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Cette thèse contient deux matières différentes. Dans la première partie, deux cas sont considérés. L'un est le modèle plus lisse de la plaque mince et l'autre est les équations des limites elliptiques avec des données limites incertaines. Dans cette partie, les convergences stochastiques des méthodes des éléments finis sont prouvées pour chaque problème.Dans la deuxième partie, nous fournissons une analyse mathématique du problème inverse linéarisé dans la tomographie d'impédance électrique multifréquence. Nous présentons un cadre mathématique et numérique pour une procédure d'imagerie du tenseur de conductivité électrique anisotrope en utilisant une nouvelle technique appelée Tentomètre de diffusion Magnéto-acoustographie et proposons une approche de contrôle optimale pour reconstruire le facteur de propriété intrinsèque reliant le tenseur de diffusion au tenseur de conductivité électrique anisotrope. Nous démontrons la convergence et la stabilité du type Lipschitz de l'algorithme et présente des exemples numériques pour illustrer sa précision. Le modèle cellulaire pour Electropermécanisme est démontré. Nous étudions les paramètres efficaces dans un modèle d'homogénéisation. Nous démontrons numériquement la sensibilité de ces paramètres efficaces aux paramètres microscopiques critiques régissant l'électropermécanisme. / This thesis contains two different subjects. In first part, two cases are considered. One is the thin plate spline smoother model and the other one is the elliptic boundary equations with uncertain boundary data. In this part, stochastic convergences of the finite element methods are proved for each problem.In second part, we provide a mathematical analysis of the linearized inverse problem in multifrequency electrical impedance tomography. We present a mathematical and numerical framework for a procedure of imaging anisotropic electrical conductivity tensor using a novel technique called Diffusion Tensor Magneto-acoustography and propose an optimal control approach for reconstructing the cross-property factor relating the diffusion tensor to the anisotropic electrical conductivity tensor. We prove convergence and Lipschitz type stability of the algorithm and present numerical examples to illustrate its accuracy. The cell model for Electropermeabilization is demonstrated. We study effective parameters in a homogenization model. We demonstrate numerically the sensitivity of these effective parameters to critical microscopic parameters governing electropermeabilization..

Cell transplantation therapy is a potentially powerful tool and can be used to replace defective cells with healthy cells. This offers the possibility of alleviating the destructive symptoms for many diseases such as Parkinson's disease, Alzheimer's disease, stroke, spinal cord trauma, Type I diabetes and many more. While there are many diseases that could be positively impacted from cell transplantation therapy, the focus of this research is insulin dependent, Type I Diabetes. The Islets of Langerhans are composed of various types of cells located in the pancreas and are responsible for a variety of biochemical functions. Specifically, the beta Islet cells are responsible for production of the hormone insulin that regulates and aids in biosynthesis of glucose. Transplantation of isolated allografted pancreatic islets, which contain insulin producing cells, into diabetic rats has proven to be highly successful. However, these transplantations involve using medications for long term immunosuppression to defend against an undesired host immune response. Immunosuppressive medications are both costly and illicit additional side effects that can be detrimental to the host. This research focuses on the use of testicular derived Sertoli cells that have been publicized to provide localized immunoprotection. Electrofusion is a process that can be used to fuse homogeneous and heterogeneous cell types by promoting the creation of micropores in the cell's lipid bilayer. This renders the cell temporarily fusogenic, or capable of facilitating fusion. Cells must then be brought into contact with one another via mechanical, chemical or viral means. This research study proposes to optimize electrofusion technology to create novel, secretory hybrids composed of Islet and Sertoli cells that are immunoprotected and produce insulin in response to a glucose challenge. The components of the electrofusion device include a Sterlitech 0.2 ìm microporous membrane, a woven cellulose absorbent pad, two aluminum electrodes and a chamber body and top injection molded using Delrin. Preliminary experiments using B16-F10 murine melanoma cells incorporated with centrifugation to increase cell to cell contact resulted in an average fusion yield of 18.9% ± 8.1 SD using a field strength of 2500 V/cm, 8 pulses and a 250 ìs pulse length. Additionally, lab synthesized electroporation buffers containing 8.5% sucrose (w/v) and 0.3% glucose increased total and viable fusion yields to 37.1% ± 9.3 SD and 13.8% ± 2.1 SD, respectively. These results showed promise and should be further validated with additional cell lines and tissues to corroborate reproducibility.

The most common and aggressive malignant brain tumor, glioblastoma (GBM), demonstrates on average a 5-year survival rate of only 6.8%. Difficulties arising in the treatment of GBM include the inability of large molecular agents to permeate through the blood-brain barrier (BBB); migration of highly invasive GBM cells beyond the solid tumor margin; and gross, macroscopic intratumor heterogeneity. These characteristics complicate treatment of GBM with standard of care, resulting in abysmal prognosis. Electroporation-based therapies have emerged as attractive alternates to standard of care, demonstrating favorable outcomes in a variety of tumors. Notably, irreversible electroporation (IRE) has been used for BBB disruption and nonthermal ablation of intracranial tumor tissues. Despite promising results, IRE can cause unintended muscle contractions and is susceptible to electrical heterogeneities. Second generation High-frequency IRE (H-FIRE) utilizes bursts of bipolar pulsed electric fields on the order of the cell charging time constant (~1 μs) to ablate tissue while reducing nerve excitation, muscle contraction, and is far less prone to differences in electrical heterogeneities. Throughout my dissertation, I discuss investigations of H-FIRE for the treatment of malignant gliomas and other intracranial disorders. To advance the versatility, usability, and understanding of H-FIRE for intracranial applications, my PhD thesis focuses on: (1) characterizing H-FIRE-mediated BBB disruption effects in an in vivo healthy rodent model; (2) the creation of a novel, real-time impedance spectroscopy technique (Fourier Analysis SpecTroscopy, FAST) using waveforms compatible with existing H-FIRE pulse generators; (3) development of FAST as an in situ technique to monitor ablation growth and to determine patient-specific ablation endpoints; (4) conducting a preliminary efficacy study of H-FIRE ablation in an orthotopic F98 rodent glioma model; and (5) establishing the feasibility of MRI-guided H-FIRE for the ablation malignant gliomas in a spontaneous canine glioma model. The culmination of this thesis advances our understanding of H-FIRE in intracranial tissues, as well as develops a novel, intraoperative impedance spectroscopy technique towards determining patient-specific ablation endpoints for intracranial H-FIRE procedures. / Doctor of Philosophy / The most aggressive malignant brain tumor, glioblastoma (GBM), demonstrates on average a 5-year survival rate of only 6.8%. Difficulties arising in the treatment of GBM include the inability of chemotherapy agents to diffuse into brain tumor tissue as these molecular are unable to pass the so-called blood-brain barrier (BBB). This tumor tissue also presents with cells with the propensity to invade healthy tissue, to the point where diagnostic scans are unable to capture this migration. These characteristics complicate treatment of GBM with standard of care, resulting in abysmal prognosis. Electroporation-based therapies have emerged as attractive alternates to standard of care, demonstrating favorable outcomes in a variety of tumors. For instance, irreversible electroporation (IRE) has been used to successfully treat tumors in the prostate, liver, kidney, and pancreas. Second generation High-frequency IRE (H-FIRE) may possess even greater antitumor qualities and this is the focus of my dissertation. Throughout my dissertation, I discuss investigations of H-FIRE with applications to treat malignant gliomas and other intracranial disorders. My PhD thesis focuses on: (1) characterizing H-FIRE effects for enhanced drug delivery to the brain; (2) the creation of a new, real-time electrical impedance spectroscopy technique (Fourier Analysis SpecTroscopy, FAST) using waveforms compatible with existing H-FIRE pulse generators; (3) development of FAST as a technique to determine H-FIRE treatment endpoints; (4) conducting a preliminary efficacy study of H-FIRE to ablate rodent glioma tumors; and (5) establishing the feasibility of MRI-guided H-FIRE for the ablation malignant gliomas in a spontaneous canine glioma model. The culmination of this thesis advances our understanding of H-FIRE in intracranial tissues, as well as develops a new impedance spectroscopy technique to be used in determining patient-specific ablation endpoints for intracranial H-FIRE procedures.

Irreversible electroporation (IRE) is a non-thermal tissue ablation modality in which electrical pulses are used to generate targeted disruption of cellular membranes. Clinically, IRE is administered by inserting one or more needles within or around a region of interest, then applying a series of short, high amplitude pulsed electric fields (PEFs). The treatment effect is dictated by the local field magnitude, which is quite high near the electrodes but dissipates exponentially. When cells are exposed to fields of sufficient strength, nanoscale "pores" form in the membrane, allowing ions and macromolecules to rapidly travel into and out of the cell. If enough pores are generated for a substantial amount of time, cell homeostasis is disrupted beyond recovery and cells eventually die. Due to this unique non-thermal mechanism, IRE generates targeted cell death without injury to extracellular proteins, preserving tissue integrity. Thus, IRE can be used to treat tumors precariously positioned near major vessels, ducts, and nerves. Since its introduction in the late 2000s, IRE has been used successfully to treat thousands of patients with focal, unresectable malignancies of the pancreas, prostate, liver, and kidney. It has also been used to decellularize tissue and is gaining attention as a cardiac ablation technique. Though IRE opened the door to treating previously inoperable tumors, it is not without limitation. One drawback of IRE is that pulse delivery results in intense muscle contractions, which can be painful for patients and causes electrodes to move during treatment. To prevent contractions in the clinic, patients must undergo general anesthesia and temporary pharmacological paralysis. To alleviate these concerns, high-frequency irreversible electroporation (H-FIRE) was introduced. H-FIRE improves upon IRE by substituting the long (~100 µs) monopolar pulses with bursts of short (~1 µs) bipolar pulses. These pulse waveforms substantially reduce the extent of muscle excitation and electrochemical effects. Within a burst, each pulse is separated from its neighboring pulses by a short delay, generally between 1 and 5 µs. Since its introduction, H-FIRE burst waveforms have generally been constructed simply by choosing the duration of constitutive pulses within the burst, with little attention given to this delay. This is quite reasonable, as it has been well documented that pulse duration plays a critical role in determining ablation size. In this dissertation, we explore the role of these latent periods within burst waveforms as well as their interaction with other pulse parameters. Our central hypothesis is that tuning the latent periods will allow for improved ablation size with reduced muscle contractions over traditional waveforms. After gaining a simple understanding of how pulse width and delay interact in vitro, we demonstrate theoretically that careful tuning of the delay within (interphase) and between (interpulse) bipolar pulses in a burst can substantially reduce nerve excitation. We then analyze how pulse duration, polarity, and delays affect the lethality of burst waveforms toward determining the most optimal parameters from a clinical perspective. Knowing that even the most ideal waveform will require slightly increased voltages over what is currently used clinically, we compare the clinical efficacy of two engineered thermal mitigation strategies to determine what probe design modifications will be needed to successfully translate H-FIRE to the clinic while maintaining large, non-thermal ablation volumes. Finally, we translate these findings in two studies. First, we demonstrate that burst waveforms with an improved delay structure allow for enhanced safety and larger ablation volumes in vivo. And finally, we examine the efficacy of H-FIRE in spontaneous canine liver tumors while also comparing the ablative effect of H-FIRE in tumor and non-neoplastic tissue in a veterinary clinical setting. / Doctor of Philosophy / Cancer is soon to become the most common cause of death in the United States. In 2023, approximately 2 million new cases of cancer will be diagnosed, leading to roughly 650 thousand lost lives. Interestingly, about half of newly diagnosed cancers are caught in the early stages before the disease has spread throughout the body. With effective local intervention, these patients could potentially be cured of their malignancy. Surgical removal of the tumor is the gold standard, but it is often not possible due to tumor location, patient comorbidities, or organ health status. In some instances, focal thermal ablation with radiofrequency or microwave energy can be performed when resection is not possible. These treatments entail the delivery of thermal energy through a needle electrode, which causes local tissue damage through coagulation (cooking) of the tissue. However, thermal ablation destroys tissue indiscriminately, meaning that any nearby blood vessels or neural components will also be damaged, which precludes thousands of patients from treatment each year. Irreversible electroporation (IRE) was introduced to overcome these challenges and provide a treatment option for patients diagnosed with otherwise untreatable tumors. IRE uses pulsed electric fields to generate nanoscale pores in cell membranes, which lead to a homeostatic imbalance and cell death. Because IRE is a membrane-based effect, it does not rely on thermal effects to generate cellular injury, which allows it to be administered to tumors that are adjacent to critical tissue structures such as major nerves and vasculature. Though IRE opened the door to treating otherwise inoperable tumors, procedures are technically challenging and require specialized anesthesia protocols. High-frequency irreversible electroporation (H-FIRE) was introduced by our group roughly a decade ago to simplify the procedure through the use of an alternate pulsing strategy. These higher frequency pulses offer several advantages such as limiting muscle contractions and reducing the risk of cardiac interference, both of which were concerns with IRE. However, H-FIRE ablations have been limited in size, and there is limited knowledge regarding the optimal pulsing strategy needed in order to maximize the ratio of therapeutic benefits to undesirable side effects like muscle stimulation and Joule heating. In this dissertation, we sought to understand how different pulse parameters affect these outcomes. Using a combination of computational, benchtop, and in vivo experiments, we comprehensively characterized the behavior of user-tunable pulse parameters and identified optimal methods for constructing H-FIRE protocols. We then translated our findings in a proof-of-principle study to demonstrate the ability of newly introduced waveform designs to increase ablation size with H-FIRE. Overall, this dissertation improves our understanding of how H-FIRE waveform selection affects clinical outcomes, introduces a new strategy for maximizing therapeutic outcomes with minimal side effects, and provides a framework for selecting parameters for specific applications.

La perméabilisation des cellules à l’aide d’impulsions électriques intenses, appelée électroperméabilisation, est un phénomène biologique impliqué dans des thérapies anticancéreuses récentes. Elle permet, par exemple, d’améliorer l’efficacité d’une chimiothérapie en diminuant les effets secondaires, d’effectuer des transferts de gènes, ou encore de procéder à l’ablation de tumeurs. Les mécanismes de l’électroperméabilisation restent cependant encore méconnus, et l’hypothèse majoritairement admise par la communauté de formation de pores à la surface des membranes cellulaires est en contradiction avec certains résultats expérimentaux.Le travail de modélisation proposé dans cette thèse est basé sur une approche différente des modèles d’électroporation existants. Au lieu de proposer des lois sur les propriétés des membranes à partir d’hypothèses à l’échelle moléculaire, nous établissons des lois ad hoc pour les décrire, en se basant uniquement sur les informations expérimentales disponibles. Aussi, afin de rester au plus prèsde ces dernières et faciliter la phase de calibration à venir, nous avons ajouté un modèle de transport et de diffusion de molécules dans la cellule. Une autre spécificité de notre modèle est que nous faisons la distinction entre l’état conducteur et l’état perméable des membranes.Des méthodes numériques spécifiques ainsi qu’un code en 3D et parallèle en C++ ont été écrits et validés pour résoudre les équations aux dérivées partielles de ces différents modèles. Nous validons le travail de modélisation en montrant que les simulations reproduisent qualitativement les comportements observés in vitro. / Cell permeabilization by intense electric pulses, called electropermeabilization, is a biological phenomenon involved in recent anticancer therapies. It allows, for example, to increase the efficacy of chemotherapies still reducing their side effects, to improve gene transfer, or to proceed tumor ablation. However, mechanisms of electropermeabilization are not clearly explained yet, and the mostly adopted hypothesis of the formation of pores at the membrane surface is in contradiction with several experimental results.This thesis modeling work is based on a different approach than existing electroporation models. Instead of deriving equations on membranes properties from hypothesis at the molecular scale, we prefer to write ad hoc laws to describe them, based on available experimental data only. Moreover, to be as close as possible to these data, and to ease the forthcoming work of parameter calibration, we added to our model equations of transport and diffusion of molecules in the cell. Another important feature of our model is that we differentiate the conductive state of membranes from their permeable state.Numerical methods, as well as a 3D parallel C++ code were written and validated in order to solve the partial differential equations of our models. The modeling work was validated by showing qualitative match between our simulations and the behaviours that are observed in vitro

Les champs électriques pulsés sont largement utilisés dans la recherche, la médecine, l'industrie alimentaire et d'autres procédés biotechnologiques. L'interaction d'une impulsion de 100 µs avec la membrane plasmique et la membrane du réticulum endoplasmique a été évaluée dans deux types cellulaires différents. La perméabilisation des organites cellulaires avec ce type d'impulsions est démontrée expérimentalement pour la première fois. L'utilisation d'une telle impulsion afin de contrôler les oscillations calciques spontanées dans les cellules souches mésenchymateuses humaines issues du tissu adipeux a été évaluée. En créant des pics calciques électro-induits d’amplitudes différentes, l'impulsion peut ou bien induire un pic calcique supplémentaire ou bien inhiber les oscillations spontanées pour quelques dizaines de minutes. Cette inhibition rend possible d’imposer à la cellule des pics d’amplitude et de fréquence désirés. Un essai d’application de l'impulsion 100 µs à des cellules souches subissant une différenciation osseuse a aussi été réalisé. Une impulsion électrique semble retarder la différenciation. Lors d'une différenciation osseuse, plusieurs couches cellulaires ont été observées. La caractérisation de ces couches a donné des résultats qui pourraient aider à obtenir des ostéoblastes matures dans un temps moindre que la normale. L'utilisation des champs électriques pulsés microsecondes, pour perméabiliser la membrane plasmique et les membranes internes des cellules, ainsi que pour moduler les concentrations du calcium intracellulaire, semble donc très intéressante pour étudier le rôle du calcium dans de nombreux processus physiologiques et pour manipuler les dynamiques calciques (oscillations, vagues, pics) dans différents types de cellules. Ainsi, cette technologie simple, facile à appliquer et disponible dans beaucoup de laboratoires serait envisageable pour la modulation et le contrôle de fonctions cellulaires basiques telles que la prolifération, la différenciation et l'apoptose. / Pulsed electric fields are widely used in research, medicine, food industry and other biotechnological processes. The interaction of one 100 µs pulse with the plasma membrane and the endoplasmic reticulum membrane was evaluated in two different cell types. Pulse amplitude ranged between 100 and 3 000 V/cm. Organelles membrane permeabilization using this kind of pulses was experimentally demonstrated for the first time. The use of such a pulse to control the spontaneous calcium oscillations in human-adipose mesenchymal stem cells was also assessed. By creating electro-induced calcium spikes of different amplitudes, the pulse can either add a supplementary spike, or, on the contrary, inhibit the spontaneous oscillations for some tens of minutes. During this inhibition period, the electric pulse-mediated addition of calcium spikes of desired amplitude and frequency is still possible. The delivery of 100 µs pulses to stem cells undergoing osteodifferentiation was also performed. The electric pulse seemed to delay the differentiation. Moreover, during osteogenic differentiation, cells cultures displayed an organization in a few cell layers. The characterization of these layers gave results that may help to obtain mature osteoblast in less time than usual one. The use of the microsecond electric pulses technology to permeabilize the plasma and the internal cell membranes as well as to modulate internal calcium concentrations is therefore interesting to study the role of calcium in many physiological processes and to manipulate the cell calcium dynamics (oscillations, waves, spikes) in different cell types. Doing so, this available, simple and easy to apply technology could be used for the modulation and the control of basic cellular functions such as proliferation, differentiation and apoptosis.

Ce travail de recherche rapporte l'utilisation de techniques biophotoniques pour investiguer des questions biomédicales, de la recherche fondamentale (interaction champs électriques impulsionnels / cellules) aux études cliniques (toxicité cutanée induite chez les patients traités par des thérapies ciblées).La microspectroscopie confocale Raman et de la microscopie terahertz ont été utilisées pour étudier le processus d’électroperméabilisation cellulaire d'un point de vue moléculaire. Nos résultats démontrent l'implication des protéines. De plus, nous avons montré que la signature Raman des cellules peut être utilisée comme un biomarqueur précis des différents états des cellules exposées aux chocs électriques, correspondant à une électroperméabilisation non détectable, électroperméabilisation et irréversibleEn tant que projet parallèle de ce doctorat, une recherche clinique a été réalisée afin d'étudier la toxicité cutanée induite chez les patients traités par des thérapies anticancéreuses ciblées. Bien que l'efficacité de ces thérapies ne soit pas discutée, de nombreux effets cutanées secondaires graves sont associés. Dans cette étude, nous avons étudié l'opportunité de prédire l’apparition de la toxicité cutanée au moyen de la microspectroscopie Raman confocale réalisée sur la peau des patients. Nous avons réussi à déterminer un nouveau biomarqueur pharmacodynamique spécifique de la toxicité cutanée grâce aux signatures Raman de la peau des patients; alors que l'évaluation dermatologique ou histologique n'a détecté aucune modification. / This research work reports the use of various biophotonics techniques to investigate biomedical questions, from basic research (interaction between pulsed electric fields and cells) to clinical studies (skin toxicity induced in patients treated with targeted anticancer therapies).Confocal Raman microspectroscopy and terahertz microscopy have been used to investigate cell electropermeabilization process from a molecular point of view. Our results demonstrate the involvement of the proteins in cell electropermeabilization. Moreover, we have shown that the Raman signatures of the cells could be used as an accurate biomarker of the different states of the cells exposed to pulsed electric fields, corresponding to no detectable electropermeabilization, reversible and irreversible electropermeabilization.Finally, this doctorate research demonstrates the opportunity to predict skin toxicity induced by targeted anticancer therapies by means of confocal Raman microspectroscopy. We succedded to determine a novel and specific pharmacodynamic biomarker for skin toxicity based on the Raman signatures of the patient’s skin, whereas dermatological or histologicalevaluation did not detect any modifications.

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Irreversible electroporation is a minimally invasive technique for the non-thermal destruction of cells in a targeted volume of tissue, using brief electric pulses, (~100 µs long) delivered through electrodes placed into or around the targeted region. These electric pulses destabilize the integrity of the cell membrane, resulting in the creation of nanoscale defects that increase a cell’s permeability to exchange with its environment. When the energy of the pulses is high enough, the cell cannot recover from these effects and dies in a non-thermal manner that does not damage neighboring structures, including the extracellular matrix. IRE has been shown to spare the major vasculature, myelin sheaths, and other supporting tissues, permitting its use in proximity to these vital structures. This technique has been proposed to be harnessed as an advantageous non-thermal focal ablation technique for diseased tissues, including tumors. IRE electric pulses may be delivered through small (ø ≈ 1 mm) needle electrodes, making treatments minimally invasive and easy to apply. There is sub-millimeter demarcation between treated and unaffected cells, which may be correlated with the electric field to which the tissue is exposed, enabling numerical predictions to facilitate treatment planning. Immediate changes in the cellular and tissue structure allow real-time monitoring of affected volumes with imaging techniques such as computed tomography, magnetic resonance imaging, electrical impedance tomography, or ultrasound. The ability to kill tumor cells has been shown to be independent of a functioning immune system, though an immune response seems to be promoted by the ablation. Treatments are unaltered by blood flow and the electric pulses may be administered quickly (~ 5 min). Recently, safety and case studies using IRE for tumor therapy in animal and human patients have shown promising results. Apart from these new studies, previous work with IRE has involved studies in healthy tissues and small cutaneous experimental tumors. As a result, there remain significant differences that must be considered when translating this ablation technique towards a successful and reliable therapeutic option for patients. The dissertation work presented here is designed to develop irreversible electroporation into a robust, clinically viable treatment modality for targeted regions of diseased tissue, with an emphasis on tumors. This includes examining and creating proving the efficacy for IRE therapy when presented with the many complexities that present themselves in real-world clinical patient therapies, including heterogeneous environments, large and irregular tumor geometries, and dynamic tissue properties resulting from treatment. The impact of these factors were theoretically tested using preliminary in vitro work and numerical modeling to determine the feasibility of IRE therapy in heterogeneous systems. The feasibility of use was validated in vivo with the successful treatment of human mammary carcinomas orthotopically implanted in the mammary fat pad of mice using a simple, single needle electrode design easily translatable to clinical environments. Following preliminary theoretical and experimental work, this dissertation considers the most effective and accurate treatment planning strategies for developing optimal therapeutic outcomes. It also experimentally characterizes the dynamic changes in tissue properties that result from the effects of IRE therapy using ex vivo porcine renal cortical tissue and incorporates these into a revised treatment planning model. The ability to use the developments from this earlier work is empirically tested in the treatment of a large sarcoma in a canine patient that was surgically unresectable due to its proximity to critical arteries and the sciatic nerve. The tumor was a large and irregular shape, located in a heterogeneous environment. Treatment planning was performed and the therapy carried out, ultimately resulting in the patient being in complete remission for 14 months at the time of composing this work. The work presented in this dissertation finishes by examining potential supplements to enhance IRE therapy, including the presence of an inherent tumor-specific patient immune response and the addition of adjuvant therapeutic modalities. / Ph. D.