<div>Pulsed electric fields (PEFs) can induce numerous biophysical phenomena, especially perturbation of the outer and inner membranes, that may be used for applications that include nonthermal pasteurization, enhanced permeabilization of tumors to improve the transport of chemotherapeutics for cancer therapy, and enhanced membrane permeabilization of individual cells to enhance RNA and DNA delivery for gene therapy. The applied electric field and pulse duration determine the density, size, and reversibility of the created membrane pores. PEFs with durations longer than the outer membrane’s charging time will induce pore formation with the potential for application in irreversible electroporation for cancer therapy and microorganism inactivation. Shorter duration PEFs, particularly on the nanosecond timescale (nsPEFs), induce a larger density of smaller membrane pores with the potential to permeabilize intracellular membranes, such as the mitochondria, to induce programmed cell death. Thus, the PEFs can effectively kill multiple types of cells, dependent upon the cells. This thesis assesses the ability of nsPEFs to kill different cell types, specifically microorganisms with and without antibiotics as well as varying the parameters to affect populations of immortalized leukemia cells (Jurkats).</div><div>Antibiotic resistance has been an acknowledged challenge since the initial development of penicillin; however, recent discoveries by the CDC and the WHO of microorganisms resistant to last line of defense drugs combined with predictions of potential infection cases reaching 50 million a year globally and the absence new drugs in the discovery pipeline highlight the need to develop novel ways to combat and overcome these resistance mechanisms. Repurposing drugs, exploring nature for new drugs, and developing enzymes to counter the resistance mechanisms may provide potential alternatives for addressing the scarcity of antibiotics effective against gram-negative infections. One may also leverage the abundance of drugs effective against gram-positive infections by using nsPEFs to make them effective against gram-negative infections, including bacterial species with multiple natural and acquired resistance mechanisms. Numerous drug and microbial combinations for different doses and pulse treatments were tested and presented here.</div><div>Low intensity PEFs may selectively target cell populations at different stages of the cell cycle (quiescence and mitosis) to modify cancer cell population dynamics. Experimental studies of cancer cell growth when exposed to a low number of nsPEFs, while varying pulse duration, field intensity and number of pulses reveals a threshold beyond which cell recovery is not possible, but also a point of diminishing returns if cell death is the intention. A theory comprised of coupled differential equations representing the proliferating and quiescent cells showed how changing PEF parameters altered the behavior of these cell populations after treatment. These results may provide important information on the impact of PEFs with sub-threshold intensities and durations on cell population growth and potential recurrence.</div>

Mathematical models, that depict the dynamics of a cancer cell population growing out of the human body (in vitro) in unconstrained microenvironment conditions, are considered in this thesis. Cancer cells in vitro grow and divide much faster than cancer cells in the human body, therefore, the effects of various cancer treatments applied to them can be identified much faster. These cell populations, when not exposed to any cancer treatment, exhibit exponential growth that we refer to as the balanced exponential growth (BEG) state. This observation has led to several effective methods of estimating parameters that thereafter are not required to be determined experimentally. We present derivation of the age-structured model and its theoretical analysis of the existence of the solution. Furthermore, we have obtained the condition for BEG existence using the Perron-Frobenius theorem. A mathematical description of the cell-cycle control is shown for one-compartment and two-compartment populations, where a compartment refers to a cell population consisting of cells that exhibit similar kinetic properties. We have incorporated into our mathematical model the required growing/aging times in each phase of the cell cycle for the biological viability. Moreover, we have derived analytical formulae for vital parameters in cancer research, such as population doubling time, the average cell-cycle age, and the average removal age from all phases, which we argue is the average cell-cycle time of the population. An estimate of the average cell-cycle time is of a particular interest for biologists and clinicians, and for patient survival prognoses as it is considered that short cell-cycle times correlate with poor survival prognoses for patients. Applications of our mathematical model to experimental data have been shown. First, we have derived algebraic expressions to determine the population doubling time from single experimental observation as an alternative to empirically constructed growth curve. This result is applicable to various types of cancer cell lines. One option to extend this model would be to derive the cell cycle time from a single experimental measurement. Second, we have applied our mathematical model to interpret and derive dynamic-depicting parameters of five melanoma cell lines exposed to radiotherapy. The mathematical result suggests there are shortcomings in the experimental methods and provides an insight into the cancer cell population dynamics during post radiotherapy. Finally, a mathematical model depicting a theoretical cancer cell population that comprises two sub-populations with different kinetic properties is presented to describe the transition of a primary culture to a cell line cell population.