MATHEMATICAL MODELING OF MOLECULAR TRANSMEMBRANE TRANSPORT AND CHANGES OF TISSUES´ DIELECTRIC PROPERTIES DUE TO ELECTROPORATION

Visokonapetostni električni pulzi povečajo prepustnost celične membrane (Tsong 1991Weaver 1993Kotnik et al. 2012) skozi pore (Abidor et al. 1979), ki nastanejo na tistih njenih delih, kjer vsiljena transmembranska napetost preseže kritično vrednost (Towhidi et al. 2008Kotnik et al. 2010). Elektroporacija je reverzibilna, če si celica po pulzih opomore, in ireverzibilna, če je škoda preobsežna in celica odmre (Pakhomova et al. 2013bJiang et al. 2015a). Trenutne optične metode por ne morejo zaznati, zato njihov nastanek zaznavamo posredno, bodisi z meritvami vnosa različnih molekul v celice ali z meritvami električnih lastnosti celic (Napotnik in Miklavčič 2017). Uporaba elektroporacije V živilski industriji (Toepfl 2012Toepfl et al. 2014) uporabljamo elektroporacijo oziroma pulzirajoča električna polja (angl. pulsed electric fields), kar je uveljavljen izraz v tej industriji, za uničevanje patogenih organizmov in njihovih produktov (encimov in toksinov). V nasprotju s termično obdelavo hrane električni pulzi ne vplivajo na okus, barvo ali hranilno vrednost. V biotehnologiji uporabljamo elektroporacijo za ekstrakcijo molekul iz mikroorganizmov in rastlin, s čimer se izognemo uporabi kemičnih sredstev in ne uničimo celičnih organelov, torej se izognemo tudi dodatnemu čiščenju končnega produkta (Sack et al. 2010Haberl et al. 2013aMahnič-Kalamiza et al. 2014bKotnik et al. 2015). Primeri: ekstrakcija DNK iz bakterijsladkorja iz sladkorne pese (Haberl et al. 2013b), sokov iz sadjapolifenolov iz grozdja za izboljšanje kvalitete vina (Puértolas et al. 2010)vode pri sušenju zelene biomase, ki služi kot vir za biogorivo (Golberg et al. 2016). Elektroporacija je tudi nova metoda pri zamrzovanju celic in tkiv, angl. cryopreservation (Galindo in Dymek 2016Dovgan et al. 2017). Elektroporacijo uporabljamo tudi v medicini (Miklavčič et al. 2010Yarmush et al. 2014), in sicer pri elektrokemoterapiji (Miklavčič et al. 2012Mali et al. 2013Cadossi et al. 2014Miklavčič et al. 2014Campana et al. 2014Serša et al. 2015), netermičnem odstranjevanju tkiva z ireverzibilno elektroporacijo (Davalos et al. 2005Garcia et al. 2010José et al. 2012Cannon et al. 2013Scheffer et al. 2014bJiang et al. 2015aRossmeisl et al. 2015), genski terapiji (Golzio et al. 2002Vasan et al. 2011Gothelf in Gehl 2012Calvet et al. 2014Heller in Heller 2015Trimble et al. 2015) in vnosu učinkovin v kožo in skoznjo (Denet et al. 2004Zorec et al. 2013b). Pri genski terapiji vnesemo v celice plazmide, v katerih je zapisana sinteza določenega proteina, ki lahko spremeni biološko funkcijo celice (Aihara in Miyazaki 1998Heller in Heller 2015). Z elektroporacijo povišamo varnost genske terapije, saj se izognemo uporabi virusov in kemikalij. Mehanizmi genske terapije z elektroporacijo še niso popolnoma pojasnjeni, osnovni koraki so opisani v literaturi (Rosazza et al. 2016). Z elektroporacijo lahko zlivamo različne celice, s čimer pridobivamo celice, ki proizvajajo monoklonska protitelesa ali inzulin (Ramos in Teissié 2000Trontelj et al. 2008Rems et al. 2013). V doktorski disertaciji sem se osredotočila na uporabo elektroporacije v medicini, predvsem pri elektrokemoterapiji, netermičnem odstranjevanju tkiva z ireverzibilno elektroporacijo in pri vnosu učinkovin v kožo in skoznjo je, zato so ti trije posegi podrobneje opisani v naslednjem poglavju. Medicinski posegi z elektroporacijo – elektrokemoterapija, netermično odstranjevanje tkiva z ireverzibilno elektroporacijo in vnos učinkovin v kožo in skoznjo Elektrokemoterapija je kombinacija kemoterapije in električnih pulzov, dovedenih neposredno na tarčno tkivo. Električni pulzi povečajo prepustnost celične membrane za kemoterapevtike, zato povečamo učinkovitost zdravljenja, obenem pa zmanjšamo dovedeno dozo kemoterapevtika in omilimo stranske učinke. Celoten tumor mora biti pokrit z dovolj visokim električnim poljem, da povečamo prepustnost vseh tumorskih celic (Miklavčič et al. 2006a), zagotoviti pa moramo tudi dovolj visoko koncentracijo kemoterapevtika znotraj tumorja (Miklavčič et al. 2014). Okoliško tkivo ne sme biti uničeno, torej mora biti električno polje okoli tumorja pod mejo za ireverzibilno elektroporacijo. Pri elektrokemoterapiji običajno dovajamo osem pulzov dolžine 100 μs s ponavljalno frekvenco 1 Hz. S poskusi določena meja za povišanje prepustnosti tumorskega tkiva je 0,4 kV/cm (Miklavčič et al. 2010). Osem pulzov je bilo določenih kot optimalno število pulzov (Marty et al. 2006Mir et al. 2006), večje število dovedenih pulzov namreč že zmanjšuje preživetje (Dermol in Miklavčič 2015). Za zdravljenje tumorjev z elektrokemoterapijo so bili definirani standardni postopki (angl. standard operating procedures) (Marty et al. 2006Mir et al. 2006), kjer so glede na število tumorjev, njihovo velikost in lokacijo (na koži ali pod kožo) določeni tip elektrod, kemoterapevtik, anestezija in način dovajanja kemoterapevtika. Kemoterapevtik lahko dovedemo lokalno ali sistemsko. V elektrokemoterapiji oz. terapiji z električnimi pulzi sta najbolj razširjena kemoterapevtika cisplatin in bleomicin. Z elektrokemoterapijo je možno zdraviti tudi globlje ležeče tumorje (Miklavčič et al. 2010Pavliha et al. 2013Edhemović et al. 2014Miklavčič in Davalos 2015). V zadnjem času se uveljavlja tudi uničevanje tumorskih celic z visokimi koncentracijami kalcija in električnimi pulzi (Frandsen et al. 2015Frandsen et al. 2016Frandsen et al. 2017). Pri elektrokemoterapiji se pojavijo še dodatni učinki, ki povišajo učinkovitost elektroporacije. Vazokonstrikcija zmanjša spiranje kemoterapevtika iz tumorja in s tem ohranja visoko koncentracijo kemoterapevtika v tumorju, obenem se zmanjša pretok krvi skozi tumor, kar povzroči hipoksijo in pomanjkanje hranilnih snovi (Mir 2006Serša et al. 2008). Elektrokemoterapija sproži tudi odziv imunskega sistema, ki nato odstrani preostale tumorske celice (Serša et al. 2015). Z ireverzibilno elektroporacijo netermično odstranjujemo tumorje brez uporabe kemoterapevtika (Jiang et al. 2015a). Tako se popolnoma izognemo stranskim učinkom kemoterapevtikov, vendar na račun več dovedene energije in posledično Joulovega gretja. Pri ireverzibilni elektroporaciji dovajamo več (okoli 90) električnih pulzov, dolgih od 50 μs do 100 μs, s ponavljalno frekvenco 1 Hz. Dovedeno električno polje je v rangu nekaj kV/cm, kar je dosti več kot pri elektrokemoterapiji. Pri ireverzibilni elektroporaciji lahko z visoko natančnostjo odstranimo želeno tkivo – območje med uničenim in nepoškodovanim tkivom je široko le nekaj premerov celic (Rubinsky et al. 2007). Za odstranjevanje tumorjev tradicionalno uporabljamo termične metode (Hall et al. 2014) – radiofrekvenčno odstranjevanje in odstranjevanje s tekočim dušikom, kjer tkivo uničujemo z visoko oz. z nizko temperaturo. Prednost ireverzibilne elektroporacije pred uveljavljenimi termičnimi metodami je krajši čas zdravljenja, izognemo se učinkom hlajenja oz. gretja tkiva zaradi bližine žil (Golberg et al. 2015), pri čemer ostanejo okoliške pomembne strukture (žile, živci) nedotaknjene (Jiang et al. 2015a). Tudi pri ireverzibilni elektroporaciji je v dokončno odstranitev tumorskih celic vpleten imunski sistem (Neal et al. 2013). Pri elektrokemoterapiji in ireverzibilni elektroporaciji se zaradi daljših pulzov in ponavljalne frekvence 1 Hz pojavljajo težave zaradi krčenja mišic (Miklavčič et al. 2005), bolečine med dovajanjem pulzov, heterogenosti električnih lastnosti tkiv v tem frekvenčnem področju ter zaradi možnosti srčnih aritmij (Ball et al. 2010). Bolečini in krčenju mišic se lahko izognemo, če pulze dovajamo z višjo frekvenco, npr. 5 kHz (Županič et al. 2007Serša et al. 2010). Srčnim aritmijam se izognemo tako, da s sinhroniziramo dovedene električne pulze z električno aktivnostjo srčne mišice (Mali et al. 2008Deodhar et al. 2011aMali et al. 2015). Bolečini, krčenju mišic in heterogenosti električnih lastnosti tkiv se lahko izognemo z dovajanjem 1 μs bipolarnih pulzov (Arena et al. 2011Arena in Davalos 2012Sano et al. 2015). V zadnjem času so se pojavile tudi metode, s katerimi so vnos barvil v celico dosegli brezkontaktno s t. i. magnetoporacijo (Chen et al. 2010Towhidi et al. 2012Kardos in Rabussay 2012Novickij et al. 2015Kranjc et al. 2016Novickij et al. 2017bNovickij et al. 2017a). Elektroporacijo lahko uporabljamo ne le za zdravljenje tumorjev, temveč tudi za vnos učinkovin v kožo in skoznjo. Vnos učinkovin skozi kožo je neinvaziven, poleg tega pa se izognemo degradaciji učinkovin pri prehodu skozi prebavni trakt. Skozi kožo lahko preide le malo molekul, zato uporabljamo različne metode za povečanje prehoda učinkovin – iontoforezo, radiofrekvenčno mikroablacijo, laser, mikroigle, ultrazvok in elektroporacijo (Zorec et al. 2013b). Proces elektroporacije kože je slabo razumljen. Predpostavljamo, da pri dovajanju visokonapetostnih električnih pulzov v roženi plasti nastanejo lokalna transportna območja, kjer sta povišani električna prevodnost in prepustnost (Pliquett et al. 1996Pliquett et al. 1998Pliquett et al. 1998Pavšelj in Miklavčič 2008a). Skozi lokalna transportna območja lahko nato učinkovine še nekaj ur po dovedenih pulzih vstopajo skozi kožo v krvni obtok (Zorec et al. 2013a). Gostota teh območij je odvisna od električnega polja v koži – višje električno polje jih povzroči več. Velikost lokalnih transportnih območij je odvisna od trajanja pulza. Med samim pulzom se zaradi Joulovega gretja topijo lipidi v roženi plasti, kar povzroči njihovo širjenje (Pliquett et al. 1996Prausnitz et al. 1996Pliquett et al. 1998Weaver et al. 1999Vanbever et al. 1999Gowrishankar et al. 1999b). Načrtovanje posegov elektrokemoterapije in netermičnega odstranjevanja tkiva z ireverzibilno elektroporacijo Pri zdravljenju tumorjev z elektroporacijo lahko uporabimo standardne oblike in postavitve elektrod z že določenimi parametri električnih pulzov (Marty et al. 2006Mir et al. 2006Campana et al. 2014). Če zdravimo velike tumorje ali tumorje nepravilnih oblik, ki pogosto ležijo globlje, s standardno postavitvijo elektrod ne moremo zagotoviti ustrezne pokritosti tumorja z dovolj visokim električnim poljem. V tem primeru lahko elektrode med samim posegom večkrat premaknemo ali pa prilagodimo njihovo število in postavitev. Pri tem moramo prej pripraviti načrt posega (Kos et al. 2010Miklavčič et al. 2010Pavliha et al. 2012Linnert et al. 2012Edhemović et al. 2014). V njem zagotovimo, da bo cel tumor izpostavljen dovolj visokemu električnemu polju (Miklavčič et al. 2006a), obenem pa škoda na okoliškem tkivu minimalna. Načrtovanje posega poteka v več korakih: 1. zajem medicinskih slik (računalniška tomografija, magnetna resonanca) tumorja in okoliškega tkiva2. obdelava slik3. razgradnja slik in določitev geometrije tkiva4. vzpostavitev tridimenzionalnega modela5. optimizacija postavitve elektrod glede na obliko in velikost tumorja6. izdelava modela elektroporacije (izračun električnega polja in spremembe električne prevodnosti tkiva)7. optimizacija napetosti med elektrodami in položaja elektrod (Pavliha et al. 2012). Na sliki 1 lahko vidimo izračunano električno polje v tumorju in okoliškem tkivu pri eni izmed možnih postavitev elektrod.Electroporation is a phenomenon, which occurs when short high voltage pulses are applied to cells and tissues resulting in a transient increase in membrane permeability or cell death, presumably due to pore formation. If cells recover after pulse application, this is reversible electroporation. If cells die, this is irreversible electroporation. Electroporation is used in biotechnology for biocompound extraction and cryopreservation, in food processing for sterilization and pasteurization of liquid food and in medicine for treating tumors by electrochemotherapy or irreversible electroporation as an ablation technique, for gene electrotransfer, transdermal drug delivery, DNA vaccination, and cell fusion. In electroporation-based medical treatments, we can treat tumors with predefined electrode geometry and parameters of electric pulses. When we treat larger tumors of irregular shape treatment plan of the position of the electrodes and parameters of the electric pulses has to be calculated before each treatment to assure coverage of the tumor with a sufficient electric field. In treatment plans, currently, 1) we assume that above an experimentally determined critical electric field all cells are affected and below not, although, in reality, the transition between non-electroporated and electroporated state is continuous. 2) We do not take into account the excitability of some tissues. 3) The increase in tissues’ conductivity is described phenomenologically and does not include mechanisms of electroporation. 4) Transport of chemotherapeutics into the tumor cells in electrochemotherapy treatments is not included in the treatment plan although it is vital for a successful treatment. We focused on the mathematical and numerical models of electroporation with the aim of including them in the treatment planning of electroporation-based medical treatments. We aimed to model processes happening during electroporation of tissues, relevant in the clinical procedures, by taking into account processes happening at the single cell level. First, we used mathematical models of cell membrane permeability and cell death which are phenomenological descriptions of experimental data. The models were chosen on the basis of the best fit with the experimental data. However, they did not include mechanisms of electroporation, and their transferability to tissues was questionable. We modeled time dynamics of dye uptake due to increased cell membrane permeability in several electroporation buffers with regard to the electrosensitization, i.e., delayed hypersensitivity to electric pulses caused by pretreating cells with electric pulses. We also modeled the strength-duration depolarization curve and cell membrane permeability curve of excitable and non-excitable cell lines which could be used to optimize pulse parameters to achieve maximal drug uptake at minimal tissue excitation. Second, we modeled change in dielectric properties of tissues during electroporation. Model of change in dielectric properties of tissues was built for skin and validated with current-voltage measurements. Dielectric properties of separate layers of skin before electroporation were determined by taking into account geometric and dielectric properties of single cells, i.e., keratinocytes, corneocytes. Dielectric properties of separate layers during electroporation were obtained from cell-level models of pore formation on single cells of lower skin layers (keratinocytes in epidermis and lipid spheres in papillary dermis) and local transport region formation in the stratum corneum. Current-voltage measurements of long low-voltage pulses were accurately described taking into account local transport region formation, pore formation in the cells of lower layers and electrode polarization. Voltage measurements of short high-voltage pulses were also accurately described in a similar way as with long low-voltage pulseshowever, the model underestimated the current, probably due to electrochemical reactions taking place at the electrode-electrolyte interface. Third, we modeled the transport of chemotherapeutics during electrochemotherapy in vivo. In electrochemotherapy treatments, transport of chemotherapeutics in sufficient amounts into the cell is vital for a successful treatment. We performed experiments in vitro and measured the intracellular platinum mass as a function of pulse number and electric field by inductively coupled plasma – mass spectrometry. Using the dualporosity model, we calculated the in vitro permeability coefficient as a function of electric field and number of applied pulses. The in vitro determined permeability coefficient was then used in the numerical model of mouse melanoma tumor to describe the transport of cisplatin to the tumor cells. We took into account the differences in the transport of cisplatin in vitro and in vivo caused by the decreased mobility of molecules and decreased membrane area available for the uptake in vivo due to the high volume fraction of cells, the presence of cell matrix and close cell connections. Our model accurately described the experimental results obtained in electrochemotherapy of tumors and could be used to predict the efficiency of electrochemotherapy in vitro thus reducing the number of needed animal experiments. In the thesis, we connected the models at the cell level to the models at the tissue level with respect to cell membrane permeability and depolarization, cell death, change in dielectric properties and transport. Our models offer a step forward in modeling and understanding electroporation at the tissue level. In future, our models could be used to improve treatment planning of electroporation-based medical treatments

Técnicas de eletroporação: dispositivo eletrônico e ensaios em leveduras

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia Elétrica, Florianópolis, 2018.A eletroporação (EP) é o fenômeno do aumento da permeabilidade da membrana celular quando a célula é exposta a campos elétricos de amplitude acima de dezenas de kV/m e durações de nano segundos a segundos. O aumento da permeabilidade é explicado pela formação de poros na membrana celular. Dependendo da configuração do protocolo aplicado, a membrana plasmática pode se fechar, caracterizando EP reversível, ou pode não se recuperar (processo irreversível e morte celular). As aplicações da EP são: tratamento de câncer, transferência genética, extração de material intracelular e pasteurização. Esse trabalho teve como objetivo desenvolvimento de equipamento para tratamentos por campos elétricos pulsados, estudos de viabilidade celular, alteração de propriedades elétricas e de membrana de células. Foram utilizadas leveduras Saccharomyces Cerevisiae como modelo de células tumorais e campos elétricos de 200 a 800 kV/m. O equipamento desenvolvido é um gerador de sinais programável e compatível aos protocolos de EP para tratamento de câncer (ESOPE), transferência genética e extração de conteúdo intracelular. O protótipo suporta diferentes configurações de eletrodos, possui saída variável em tensão (até 800 V e corrente máxima de saída de 12 A) e possui módulo de aquisição de sinais (frequência de aquisição de 200 kHz) de tensão (resolução de < 7 V) e corrente (resolução < 50 mA até 5 A ou resolução < 240 mA até 12 A). O estudo com leveduras concluiu perda de viabilidade e perda da integridade da estrutura celular em protocolos superiores a 300 kV/m. Foram detectados indícios de correlação entre alterações de condutividade e perda de viabilidade celular por eletroporação irreversível. Os estudos com microscopia eletrônica forneceram detalhes que não são percebidos em análises de propriedades elétricas macroscópicas.Abstract : Electroporation (EP) is the phenomenon of increased cell membrane permeability when the cell is exposed to electric fields of amplitude above tens of kV/m and durations of nanoseconds to seconds. The increase in permeability is explained by the formation of pores at the plasma membrane. Depending on the protocol configuration, the plasma membrane may close, characterizing a reversible electroporation, or it may not recover, causing an irreversible electroporation and cell death. The applications of EP are: cancer treatment, genetic transfer, extraction of intracellular material and pasteurization. The objective of this work was the development of equipment for pulsed electric fields treatments, study of cell viability, changes in electrical and cell membrane properties. Saccharomyces Cerevisiae yeast was used as a model of tumor cells and electric fields from 200 to 800 kV/m were applied. The developed equipment is a programmable signal generator compatible with EP protocols for treatment of cancer (ESOPE), gene transfer and intracellular content extraction. The prototype supports different electrode configurations, has variable voltage output (up to 800 V and maximum output current of 12 A) and has a voltage acquisition module (200 kHz acquisition frequency) (< 7 V resolution) and current (resolution < 50 mA up to 5 A or resolution of < 240 mA up to 12 A). Based on the yeast study loss of viability and loss of cellular structure occurs when protocols are over 300 kV/m. Changes in electrical conductivity and loss of cell viability by irreversible electroporation may be correlated. Electron microscopy study provided details that are not observed in the macroscopic analysis of electrical properties

Development of a model to assess cleaning and disinfection of complex root canal systems

The remaining debris and biofilm in the anatomical complexities of root canal systems can affect treatment outcomes. Files with asymmetric cross-section design may improve debris and biofilm removal from these difficult spaces during canal preparation. Tooth opacity and different densities of the remaining materials prevent the direct systematic assessment of the preparation process. The present study assessed remaining debris and biofilm using a novel transparent root canal model with novel approaches. Natural and simulated root canal samples with isthmus space were evaluated. Canal preparation by ProTaper Next and Revo-S asymmetric systems was evaluated in comparison to the standard ProTaper Universal symmetric system. The root canals were investigated by microcomputed tomography (micro-CTL confocal laser scanning microscopy (CLSML and optical coherence tomography (OCT) imaging tools. Data analysis was undertaken with SPSS (V. 24). Files with asymmetric cross-section and constant taper removed more debris and biofilm from the complex root canal system. The model allowed direct assessment of remaining materials and confirmed the novel imaging approach with the OCT. In conclusion, the asymmetric design improves debris and biofilm removal especially when used with a constant taper. The model was verified as an ideal system for assessing root canal treatment in vitro