration when

3 comparing the efficacy of EChT to that of conventional anti-tumour therapies in occidental countries.

Occidental studies in animals and patients Research groups in Europe, North America and Japan have, in parallel with Nordenström’s work and the clinical activities in China, applied EChT in many different experimental tumour models and in a few clinical case studies. Several different approaches for the application of current have been employed, including different electrode shapes, materials and configurations as well as different current intensities and treatment times. In most of the reports, treatments were carried out with constant current, but in a few cases a constant voltage was applied. An overview of the experiences gained from different occidental research groups is presented in this section. Current levels and treatment times used in some of these studies are listed in Table 1. As can be seen from the table, the applied currents ranged from µA to tens of mA, while the duration varied from 15 min single treatments to continuous 24 hours per day treatments. Schauble et al. [16] evaluated the effect of three different current levels on the growth of melanoma tumours in hamsters. A stainless steel point electrode was placed in the tumour, as either the anode or cathode, and a planar wire mesh electrode was applied to the skin of the chest. Tumour growth was inhibited and metastases were reduced. The effects were most pronounced with the anodic treatment by which the two higher currents produced necrosis. Habal [17] treated hepatoma tumours in rats with a small direct current via an implanted power source [18]. A point-shaped platinum anode was placed in the centre of the tumour and a plate stainless steel cathode was placed on the surface of the power unit, which was in turn in contact with normal tissue. The power sources were implanted at different time following the tumour implant, and it was found that tumour growth retardation only occurred when treatments were started at an early stage. Moreover, tumour growth was enhanced when treatment was started at an early stage and then subsequently discontinued. Samuelsson and co-workers tested EChT as a possible method for the destruction of tumours, especially lung metastases. One study [19] compared results from the electrolytic treatment of colon adenocarcinoma tumours in rats with those obtained by surgery and came to the conclusion that the efficiency of the treatments were approximately equal. Current was applied by two torpedo-shaped platinum electrodes, with an anode placed in the centre of the tumour and a cathode positioned at the tumour surface. A subsequent article by the same research team reported a 60-80% tumour

4 mass reduction from treatments of five lung tumours in four patients [20]. Samuelsson and collaborators also studied the effect of EChT with subsequent radiotherapy, both in experimental colon carcinoma tumours in rats [21] and in a lung tumour patient [22]. In the former study, the combined treatment resulted in tumour growth inhibition and, in 75% of the cases, the tumours disappeared. In the group that received only radiotherapy 75% of the tumours remained. David et al. [23] treated hamster melanoma tumours with different currents. A needle electrode made of either stainless steel or platinum-iridium alloy was placed in the tumour and served as either the anode or cathode. The counter electrode, made of aluminum foil, was applied to the skin of either the abdomen or left side of the hamster. Tumour growth reduction was obtained in all treatment groups, irrespective of electrode material or polarity. Marino et al. [24] investigated the effect of direct current on the growth of implanted lung carcinoma in mice. Two platinum wire electrodes were placed parallel to each other in the tumour. Morris et al. [25] conducted a similar study, but used larger tumours and current. These two studies showed that EChT treatment was able to lessen tumour burden. Moreover, the treatment did not increase the presence of metastasis or growth rate in the unaffected fraction of the tumour.

Table 1. Currents and treatment times used in different occidental studies.

Authors Current Treatment time Ref.

Schauble et al. 3, 0.5 and 0.001 mA 1 h/day, 4 consecutive days [16] Habal 0.4-0.6 µA 10-24 consecutive days [17] Samuelsson 10-40 mA 1 h, 1-3 treatments [19] David et al. 0.1-2.4 mA 1 h/day, 5 consecutive days [23] Marino et al. 2 mA 1 h, 1-3 treatments [24] Morris et al. 20 mA 15 min, 1-3 treatments [25] ∨∨ ∨ Miklavcic , Sersa 0.2-1.8 mA 30-90 min, 1-3 treatments [28-31] and colleagues 0.6 mA 15 min/day, 9 consecutive days [27] ∨ Plesnicar et al. 1 mA 30 min [37] Matsushima et al. 10-40 mA 40-90 min [44] Griffin et al. 1-5 mA 30-90 min [45]

5 Heiberg et al. [26] applied different constant voltages, ranging between 2.5- 12.5 V, on colon adenocarcinoma in mice, by means of two gold needles placed parallel to each other within the tumour. All the treated tumours showed significant volume reduction. ∨∨ ∨ Miklavcic , Sersa and collaborators, in a series of papers, studied the effect of current on fibrosarcoma and melanoma tumours in mice [27-31]. Their studies involved both single and repetitive treatments, as well as different electrode configurations and materials (Pt, Pt-Ir, Au, Ag, Ti and stainless steel). Some of the experiments were run with one electrode placed in the tumour and a second placed subcutaneously in healthy tissue. Another electrode configuration involved two electrodes placed in healthy tissue on opposite sides of the tumour. Tumour growth retardation was obtained in all experiments, irrespective of electrode material and electrode configuration. The anti-tumour effect depended proportionally on the current level, and cathodic treatments exhibited a better effect than anodic treatments [28, 30]. The best effect was achieved in a study on melanoma tumours using a multiple-array electrode with three Pt-Ir cathodes placed in the tumour and two anodes placed subcutaneously in healthy tissue [28]. Here, tumours showed regression with a cure rate of 40% after a period of 4 months. The same research team also published papers describing EChT in ∨ combination with other anti-tumour therapies in mice. Sersa et al. [32] studied the effect of EChT followed by systemic bleomycin treatment. The combined treatment was found to be more effective than either treatment acting alone. Other works [33-36] concern the beneficial effects of EChT in combination with different immunomodulators. ∨ Plesnicar et al. [37] treated melanoma skin tumours in five patients, where a steel needle cathode was inserted into the tumour and three or four self- adhesive plate anodes were placed on the skin, several centimetres from from the lesion edges. All of the patients, with one exception, received electric treatment in combination with systemic chemo- and/or immuno- therapy. The treatments resulted in tumour mass reduction in all of the evaluable lesions (10 out of 12), although no complete responses were observed. A number of papers have been published in Japanese language journals that describe the anti-tumour effect of EChT in animals and humans, either as a single type of therapy [38] or in combination with chemo- or radio-therapy [39-43]. In one article [44], published in The European Journal of Surgery, Matsushima et al. reviewed their clinical experiences (27 tumours in 26 patients) with EChT alone, and in combination with systemic chemotherapy. The current was supplied by two platinum electrodes placed in the tumour.

6 More than 70% of the tumours showed regression and in two of the cases, where only EChT was used, complete regression was observed. Griffin et al. [45] evaluated the effect of different currents on inoculated mammary carcinomas in mice. The animals were placed on a copper plate electrode, while a gold wire was placed inside the tumour and used as either the anode or cathode. The results showed that the volume of tumour destruction, obtained at a given coulomb dosage, was significantly greater with anodic treatment over cathodic treatment. Chou et al. [46] treated implanted fibrosarcoma tumours in mice and rats with a constant voltage load ( ≤10 V) for different durations, whilst using various electrode configurations. Two to five platinum wire electrodes were inserted into the mice tumours, whereas four to seven electrodes were used in the rat tumour treatments. All of the treated tumours showed regression although, in many of the animals, the tumours recurred. After multiple treatments, the best mouse tumour cure rate was 59% after three months, and 75% after six months, for the rats.

1.2. Destruction mechanisms Several contributory factors seem to be involved in the tumour destruction, although their respective roles are not yet fully understood. However, the primary tissue destruction, obtained in the electrodes’ close vicinity, is most probably caused by the toxic species produced in the electrochemical reactions during electrolysis. The reaction products are toxic to both tumours and healthy tissue, although normal cells and tumour cells might show differences in their sensitivity to these species. The current yield of the different electrochemical reactions, occurring in the electrolysis of aqueous saline solutions, strongly depends on the choice of electrode material and operating conditions [47]. If the anode material is electrochemically soluble (e.g. copper), the major part of the anodic current will consist of metal dissolution. A small amount of the anodic current is transferred by the oxidation and reduction of certain species already dissolved in the tissue. Some dissolvable metals (e.g. silver) form a non- conducting compound on the anode surface, which may cause current fluctuations. In cases where the anode material is made of a metal that can be passivated, such as platinum, metal dissolution is negligible. Passivity is caused by the formation of a thin, electron conducting, oxide film that acts as a barrier to the anodic metal dissolution reaction. The main reactions in these cases are the decomposition of water and oxidation of chloride ions:

→ +- 2H22 O ← O + 4H + 4e (1)

- → - 2Cl ← Cl2 + 2e (2)

7 The cathode material is protected against electrochemical dissolution by the applied cathodic current, and the major electrochemical reaction is, in all cases, the decomposition of water into molecular hydrogen and hydroxyl ions:

- → - 2H2 O + 2e ← H2 + 2OH (3)

Since convective transport are obstructed by the dense structure of tissue, species produced at the anode and cathode are mainly transported to the surrounding tissue by diffusion, due to concentration gradients, and by migration (charged species), due to the potential gradient. The electrochemical reaction products may also react with organic and inorganic tissue constituents, to potentially form new toxic products. The presence of extreme local pH changes in tissue surrounding the electrodes, during and after EChT treatment, has been confirmed in many studies [5, 29, 48-49]. pH values down to 1 have been detected in tissue adjacent to the anode [29], while a pH as high as 13 has been measured near the cathode [48]. At these non-physiological conditions, vital proteins become denatured and precipitated [5, 48, 50]. The extreme pH conditions in the vicinity of the electrodes have also been predicted in several theoretical studies. Cvirn et al. [51] estimated the spreading of the alkaline zone around a spherical cathode while Berendson and colleagues [52, 53] studied the spreading of hydrogen ions and molecular chlorine around spherical and planar platinum anodes. Several authors have identified chlorine [5, 48, 54] and hydrogen [5, 48] evolving from the anode and cathode sites, respectively. Samuelsson and Jönsson [55] measured the content of organically bound chlorine in anodic lesions, produced around platinum anodes in the lungs of pigs, and found it to be significantly elevated compared with healthy tissue. They concluded that chlorine, through its oxidative properties, is the main agent responsible for the tissue destruction obtained in EChT treatments. Their conclusion was contradicted by Berendson and colleagues [52, 53]. Their calculations indicated that the acidified zone around the anode is significantly larger than the chlorinated zone and thereby determines the extent of tissue destruction. It has been suggested that the extreme pH condition in the vicinity of the electrodes causes electrocoagulation and thereby the shutdown of blood flow to the tumour [56, 57]. This mechanism could possibly explain the anti- tumour effect obtained in EChT studies where the electrodes are placed outside the tumour. Jarm and colleagues [58, 59] tested this hypothesis and obtained promising results on fibrosarcoma tumours in mice. In one experiment [59], the relative tissue perfusion of the tumours was found to decrease by more than 50%.

8 The production of toxic electrolytic products may not fully explain the anti- tumour effects obtained in EChT studies. A series of in vitro studies with direct current, on both malignant and normal cells, has shown that the electric field itself influences both survival and proliferation of the cells [36, 60-64]. The mechanism by which the electric field affects cell growth and survival has not yet been elucidated, but it is most probably a complex process. The electric field causes a flux of interstitial water (electro-osmosis) from the anode towards the cathode and, consequently, the tissue surrounding the anode dehydrates while oedema is obtained around the cathode [5, 65]. Charged substances, dissolved or suspended in tissue, migrate in the electric field and accumulations of ions and charged tissue constituents are obtained at certain and different locations in the electric field. The electric field influences the ion exchange across the cell membranes and thereby the conditions for many essential enzyme-regulated reactions [5]. The possibility of direct current in inducing an immune response or enhancing the toxicity of immune cells has also been discussed [66].

1.3. Dose planning A dose planning methodology is a prerequisite for reproducible and predictable treatment results. When Nordenström first started his clinical work, few guidelines existed for an optimal choice of treatment parameters, so that an arbitrary dose of about 100 C/cm of tumour diameter was chosen [5]. Xin and colleagues adopted this preliminary dose unit and, based on their clinical experiences, later adapted the coulomb dose depending on the type of tumour, see Section 1.1 [12]. Several authors have systematically investigated the dose-response relationship between the applied current, treatment time, coulomb dosage and tissue destruction in order to develop an optimised dose planning methodology. Samuelsson et al. [49] treated normal lung and liver tissues in rabbits, with different coulomb dosages and found a linear relationship between the volume of tissue destruction, around the anode, and coulomb dosage. Griffin et al. treated mouse mammary carcinomas [45] and normal rat livers [56] and found a linear relationship between the volume of primary tissue destruction and coulomb dosage around both anode and cathode. Moreover, no differences could be detected between the lesion sizes obtained at lower and higher currents at a given coulomb dosage. Robertson et al. [67] conducted a similar study in normal rat livers and came to the same conclusions. While the above data supports the hypothesis that coulomb dosage is a reliable dose parameter, other workers have reported otherwise. Yen et al. [62] studied the growth retardation and survival of human KB cells after

9 electrochemical treatment and found that the cytotoxicity of EChT is related, not only to coulomb dosage, but also to the way by which the coulomb dosage was delivered. Treatments with low current and longer treatment times resulted in lower cell viability, compared to treatments with higher current and shorter treatment time. Xin et al. [14] reported analogous results from clinical treatments of lung tumours.

1.4. Objectives of this thesis EChT offers considerable promise as a safe and simple anti-tumour therapy for treatment of localised malignant as well as benign tumours. Before clinical trials can be conducted outside of China, further systematic investigations of the destruction mechanisms must be done and a reliable dose planning strategy has to be developed. One approach towards both a deeper understanding of the underlying destruction mechanism behind EChT and a reliable dose planning methodology is the use of physicochemical simulation models. Such models are based on a set of physicochemical differential equations that describe the transport and reaction processes occurring at the electrodes during EChT. By solving these equations, concentration profiles of substances dissolved in tissue, and the potential profile within the tissue itself, can be simulated as functions of time. Hitherto, only a few and very simplified mathematical models of EChT have been reported in literature, see Section 1.2 [51-53]. The objective of this thesis is to develop mathematical models that are able to describe the concentration profiles of species, dissolved in tissue surrounding the electrodes, during the electrochemical treatment. The hypothesis is that these models will serve as useful tools in investigating the underlying destruction mechanisms behind EChT, as well as in developing a dose planning strategy. For simplicity, the mathematical modelling is focused on treatments with spherical electrodes. In addition to the modelling work, the thesis includes an experimental EChT study on healthy mammary tissue in rats. The results from this study enable an investigation of the validity of the mathematical models, as well as of their applicability for dose planning.

10 2. EXPERIMENTAL

The experimental work, included in this thesis, is a study in which normal mammary tissue in rats was treated with three different currents and coulomb dosages. The macroscopic tissue destruction, obtained directly after treatment, was measured along with the pH profile in tissue surrounding the electrodes. In this section, the experimental procedure of these treatments is summarised. A detailed account of the experiments is found in Paper I.

Animals and sorting Normal adult female CD rats, of a weight of about 270-350 g, were treated with EChT under general anaesthesia. The animals were randomly divided into 6 treatment groups, see Table 2. Each group was treated with a constant direct current of 1, 2.5 or 5 mA for a specific duration of time, corresponding to a coulomb dosage of 2.5, 5 or 10 C.

The electrochemical treatment Two spherical electrodes, made of Pt:Ir (9:1) and with a diameter of 1 mm, were placed intramammarily in the left and right fourth mammae. The spheres were joined to electrically insulated Pt:Ir rods, 0.5 mm in diameter. The electrodes were inserted in a caudal-cranial direction with the rat in dorsal recumbency. In all procedures, the electrode on the animal’s right side was chosen to be the anode. Direct current was passed through the electrodes by means of a constant-current power supply, consisting of a potentiostat coupled to an adjustable resistor. The current and voltage were continuously monitored. To avoid muscle twitching, linear current ramps with a length of 2 minutes were used at the beginning and end of the treatment.

Table 2. Treatment conditions in terms of current and coulomb dosage. The number of samples used in the measurements of the macroscopic destruction zone is denoted nmd. The number of samples used in the pH measurements is indicated by npH.

Treatment Current Coulomb dosage nmd npH group [mA] [C]

I1 5 87 II 2.5 5 9 7 III 2.5 10 10 8 IV 5 2.5 10 8 V5 5 76 VI 5 10 8 8

11 Macroscopic destruction zone After the treatment, the rats were euthanised and the lesions were extracted and transversally cleaved in half, along the insertion of the electrodes. Subsequently, the macroscopic destruction zone, here defined by the dark coloured zone around the electrodes, was measured. The characteristic dimensions of the destruction zone are shown in Fig. 1 and are defined by the diameter along the inserted electrode, d1, and the diameter perpendicular to this, d2. Statistical evaluations were performed by means of Student t-tests (paired and two sample), comparing destruction diameters in different experimental groups of interest. Values of P<0.05 were considered indicative of statistical significance. pH measurements pH measurements were done using a micro-combination pH glass electrode encased in a stainless steel needle. The tip of the needle had a diameter of 1.3 mm. Measurements were made in the centre of the lesion, where the spherical electrode had been situated during the treatment, and at every second mm from this point along d2 until well out into the healthy tissue, see Fig. 1. The first pH measurement, in tissue that had been surrounding the anode, was performed about 5 min after current shutdown while the last was conducted 5-10 min later. After this, pH measurements were made in tissue that had been surrounding the cathode. The last measurement was performed about 15-20 min after current shutdown.

d2

macroscopic destruction zone

d1 pH

electrode

Fig. 1. Schematic of a spherical electrode and characteristic dimensions of the macroscopic destruction zone, d1 and d2. The pH measurements were made along d2.

12 3. MATHEMATICAL MODELLING

The modelling work is divided into four studies; three concerning the anode (Paper II-IV) and one devoted to the cathode (Paper V). The first anode study treats a highly simplified model in which tissue was treated as an aqueous solution of sodium chloride. The model was further developed, in the subsequent studies, to firstly include a bicarbonate buffer system and then the influence of chlorine. Based on the experiences from the anode modelling, a similar development was carried out on the cathode. A brief description of the development of the anode and cathode models is given in this section.

3.1. General problem definition The mathematical modelling focuses on tissue surrounding a spherical platinum electrode when applying a continuous direct current. The spherical geometry of the models and symbols used to denote its geometrical dimensions are illustrated in Fig. 2. The electrolyte domain, Ω , is bounded ∂Ω by an inner and outer spherical surface. The inner boundary surface, e , represents the spherical electrode with a radius re . The outer boundary, ∂Ω r , represents a spherical surface with a radius r r , at a distance large enough from the electrode to assure constant concentrations. The electrode is assumed to be placed at a distance far enough from its opposite to ensure that the anodic and cathodic reaction zones do not interact. Tissue is a heterogeneous medium containing a discontinuous cellular phase and a continuous extracellular phase. When current is applied to tissue, it is mainly transported through the channels of extracellular fluid. This is confirmed by the electro-osmotic effects, which have been shown to arise during EChT [5]. The current is carried by diffusible ions in the extracellular fluid and substantial concentration gradients of these ions arise during electrolysis. Due to the transport of solutes across the cell membranes, changes in extracellular concentrations also affect the composition of electrolyte in the intracellular compartment. However, the nature and time dependence of this interplay, during the electrochemical treatment, is poorly understood. Transport of current is assumed to occur solely through the extracellular fluid in this work. Tissue is treated as a dilute and homogeneous aqueous solution, so that no consideration is taken to the fact that, in real tissue, the cells serve as obstacles for transport of species in the extracellular fluid. Hence, the transport properties of the involved species are approximated to being those found in aqueous solutions. In order to take into account the structure of tissue, effective transport coefficients, which include porosity and turtuosity as parameters, should be introduced. However, the effective

13 transport properties in tissue are not known and it is out of the scope of this thesis to determine these entities. Two transport mechanisms, diffusion and migration, are assumed to contribute to the transport of the solute species in the tissue. The flux of species due to convection is neglected. This assumption is justified as convection is strongly obstructed by the dense structure of tissue. Moreover, the gas bubbles, formed in tissue surrounding the electrodes, are assumed to not affect the conductivity of the electrolyte. The electro-osmotic effects are neglected in this analysis. In reality, the electric field causes a flux of extracellular water from the anode towards the cathode and, consequently, the tissue surrounding the anode dehydrates while oedema occurs around the cathode [5]. Inputs to the models are the current density, applied at the electrode, and the sizes of the electrode and electrolyte domain. Outputs from the models are the concentration profiles, of substances dissolved in the tissue, and the potential profile within the tissue, both as functions of time.

∂Ω electrode surface e

electrolyte domain Ω

rr

outer boundary ∂Ω r

re

r

Fig. 2. Spherical geometry of the model and symbols used to denote its dimensions.

14 3.2. Anode modelling The development of the anode model is carried out in three steps, corresponding to separate models; the sodium chloride, bicarbonate buffer and chlorine models. The stepwise model development enables a thorough investigation of separate features influencing the concentration and potential profiles in tissue surrounding the anode.

The sodium chloride model In the sodium chloride model, tissue is approximated by an aqueous solution of 0.16 M sodium chloride at a pH of 7. The chosen tissue composition is justified by the fact that sodium and chloride ions are those predominant in the extracellular fluid, where the total ionic concentration in -3 plasma and interstitial fluid is 0.161 and 0.153 eq dm H2O, respectively, and pH is about 7.4 [68]. The electrochemical reactions, considered in the model, are the competing oxygen and chlorine evolution reactions:

→ +- 2H22 O ← O + 4H + 4e (4)

- → - 2Cl ← Cl2 + 2e (5) while the considered homogeneous chemical reaction is the water protolysis reaction:

+-→ H + OH ← H2 O (6)

The solution near the electrode is assumed to be saturated with respect to oxygen and chlorine. Small gas bubbles, with an internal pressure of 1 atm containing either oxygen or chlorine, are assumed to be in equilibrium with the platinum electrode surface. More details concerning the sodium chloride model are found in Paper II.

The bicarbonate buffer model A natural step in the development of the anode model is to introduce the limiting effect that the buffer capacity of tissue has on the spreading of the hydrogen ions, produced in the oxygen evolution reaction (4). As the bicarbonate buffer is the most important buffer system in the extracellular fluid [68], it is implemented into the sodium chloride model, as a first approximation to tissue’s buffer capacity. The bicarbonate buffer system is modelled by the following reaction:

+ - → + ← H HCO3 CO2 (aq) + H2 O (7)

15 The initial concentrations of the ionic species, treated in the model, corresponds to an aqueous solution with a total concentration of 0.16 M with a pH of 7.4. The bicarbonate concentration is set to 27 mM. This choice of bicarbonate concentration is justified by the fact that the concentration in -3 plasma and interstitial fluid is 25.8 and 27.1 meq dm H2O, respectively [68]. The concentration of CO2(aq) is assumed to be constant throughout the solution domain. The validity of this assumption along with more details about the bicarbonate buffer model, is presented in Paper III.

The chlorine model Conflicting opinions can be found in the literature over the role of chlorine in the destruction of tissue around the anode. In order to investigate the impact of chlorine in EChT treatments, the model is, in a third stage of development, extended to take into account the transport and reaction processes of chlorine. The study focuses on the relative spreading of the chlorinated and acidic zones around the anode, as well as the role of chlorine as a source for the production of hydrogen ions. The chlorine model brings about six additional homogeneous chemical reactions to the analysis. Molecular chlorine, produced in the chlorine evolution reaction (5) at the anode, reacts with water to form hypochlorous acid, chloride and hydrogen ions:

→ -+ Cl2 (aq) + H2 O ← HClO + Cl + H (8)

Cl2(aq) and HClO are highly reactive and are known to have strong toxic effects [69]. The principal chemical reactions of Cl2(aq) and HClO with a variety of organic constituents, in aqueous solutions, are discussed in Paper IV. The reactions may be divided into three general groups; addition, substitution and oxidation [69-73]. Addition reactions occur when Cl2(aq) and HClO add across reactive organic double bonds. Substitution reactions involve the replacement of one atom or functional group with another. In addition to acting as chlorinating agents, Cl2(aq) and HClO also act as oxidising agents.

Clearly, the reactions of Cl2(aq) and HClO with organic constituents in tissue are very complex. In this model, the substitution and addition reactions are modelled by the following simplified reactions:

→ -+ Cl2 (aq) + Org Org - Cl + Cl + H (9) → HClO + Org Org - Cl + H2 O (10) The oxidative reactions are modelled according to the following simplified reactions:

16 → -+ Cl2 (aq) + Org - red + H2 O Org - ox + 2Cl + 2H (11) → -+ HClO + Org - red Org - ox + Cl + H (12) Here, Org denotes an organic molecule susceptible to chlorination while Org-ox and Org-red denote an organic compound in its oxidised and reduced state, respectively. The organic constituents are considered to be immobile. The concentration of organic constituents, susceptible to chlorination in tissue, Org, is set to 0.28 M. This value is estimated from a study made by Samuelsson and Jönsson, where the content of organically bound chlorine in anodic lesions, was measured [55]. Tissue’s capacity to react with Cl2(aq) and HClO through oxidation is not known. However, by making an analogy to a traditional application field of chlorine chemistry, namely pulp bleaching, tissue’s capacity to react with Cl2(aq) and HClO through oxidation is estimated to be of a similar order of magnitude as that of chlorination [71, 74].

The concentration of Cl2(aq), in tissue, is limited by its saturation concentration. When the saturation concentration is exceeded in the model, small chlorine bubbles, with an internal pressure of 1 atm, are assumed to be in equilibrium with Cl2(aq):

→ Cl2 (aq) ← Cl2 (g) (13)

Hence, reaction (13) is considered only where the saturation concentration of chlorine in tissue is exceeded. A more detailed description of the chlorine model is given in Paper IV.

3.3. Cathode modelling The development of the cathode model is carried out in a stepwise process, similar to that of the anode. The first system is one in which tissue is approximated by a homogeneous aqueous solution of sodium chloride. This model is subsequently modified through the introduction of a bicarbonate buffer system. In order to investigate the impact of non-bicarbonate related buffers on the spreading of hydroxyl ions, organic constituents, susceptible to reactions with hydroxyl ions, are introduced in the third and last stage of the model development.

The sodium chloride model The cathodic sodium chloride model is in close resemblance to that of the anodic. Tissue is treated as a sodium chloride solution with a concentration of 0.16 M and pH 7.4, and the considered homogeneous chemical reaction is

17 the water protolysis reaction (6). The basic difference between the two models shows up in the electrochemical reactions at the electrode, where the hydrogen evolution reaction is considered in the cathode model:

- → - 2H2 O + 2e ← H2 + 2OH (14)

The solution near the electrode is assumed to be saturated with hydrogen. Small hydrogen gas bubbles, with an internal pressure of 1 atm, are assumed to be in equilibrium with the platinum electrode surface.

The bicarbonate buffer model The sodium chloride model is subsequently extended to take into account the impact of a bicarbonate buffer on the spreading of hydroxyl ions, produced in the hydrogen evolution reaction (14). The bicarbonate buffer system is modelled by the following reaction scheme [75, 76]:

- → - OH + CO2 (aq) ← HCO3 (15)

- - → 2- + ← OH HCO3 CO3 + H2 O (16)

The bicarbonate concentration is set to 27 mM. Respiratory or metabolic compensation of the loss of CO2(aq) are assumed to be negligible.

The extended buffer model Organic buffer systems, such as proteins and organic phosphates, may play an important role in the buffering of tissue around the cathode. In order to study the effect of these buffers on the simulation results, an immobile organic constituent that is susceptible to reactions with hydroxyl ions, H- Org, is implemented into the model. The introduction of H-Org provides a simplified way to account for the buffer capacity of proteins in the extracellular fluid, as well as the organic intracellular buffering of hydroxyl ions. No distinction is made between reactions of intracellular or extracellular organic buffers and, consequently, transport processes across cell membranes are disregarded. The buffer reaction between H-Org and hydroxyl ions is modelled by the following simplified reaction:

- → - H - Org + OH Org + HO2 (17) The organic buffer reaction commences as soon as the initial concentration of hydroxyl ions is exceeded. This simplified description of the organic buffers is made in order to isolate the consumption of the hydroxyl ions, without

18 introducing further complexity to the system, which would inhibit its understanding. The capacity of proteins and organic phosphates to react with hydroxyl ions, produced during EChT, is unknown. For this reason, calculations are run using a wide spectrum of H-Org concentration so that its influence on the simulation results can be thoroughly investigated.

3.4. Model equations The transport equations of ionic species in dilute solutions [77] provide the basis for the analysis of the transport and reaction processes occurring in tissue during EChT. In addition, kinetic expressions for the electrochemical reactions are introduced at the electrode surface [77]. The implementation of electrode kinetics into the model makes it possible to estimate the anodic and cathodic overvoltages, and, at the anode, the current yields of chlorine and oxygen evolution. The equations of electrode kinetics are based on reaction mechanisms proposed in the literature [78-80]. In this section, a general description of the model equations used in the mathematical modelling is presented. A detailed derivation of the basic transport equations and electrode kinetics, applied in the models, is presented in Paper II.

Domain equations The governing equations include differential material balances for all species considered in the solution domain, Ω :

∂ ci =−∇⋅ + NiiR (18) ∂t

Here, ci denotes the concentration, t the time, N i the molar flux and Ri represents the production of species i through homogeneous chemical reactions. The molar flux vector is expressed as:

z N =−Dc ∇ −i uc ∇Φ (19) i ii z ii i where Di is the diffusion coefficient, zi the number of charges carried by the Φ ion i, ui the ionic mobility and the potential field in the electrolyte. The production term in equation (18), Ri, is directly related to the kinetics of the chemical reactions that occur in the electrolyte domain. For example, the production term of hydroxyl ions, in the anode modelling, is expressed as:

Rkcckc−+−=− + (20) OHf H OH b HO2

19 where kf and kb denote the forward and backward rate constants of the water protolysis reaction (6), respectively. The condition of electroneutrality forms the remaining model equation in the electrolyte domain:

= ∑ zcii 0 (21) i

Boundary and initial conditions ∂Ω Mass transport of species i across the electrode surface, e , is either non- existent or equal to the charge transfer, present through virtue of the electrochemical reactions. Thus:

ν z iji j −∇⋅Dc()nn−∇⋅i uc()Φ = (22) ii z ii nF i j where n is the outward unit normal vector, nj the number of electrons transferred in the electrochemical reaction j, ν the stoichiometric coefficient ij and F is Faraday’s constant. ij denotes the current density contributed by the electrochemical reaction j. The anode current density, contributed by oxygen and chlorine evolution, respectively, are given by:

   ΦΦ+ ref  1  + ref    FE()eq,O   FE()eq,O  =− 2 − 4 2 iiO0,Oexp  ()PCO + exp  (23) 22  22RT  2 H  RT      

 ref ref    FE()ΦΦ+  1  FE ()+  eq,Cl 2 eq,Cl 2 iiC=− − exp  − ()C 2 exp  (24) Cl22 0,Cl Cl Cl 2 ()aq   22RT   RT  while the analogous expression for the current density, contributed by hydrogen evolution reaction at the cathode, is:

  ΦΦ+ ref   + ref   2  3FE()  FE() = − eq,,HH22− eq iiH () C- PH exp  exp  (25) 2 0,H 2  OH 2  22RT   RT      

= ref = ref where, Ccc i i and Ppp i i , with p denoting the partial pressure and Eref ref a reference state. eq is the potential difference between the solid and liquid phases, at equilibrium conditions and relative to a reference, and is

20 found through Nernst’s equation. i0 denotes the exchange current density, T the absolute temperature and R the universal gas constant. In addition to equation (22), formulated for the involved species, the boundary conditions at the electrode include the condition of electroneutrality (21). The concentration gradients are equal to zero at the outer boundary surface, ∂Ω r : ∇⋅ = ci n 0 (26) The potential gradient, at the outer boundary surface, is obtained through substituting the molar migration flux vector into Faraday’s law (see Paper II):

1 ()in⋅ +∇⋅∑ zuc()Φ n= 0 (27) F iii i where i is the current density vector.

Initially, there are no concentration gradients throughout the electrolyte, and the concentrations are given by the initial condition below:

= 0 cr ii(,0 ) c (28) Φ0 The initial potential at the electrode, e , is solved from the given current density, applied at the electrode, and its respective contributions obtained from equations (23)-(25). The initial potential profile throughout the solution domain, is obtained by integrating equation (27) using the boundary ΦΦ00= condition (,)ree0 .

3.5. Input data and numerical implementation The physicochemical parameters applied in the modelling work are listed in the respective papers describing the development of the anode and cathode models. All input parameters are valid at 37°C, except those used in the initial anode study, which were given at 25°C. The parameters are valid in dilute aqueous solutions and are either taken from the literature, or are derived from related literature values using relevant equations. The operator ∇ is written in spherical coordinates and, by assuming rotational symmetry, the model is reduced to a one-dimensional problem with the space coordinate r. The time derivative is approximated by the trapezoidal rule. The obtained non-linear equation system is solved by Newton’s method [81], using sparse matrix routines included in MATLAB®. The total number of grid points and the maximum time step were decided

21 through ensuring convergence of the numerical solution, i.e. when the refinement of the mesh and decrease of the time step did not affect the solution. The radius, , of the outer boundary surface was chosen to be r r large enough so as not to affect the solution of the problem A more detailed description of the numerical implementation is presented in Paper II.

22 4. RESULTS AND DISCUSSION

This section is divided into three parts, where the first part presents and discusses results obtained from the experimental study in normal rat mammary tissue (Paper I). The second and third parts summarise results from the anode (Paper II-IV) and cathode (Paper V) simulations, respectively. In these modelling sections, the validity of the mathematical models, as well as their applicability for dose planning, is investigated by comparing the simulation results with results obtained in the experimental study.

4.1. Experiments in rat mammary tissue The electrochemical treatment of healthy rat mammary tissue produced dark brown and almost spherical lesions, centred around each of the electrodes. These dark brown zones are attributed to the formation of acid and basic heamatin, at the anode and cathode, respectively [5, 50]. A diffuse grey- white zone was discernible in the centre of the anodic lesion, where the electrode had been positioned. This zone is most probably caused by the bleaching effect of chlorine and its secondary reaction products. The colour patterns of the anodic and cathodic lesions are in agreement with results found in other studies [5, 49]. The electro-osmotic transport of water, from the anode towards the cathode, caused a prominent oedema in tissue around the cathode while a severe dehydration was obtained around the anode. Measurements of the characteristic dimensions of macroscopic destruction zones surrounding the electrodes, in all animals, showed that the destruction diameter along the inserted electrode, d1, was larger than, or equal to, the diameter perpendicular to this, d2. The difference between the two diameters was, at the anode, significantly less than 15% while that at the cathode was found to be significantly less than 10%. The deviation from the expected spherical geometry can be explained by the canalisation of gases and oedema fluid along the electrode insertion. Another reason for this asymmetry is a non-uniform current distribution caused by the positioning of the current collector on the spherical electrode.

The mean diameters, dm= (d1+d2)/2, of the anodic and cathodic destruction zones, obtained after different treatment conditions, are presented in Table 3. When comparing the anodic and cathodic destruction diameters in each of the animals, the cathodic diameters were found to be significantly larger than the anodic. The mean anodic and cathodic destruction diameters, obtained in groups exposed to the same coulomb dosages, showed no significant statistical difference between a 2.5 mA or 5 mA treatment.

23 However, when comparing the 1 mA treatment with the 2.5 and 5 mA treatments, all at 5 C, significant differences were obtained in both anodic and cathodic lesion sizes. These results support the hypothesis that the effect of a specified coulomb dose is not always consistent. By decreasing the treatment current, the buffer systems of the body can, to a larger extent, counteract the spreading of toxic species around the electrodes. Thus, the number of applied coulombs corresponds to the amount of reaction products formed at the electrodes but does not directly describe their distribution in tissue. pH measurements performed in tissue surrounding the anode and cathode revealed steep pH profiles, going from non-physiologic to neutral status, within a few millimetres. The growth of the acidic and alkaline zones around the anode and cathode, respectively, was clearly observed as the coulomb dosage increased. Moreover, the pH, adjacent to the electrode surfaces, continuously decreased at the anode and increased at the cathode as the coulomb dosage increased. The anodic and cathodic pH profiles are visualised in Sections 4.2 and 4.3, where they are compared to simulated profiles, obtained from the anode and cathode modelling. The pH at the border of the anodic lesions was found to correlate to a value between 4.5 and 5.5, irrespective of the delivered current or coulomb dosage. The corresponding pH in tissue surrounding the cathode varied between 9 and 10. The fact that the pH, at the border of the anodic and cathodic lesions, was found to correlate to narrow pH ranges strongly indicates that it is the spreading of hydrogen and hydroxyl ions that determines the extent of tissue destruction around the anode and cathode, respectively.

Table 3. Lesion sizes, presented as a mean diameter ±1 standard deviation, obtained around the anode and cathode, after different treatment conditions.

Treatment Treatment Diameter of the anodic Diameter of the cathodic group conditions lesions lesions

[mm] [mm]

I 1 mA, 5 C 5.3 ± 1.0 6.1 ± 0.8 II 2.5 mA, 5 C 6.9 ± 0.8 7.5 ± 0.4 III 2.5 mA, 10 C 8.5 ± 0.8 9.3 ± 0.4 IV 5 mA, 2.5 C 4.9 ± 0.4 5.1 ± 0.6 V 5 mA, 5 C 6.7 ± 0.6 7.2 ± 1.0 VI 5 mA, 10 C 8.8 ± 0.5 9.8 ± 1.3

24 4.2. Anode modelling

General behaviour of the sodium chloride and bicarbonate buffer models The general behaviour of the anodic sodium chloride and bicarbonate buffer models are visualised and discussed in this section. The physicochemical input parameters used in these simulations are those valid at 37°C. The anode radius is set to 1 mm and the anode current density is 100 mA cm-2. Fig. 3 shows the concentration profiles of sodium, hydrogen and chloride ions, obtained from the sodium chloride model, after 10 minutes of electrolysis. Hydrogen ions, produced in the oxygen evolution reaction, form an acidic zone around the anode. Chloride is consumed in the chlorine evolution reaction, which results in the depletion of chloride ions close to the anode. The sodium ions are transported away from the anode by means of migration. The concentration profiles of all the ions are closely related through the condition of electroneutrality. The depletion of chloride ions and the fact that the electroneutrality condition has to be maintained give rise to a depletion of hydrogen ions, close to the anode, and a maximum in hydrogen ion concentration further out in the electrolyte. The mobility of the hydrogen ion is 7 times larger than that of the sodium ion, and about 5 times larger than the mobility of the chloride ion. This, together with the condition of electroneutrality, leads to a situation where the spreading rate of hydrogen ions, away from the anode, is limited by the transport of sodium and chloride ions away and towards the anode, respectively.

0.18 - 0.16 Cl

-3 0.14 + 0.12 Na

0.1

0.08

0.06

concentration / mol dm H+ 0.04

0.02

0 0 2 4 6 8 10121416 distance r / mm

Fig. 3. Concentration profiles of sodium, hydrogen and chloride ions, obtained from the sodium chloride model, after 10 minutes of electrolysis. The anode radius is 1 mm and the total anode current density is 100 mA cm-2.

25 0.16

Cl-

0.14

-3 0.12 Na+ 0.1

0.08

0.06 +

concentration / mol dm H 0.04 - HCO3 0.02

0 0 1 2 3 4 5 6 7 8 9 10 distance r / mm

Fig. 4. Concentration profiles of sodium, hydrogen, chloride and bicarbonate ions, obtained from the bicarbonate buffer model, after 10 minutes of electrolysis. The anode radius is 1 mm and the total anode current density is 100 mA cm-2.

The concentration profiles of sodium, hydrogen, chloride and bicarbonate ions, obtained from the bicarbonate buffer model, are shown in Fig. 4. The time of electrolysis in this simulation is 10 min. The spreading of hydrogen ions is counteracted by these ions’ reaction with bicarbonate. The concentration profiles of the hydrogen and bicarbonate ions cross each other in a reaction zone about 6 mm from the centre of the anode. The steep bicarbonate profile, caused by its reaction with the hydrogen ions, strongly influences the profiles of the other ions through the electroneutrality condition. A comparison between the pH profiles obtained by the sodium and bicarbonate buffer models, after different times of electrolysis, is presented in Fig. 5. The two models predict about the same pH values adjacent to the anode surface. The movement of the acidic zone, in the tissue surrounding the anode, is considerably impeded by the bicarbonate buffer system. The pH profiles predicted by the bicarbonate buffer model are much steeper than the profiles obtained from the sodium chloride model. The behaviour of the bicarbonate buffer model is similar to a shrinking core model [82]. However, in this case the shrinking part is an outer shell rather than a core.

26 8

7

6 10 min 30 min 10 min 30 min 5

pH 4

3

2 buffer model 1 NaCl model

0 0 5 10 15 20 25 30 distance r / mm

Fig. 5. Simulated pH profiles obtained from the sodium chloride model and the bicarbonate buffer model, after 10 and 30 minutes of electrolysis. The anode radius is 1 mm and the total anode current density is 100 mA cm-2.

Comparison between experimental results and the sodium chloride and bicarbonate buffer models The validity of the sodium chloride and bicarbonate buffer models was investigated by comparing simulated pH profiles with results obtained in the experimental study in normal mammary tissue in rats, presented in Section 4.1. Simulations were run using anode radius, current densities and treatment times identical to those used in the experiments. Linear current ramps were used at the beginning and end of the simulations, as in the experiments. Fig. 6 shows the simulated pH profile, obtained from the bicarbonate buffer model, when using an anode current density of 85 mA cm-2 and a total treatment time of 2120 sec. These conditions correspond to a treatment using 2.5 mA and 5 C. Also presented in the figure are the experimental profile and the simulated profile obtained from the sodium chloride model. As expected, the acidic zone around the anode is considerably overestimated by the sodium chloride model. The bicarbonate buffer model, on the other hand, predicts an acidic zone of about the same radius as that found in experiment. However, the simulated profile is more acidic than the experimental profile. One reason for this discrepancy may be that the pH measurements were not enacted immediately after current shutdown. Between current shutdown and pH measurement, the concentration profiles will relax due to diffusion and chemical reaction.

27 8

7

6

5 pH 4

3 experimental buffer model 2 NaCl model

1 0 5 10 15 20 25 30 distance r / mm

Fig. 6. Comparison between simulated pH profiles, obtained from the sodium chloride and bicarbonate buffer models, and an experimental pH profile. The total anode current density is 85 mA cm-2 and the total time of electrolysis is 2120 sec. These treatment conditions correspond to a current of 2.5 mA and a coulomb dosage of 5 C. The experimental values are given as the mean ±1 standard deviation.

8

7

6 in m 20

5 in m pH 15 4 in m 10 3 in 5 m in experimental 0 m 2 buffer model

1 0 12345678910 distance r / mm

Fig. 7. Simulated pH profiles, obtained from the bicarbonate buffer model, as a function of time following current shutdown: 0, 5, 10, 15 and 20 minutes. The initial pH profile was similarly obtained from the bicarbonate buffer model as in Fig. 6. Also shown in the figure, is the experimental pH profile (mean ±1 standard deviation).

28 A simulation in which i , i , and ∇Φ were set to zero, directly after O2 Cl2 electrolysis, was run in order to investigate the influence of diffusion- reaction relaxation on the pH profile. Fig. 7 shows the simulated pH profile as a function of time, following current shutdown. Also shown in the figure is the experimental pH profile. The pH increases continuously in the acidified zone surrounding the anode. The experimental pH profile agrees fairly well with that of simulated pH, obtained after 10-15 minutes of diffusion-reaction relaxation. This result is consistent with the fact that the last pH measurement was determined about 10-15 minutes after current shutdown. The slight difference in shape between the experimental and simulated profiles might be attributed to an overestimation of the buffer reaction rate. Simulations were also run in order to investigate the correlation between simulated pH profiles and experimental lesion radii. These results are presented in Table 4. The simulated pH, at a radius corresponding to the border of the lesions, correlates well to a value between 1.5 and 2.5. Consequently, the simulations indicate that dark brown acidic heamatin, which defined the size of the lesions in the experiments, is formed at this pH. This result is consistent with an experimental observation reported by Ito et al. [38]. According to their study, acidic heamatin is formed at pH<2. The simulation result is also in line with the clinical experiences from China, which report that it takes a pH of around 2 to cause irreversible tissue destruction [83].

Table 4. Experimental anodic lesion radii (mean ±1 standard deviation), simulated pH values, at the radius corresponding to the border of the mean lesion radii, and simulated lesion radii, at different treatment conditions. Simulated lesion radii were obtained from the pH profiles, predicted by the bicarbonate buffer model, using the condition that pH<2 gives lesions.

Treatment Treatment Experimental Simulated pH Simulated lesion group conditions lesion radius at experimental radius lesion border [mm] [mm]

I 1 mA, 5 C 2.7 ± 0.5 2.5 1.5 II 2.5 mA, 5 C 3.5 ± 0.4 2.0 3.5 III 2.5 mA, 10 C 4.3 ± 0.4 2.1 4.0 IV 5 mA, 2.5 C 2.4 ± 0.2 1.5 3.4 V 5 mA, 5 C 3.4 ± 0.3 1.7 4.3 VI 5 mA, 10 C 4.4 ± 0.3 1.8 5.2

29 The model’s ability to predict lesion radii was investigated by using the condition that a pH less than 2 causes lesion. The simulated lesion radii are tabulated in Table 4. As can be seen from the table, a fairly good agreement is obtained between simulated and experimental lesion radii. A slight discrepancy is found between the calculated and measured profiles at the low and high currents (1 and 5 mA). The difference between the simulations and experimental results, could be attributed to other sources, apart from the oxygen evolution reaction, producing hydrogen ions. Such sources of hydrogen ions could originate from the reactions of chlorine with water and organic tissue constituents. An additional evaluation of the bicarbonate buffer model was done through comparing simulated pH profiles with results from a study made by Samuelsson et al., in which normal lung and liver tissues in rabbits were treated with five different coulomb dosages [49]. These experiments were carried out with bullet-shaped platinum electrodes, which produced elliptical lesions. The bullet-shaped anode was, in the simulation, treated as a spherical anode, with a surface area identical to the experimental electrode. By assuming that pH<2 causes lesions, a very good agreement between the simulated and experimental lesion radii was obtained. The simulated lesion radii were found to be between the minor and major axes of the experimental elliptic lesions.

General behaviour of the chlorine model The general behaviour of the chlorine model is visualised and discussed in this section. Current density was linearly raised from zero to the operating current density, in the space of 2 minutes, and was subsequently kept constant during 30 minutes of electrolysis, in all of the simulations. The anode radius is, in all simulations, set to 0.5 mm. The general characteristics of the concentration profiles of sodium, hydrogen, chloride and bicarbonate ions, calculated from the chlorine model, closely resembled those obtained by the bicarbonate buffer model, and will therefore not be further discussed in this section. The simulated concentration profiles of chlorine, hypochlorous acid and reactive organic sites, after different times of electrolysis, are shown in Fig. 8. The anode current density was in this simulation set to 100 mA cm-2. Chlorine, produced in the chlorine evolution reaction, diffuses away from the anode, and its profile reaches a maximum plateau due to saturation. Some of the chlorine hydrolyses into hypochlorous acid, which also diffuses away from the anode. The fact that the concentration profiles of chlorine, hypochlorous acid and the organic constituents all meet in a very narrow reaction zone implies that reactions (9)-(12) are diffusion-controlled.

30 0.3 Org, Org-red

0.25

-3

0.2 HClO (a) (b) (c) (a) 0.15 (b) (c)

0.1 (a) concentration / mol dm (b) 0.05 (c) Cl 2(aq)

0 0.6 0.8 1 1.2 1.4 1.6

distance r / mm

Fig. 8. Simulated concentration profiles of chlorine, hypochlorous acid and reactive organic sites, after different times of electrolysis: (a) 2+10 min, (b) 2+20 min and (c) 2+30 min. The anode current density was, in this simulation, linearly raised from zero to 100 mA cm-2 in 2 minutes, and was subsequently kept constant during 30 minutes.

Calculations were done in order to investigate the influence of current density on chlorination and acidification around the anode. Fig. 9 shows the extension of the chlorinated and acidic zones, in tissue surrounding the anode, as functions of current density. The extension of the acidic zone is plotted for pH values of 2, 3 and 7. The radii corresponding to these pH values are obtained from individual pH profiles at different current densities. The simulations show that the size of the acidic zone increases significantly with increasing current density. On the other hand, the chlorinated zone increases only slightly with increasing current density. In fact, at current densities greater than 75 mA cm-2, the radius of the chlorinated zone is almost constant. The explanation for this behaviour is that tissue already becomes saturated with chlorine at low current densities, so that subsequent produced chlorine is lost to the gas phase as current density increases. Generally, it can be stated that the outer boundary of the acidic zone is always ahead of the boundary of the chlorinated zone. This does not necessarily mean that it is always the hydrogen ion that plays the role as principal destructive agent, since it most probably takes a pH between 2 and 3 to cause irreversible tissue destruction [50, 38, 83]. Moreover, the pH needed to cause irreversibly cell damage may also be dependent on the time of exposure [14, 62]. Fig. 9 shows that the hydrogen ion is the principal

31 destructive agent at current densities higher than 25 mA cm-2, assuming that pH<2 causes lesions. At lower current densities, the spreading of chlorine and hypochlorous acid determines the size of the destruction zone. If a pH<3 is instead used as the destruction condition, then the simulations indicate that it is the acidification that causes tissue destruction, irrespective of the applied current density.

8

7 pH=7 6 pH=3 5 / mm r 4 pH=2

3 distance

2 Cl2(aq)

1

0 0 20 40 60 80 100 120 140 160

current density / mA cm-2

Fig. 9. Simulated extensions of chlorinated and acidic zones around the anode, as functions of current density. The extension of the acidic zone is plotted for pH values of 2, 3 and 7. The anode current density was, in this simulation, linearly raised from zero to operating current in 2 minutes, and was subsequently kept constant during 30 minutes. Secondary reactions, arising from chlorine production at the anode, play important roles as generators of hydrogen ions. Fig. 10 shows the normalised contribution of the reactions of chlorine with tissue (i.e. reactions (8), (9), (11) and (12)), to the total production of hydrogen ions, as a function of time at different current densities. Chlorine is responsible for as much as 97% of the acidification surrounding the anode, at the two lowest current densities of 5 and 10 mA cm-2. The impact that chlorine has on acidification around the anode is considerably decreased with increasing current density. The reason for this is that the current yield of chlorine varies with applied current density. The normalised part of the total current density, contributed by the chlorine evolution reaction, is plotted in Fig. 11 as a function of time at different total current densities. At low current densities, where there is an absence of mass transport limitations, the chlorine evolution reaction is kinetically favoured by its high exchange current density. When the current density is increased, the chlorine evolution reaction becomes mass transport limited and its current yield decreases significantly.

32 1 5, 10 mA cm -2 25 0.9

0.8

0.7 + 50 0.6

0.5 75

Yield of H 0.4 100 0.3 125 0.2 150 0.1

0 0 200 400 600 800 1000 1200 1400 1600 1800

time / s

Fig. 10. Simulated normalised contributions, from the reactions of chlorine with tissue, to the total production of hydrogen ions, as a function of time at the different anode current densities: 5, 10, 25, 50, 75, 100, 125 and 150 mA cm-2. The anode current density was, in this simulation, linearly raised from zero to operating current in 2 minutes, and was subsequently kept constant during 30 minutes.

-2 1 5, 10 mA cm

0.9 25 0.8 50 0.7 ) i 0.6 75

2 /

Cl 100 i

( 0.5 125 0.4 150 0.3

0.2

0.1

0 0 200 400 600 800 1000 1200 1400 1600 1800

time / s

Fig. 11. Simulated normalised contributions from the chlorine evolution reaction, to the total anode current density, as a function of time at different total current densities: 5, 10, 25, 50, 75, 100, 125 and 150 mA cm-2. The anode current density was, in this simulation, linearly raised from zero to operating current in 2 minutes, and was subsequently kept constant during 30 minutes.

33 It is important to note that, except for the two lowest current densities, the yield of hydrogen ions originating from the reactions of chlorine with tissue is significantly less than the corresponding current yield of chlorine, see Fig. 10 and 11. This can partly be explained by comparing the number of hydrogen ions produced, per transferred electron in the chlorine and oxygen evolution reactions, respectively. One hydrogen ion is produced per transferred electron in the oxygen evolution reaction. The chlorination of organic constituents, through reaction (9), gives rise to a net production of half a hydrogen ion per transferred electron, from the chlorine evolution reaction. The oxidation reactions, (11) and (12), correspond to a net production of one hydrogen ion. In addition, the production of hypochlorous acid alone, reaction (8), without subsequent reactions with organic constituents, generates half a hydrogen ion per transferred electron from the chlorine evolution reaction. This implies that the number of hydrogen ions produced through chlorine's reactions in tissue is 0.5 or 1. If no reaction occurs, which happens when chlorine is released to the gas phase, no hydrogen ion is produced. This comparison clearly shows that the acidifying power of the chlorine evolution reaction is, although not negligible, considerably less than that through oxygen evolution.

Comparison between experimental results and the chlorine model The chlorine model was evaluated, in a fashion similar to the sodium chloride and bicarbonate buffer models, by comparing the simulated pH profiles with results obtained in the experimental study in normal mammary tissue in rats. Three different treatment conditions were simulated: 1, 2.5 and 5 mA, all at a coulomb dosage of 5 C. These currents correspond to anode current densities of 34, 85 and 171 mA cm-2. The simulated pH profiles, obtained immediately after current shutdown and after 10 and 15 minutes of diffusion-reaction relaxation, are presented in Fig. 12. Also shown in Fig. 12 are the experimentally measured pH profiles, which agree well with the simulated profiles. The slight difference in shape between the simulated and experimental profiles could possibly be explained by an underestimation of tissue’s buffer capacity and/or an overestimation of the buffer reaction rate. The model’s ability to predict the pH profile in tissue surrounding the anode, within a wide range of current densities, strongly supports its general validity. The correlation between the experimentally measured lesions, and the simulated size of the chlorinated zone, were investigated along with the simulated pH obtained at a radius corresponding to the border of the experimental lesions. The experimental lesion radii were, in all treatment groups, considerably larger than the simulated radii of the chlorinated

34 zones. Furthermore, and as expected in view of the bicarbonate buffer model, the simulated pH at the border of the experimental lesions was found to correlate well to a value of around 2. These findings clearly indicate that, at this present range of current densities, the size of the destruction zone is determined by the spreading of hydrogen ions.

8 8 8

7 7 7

6 in 6 6 m 15 5 5 5

min in

10 pH pH

pH m 4 4 15 4 in

in m m 15 n in 3 3 10 3 m mi n 10 0 mi in 0 m 2 2 2 0 experimental experimental experimental 1 chlorine model 1 chlorine model 1 chlorine model

0 2 4 6 8 10 0 2 4 6 8 10 0246810

distance r / mm distance r / mm distance r / mm

(a) (b) (c)

Fig. 12. Comparison between simulated pH profiles, obtained from the chlorine model, and experimental pH profiles at different treatment conditions: (a) 1 mA, (b) 2.5 mA and (c) 5 mA. The treatment times were adjusted so that, in each of the experiments, a total charge of 5 C was passed between the electrodes. The experimental values are given as the mean ±1 standard deviation. The simulated pH profiles are presented as a function of time: 0, 10 and 15 min following current shutdown.

4.3. Cathode modelling

The sodium chloride model The general behaviour of the concentration profiles of sodium, hydroxyl and chloride ions, obtained in the cathodic sodium chloride model, is visualised in Fig. 13. These concentration profiles were obtained after 15 minutes of electrolysis, using a cathode current density of 100 mA cm-2 and a cathode radius of 0.5 mm. Hydroxyl ions, produced in the hydrogen evolution reaction, are transported away from the cathode, forming an alkaline zone around the electrode. Due to the production of hydroxyl ions and the fact that the electroneutrality condition has to be maintained, the sodium ion is accumulated around the cathode while the chloride ion is depleted. The mobility of the hydroxyl ion is 4 times larger than that of the sodium ion, and more than twice the mobility of the chloride ion. This leads to a situation where the spreading of hydroxyl ions is limited by the transport

35 properties of the sodium and chloride ions. The simulated depletion and accumulation of the respective ions is in qualitative accordance with experimental observations reported by Li et al., in their EChT study on healthy dog liver [48]. The validity of the sodium chloride model was evaluated by comparing simulated pH profiles with experimental profiles, obtained in the experimental study in normal mammary tissue in rats, presented in Section 4.1. Simulations were run using current densities and treatment times identical to those used in the experiments. The last pH measurement in the tissue surrounding the cathode was done about 15-20 min after current shutdown. The diffusion-reaction processes, occurring between current shutdown and the pH measurement, were also modelled. Fig. 14 shows the simulated and experimentally measured pH profiles, when using a current of 2.5 mA and a coulomb dosage of 5 C. The simulated profiles, corresponding to 0, 15 and 20 min of diffusion-reaction relaxation following current shutdown, are plotted separately. The sodium chloride model considerably overestimates the size of the alkaline zone around the cathode. Moreover, the model predicts higher pH values than what was found in the experiments. These results were expected and are in line with the results obtained from the anode modelling.

0.5

0.45

-3 0.4

0.35

0.3 + 0.25 Na

0.2

0.15 concentration / mol dm Cl- 0.1

0.05 OH - 0 0 12345678910

distance r / mm

Fig. 13. Simulated concentration profiles of sodium, chloride and hydroxyl ions, obtained from the sodium chloride model, after 15 min of electrolysis. The cathode radius is 0.5 mm and the cathode current density is 100 mA cm-2.

36 13 sodium chloride 0 min model experimental 12

11

pH 10 15 min 20 min

9

8

7 0 5 10 15 20 25 30 35 40

distance r / mm

Fig. 14. Comparison between the simulated profiles, obtained from the sodium chloride model, and an experimental pH profile. The simulated pH profiles are presented as a function of time: 0, 15 and 20 min following current shutdown. The experimental values are given as the mean ±1 standard deviation. The total cathode current density is 85 mA cm-2 and the total time of electrolysis is 2120 s. These treatment conditions correspond to a current of 2.5 mA and a coulomb dosage of 5 C.

The bicarbonate buffer model A simulation was run in order to visualise the general characteristics of the concentration profiles calculated from the bicarbonate buffer model. Fig. 15 shows the simulated concentration profiles of sodium, hydroxyl, chloride, bicarbonate and carbonate ions obtained from the bicarbonate buffer model after 15 min of electrolysis, when using a cathode current density of 100 mA cm-2 and a cathode radius of 0.5 mm. The concentration profiles of the sodium and chloride ions closely resemble those obtained by the sodium chloride model, except for the fact that the bulk concentration of chloride is lower in the bicarbonate buffer model. The spreading of hydroxyl ions is, in this model, counteracted by their reaction with the bicarbonate ion and carbon dioxide. The concentration profiles of the hydroxyl and bicarbonate ions cross each other in a reaction zone about 4-5 mm from the centre of the cathode. The carbonate ion, formed in the reaction between the hydroxyl and bicarbonate ions, shows a maximum concentration at this reaction zone. The depletion of carbonate ions behind the reaction zone is caused by their migration away from the cathode, while both diffusion and migration causes their spreading ahead of the reaction front. Due to its reaction with the hydroxyl ions, the

37 concentration of carbon dioxide is practically zero within the alkaline zone surrounding the cathode. The concentration of carbon dioxide is not shown in Fig. 15 since it is not of the same order of magnitude as the other species.

0.5

0.45

0.4

-3 0.35

0.3 Na+

0.25

0.2 - 0.15 OH - concentration / mol dm Cl 0.1

0.05 2- HCO - CO 3 3 0 0 12345678910

distance r / mm

Fig. 15. Simulated concentration profiles of sodium, chloride, hydroxyl, bicarbonate and carbonate ions, obtained from the bicarbonate buffer model, after 15 min of electrolysis. The cathode radius is 0.5 mm and the cathode current density is 100 mA cm-2.

The bicarbonate buffer model was evaluated, in a fashion similar to the sodium chloride model, by comparing simulated pH profiles with those obtained after EChT treatment of mammary tissue in rats. Fig. 16 shows the simulated and experimentally measured pH profiles, when using a current of 2.5 mA and a coulomb dosage of 5 C. The simulated profiles, obtained immediately after current shutdown and after 15 and 20 minutes of diffusion-reaction relaxation, are plotted separately. It can be seen from the figure that the extension of the alkaline zone around the cathode is larger compared to the experimental results. The overestimation of the alkaline zone is, however, not as pronounced in this model in comparison to the simple sodium chloride model. One possible explanation for the discrepancy between the simulated and experimental pH profiles, shown in Fig. 16, is the influence of convection - a transport mechanism not considered in the model. Convective transport of bicarbonate and carbon dioxide towards the cathode would enhance tissue’s capacity to withstand alkalisation. Furthermore, a convective transport of hydroxyl ions away from the cathode would lead to less extreme pH values within the alkaline zone, compared to the values predicted by the model. In

38 view of the anode modelling, convective transport appears to have a minor impact on the transport of species around the anode. There are, however, distinct differences between the microenvironments around the anode and cathode, which could explain the larger impact of convection in the cathodic zone. The electro-osmotic effect causes oedema around the cathode while dehydration, which strongly obstructs convective transport, is obtained at the anode.

13 0 min bicarbonate buffer model 12 experimental

11

pH 10

15 min 9 20 min

8

7 02468101214161820

distance r / mm

Fig. 16. Comparison between simulated profiles, obtained from the bicarbonate buffer model, and an experimental pH profile. The simulated pH profiles are presented as a function of time: 0, 15 and 20 min following current shutdown. The experimental values are given as the mean ±1 standard deviation. The total cathode current density is 85 mA cm-2 and the total time of electrolysis is 2120 s. These treatment conditions correspond to a current of 2.5 mA and a coulomb dosage of 5 C.

The discrepancy between predicted and measured pH profiles could also be attributed to an underestimation of the tissue’s buffer capacity. Other buffer systems, such as the organic buffer systems, might play prominent roles in limiting the spreading of hydroxyl ions around the cathode. Although the anode modelling indicated that the impact of these buffers were of subordinate importance in counteracting the spreading of hydrogen ions around the anode, the analogous situation is not necessarily true about hydroxyl ions around the cathode. Intracellular proteins and organic phosphates might be more accessible in or near the cathodic destruction zone, in comparison to the anodic. This hypothesis is strengthened by results reported from histologic examinations of healthy rat mammary tissue treated with EChT, performed by the co-authors of Paper I and appended in

39 the same paper. In these examinations, the oedematous tissue surrounding the cathode showed a profound lack of histologic architecture, while that of tissue around the anode showed to be affected but was still rather evident.

The extended buffer model The bicarbonate buffer model was refined in order to investigate if the discrepancy, between experimental and simulated pH profiles, could be attributed to non-bicarbonate related buffer systems in the tissue. In the extended buffer model, a simplified organic constituent susceptible to reactions with hydroxyl ions, H-Org, was introduced. The extended buffer model was run using a wide spectrum of initial H-Org 0 concentrations. It was found that with c − set to 50 mM, the simulated pH H Org profiles showed a good correlation to the corresponding experimental profiles, obtained in the experimental study in rat mammary tissue. Fig. 17 shows simulated and experimental profiles, when using a current of 2.5 mA and a coulomb dosage of 5 C. The experimental pH profile agrees well with the simulated profiles obtained 15-20 min after current had been shut off. The slight difference in shape, between experimental and simulated profiles, might be caused by the assumption of irreversibility in the reaction between H-Org and hydroxyl ions.

13 0 min extended buffer model 12 experimental

11 pH 10 15 min

9 20 min

8

7 0 1 2 3 4 5 6 7 8 9 10

distance r / mm

Fig. 17. Comparison between the simulated profiles, obtained from the extended buffer model and an experimental pH profile. The simulated pH profiles are presented as a function of time: 0, 15 and 20 min following current shutdown. The initial concentration of H-Org was set to 50 mM. The experimental values are given as the mean ±1 standard deviation. The total cathode current density is 85 mA cm-2 and the total time of electrolysis is 2120 s. These treatment conditions correspond to a current of 2.5 mA and a coulomb dosage of 5 C.

40 The correlation between the simulated pH profiles, obtained from the extended buffer model, and the corresponding lesion sizes, measured in the experimental study in rat mammary tissue, was investigated and the results tabulated in Table 5. As can be seen from the table, the simulated pH, at a radius corresponding to the border of the experimental lesions, correlates well to a narrow pH range between 11.7 and 12.3. This result is consistent with the clinical experiences from China that report that it takes a pH of around 12, or greater, to cause irreversible tissue destruction [83]. The simulated pH data also reveals another interesting result; namely that the simulated pH at the border of the experimental lesions decreases with increasing treatment time. This implies that the pH needed to cause irreversible cell damage is dependent on the time of exposure – a finding in line with observations reported from both in vitro studies and clinical treatments with EChT [14, 62]. The fact that the extended buffer model is able to describe experimentally measured pH profiles, and that the simulated pH at the border of the experimental lesions correlates to a narrow pH range, indicate that alkalisation is the principal destruction mechanism around the cathode during EChT. In order to investigate the model’s ability to predict lesion sizes, all four simulated pH values obtained at the border of the experimental lesions (see Table 5) were tried as destruction conditions. The best fit was obtained when using the destruction condition that pH>11.7 causes lesions. As can be seen from the results, tabulated in Table 5, a good agreement was obtained between simulated and experimental lesion radii. The model slightly overestimates the lesion radii at the treatment conditions, which correspond to the two shortest treatment times. This overestimation can be explained by the earlier discussed influence of treatment time on tissue destruction.

Table 5. Experimental cathodic lesion radii (mean ±1 standard deviation), simulated pH values, at the radius corresponding to the border of the mean lesion radii, and simulated lesion radii, at different treatment conditions. Simulated lesion radii were obtained from the pH profiles, predicted by the extended buffer model, using the conditions that pH>11.7 gives lesions.

Treatment Treatment Experimental Simulated pH Simulated lesion group conditions lesion radius at experimental radius lesion border [mm] [mm]

I 1 mA, 5 C 3.0 ± 0.4 11.7 2.9 II 2.5 mA, 5 C 3.8 ± 0.2 11.7 3.8 III 2.5 mA, 10 C 4.6 ± 0.2 11.7 4.6 IV 5 mA, 2.5 C 2.5 ± 0.3 12.3 3.1 V 5 mA, 5 C 3.6 ± 0.5 12.0 4.0 VI 5 mA, 10 C 4.9 ± 0.6 11.8 5.0

41 5. CONCLUSIONS

The studies presented in this thesis have given a strong indication of the destruction mechanism involved in EChT. It is shown by the modelling work, in combination with the experiments, that the most probable cause of tissue destruction is acidification at the anode and alkalisation at the cathode. The pH profiles obtained from the theoretical models have shown a good correlation with the experimentally measured destruction zones, assuming that a pH above and below certain values cause tissue destruction. The simulated pH profiles correlated well to the tissue destruction obtained after EChT treatments of both healthy mammary tissue, in rats, and normal lung and liver tissues in rabbits [49]. This, together with the fact that EChT has been shown to induce similar lesion sizes in mammary and liver tissues in rats [84], strongly indicate that the mechanism underlying EChT is independent of the type of tissue being treated. Since the structure of tumour tissue is similar to that of healthy tissue, and since tumour cells and healthy cells are both sensitive to upsets in their environment, conclusions about the destruction mechanisms should also be valid in tumour tissues. This implies that the models presented in this thesis could be of use in predicting the tumour destruction produced through EChT, and thereby provide a basis for a systematic dose planning. Modelling of the anode processes has explained the role of chlorine in the underlying destruction mechanism behind EChT. A considerable amount of the chlorine, produced at the anode, reacts with water to form hypochlorous acid. Chlorine and hypochlorous acid are potent chlorinating and oxidising agents, with strongly toxic properties. Their impact in the overall destruction mechanism was, however, found to be very limited, since the acidic zone always reaches further out from the anode than the chlorinated zone does. Although chlorine and hypochlorous acid themselves are found to have limited roles in the destruction mechanism of EChT, their secondary reactions with tissue are shown to be important sources of hydrogen ions. The contribution of these reactions, to the acidification of tissue surrounding the anode, is strongly dependent on the applied current density and increases with decreasing current density. The buffer systems, not related to bicarbonate, seem to play a prominent role at the cathode in contrast to the anode. This could be explained by differences in the histologic architecture, between the anodic and cathodic destruction zones. The mathematical models, developed in this thesis, are valuable tools in optimising the operating conditions of EChT. It is possible to extend the use of the models, to predict the effect of the treatment in clinical situations,

42 using several electrodes. Predictions could be made for optimising an appropriate number and the positions of electrodes in a tumour, and is not limited to the single electrode models treated here. The modelling work presented in this thesis concerns the use of spherical electrodes and relatively small coulomb dosages. Before the models could be put to use in the clinical dose planning of EChT, they have to be adopted to the needle electrode geometry used in most clinical applications. The models should be compared with experimental results obtained from treatments in large animals with tumours, where the animals are allowed to survive. Moreover, the pH thresholds needed to cause irreversible tumour destruction require further investigation.

43 6. REFERENCES

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