Date of Award

Summer 2007

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Electrical & Computer Engineering

Program/Concentration

Electrical Engineering

Committee Director

Ravindra P. Joshi

Committee Member

Linda L. Vahala

Committee Member

Mournir Laroussi

Call Number for Print

Special Collections LD4331.E55 N57 2007

Abstract

Calcium modulation is an important signaling process and could even contribute to cell apoptosis through ionic-induced perturbations in trans-membrane potential at the mitochondria. In this research, the numerical study constitutes a first step in quantitatively probing the time- and spatially-dependent modulation of calcium dynamics through the application of external electrical fields. The research uses both widely accepted deterministic continuum and discrete stochastic intracellular calcium models coupling with external electric field, with a focus on high-intensity ultrashort pulse electrical field.

For deterministic continuum intracellular calcium models with electric field assisted, numerical simulations for electrically induced, intra-cellular calcium-release from the endoplasmic reticulum are reported. A two-step model is used for self­ consistency. Distributed electrical circuit representation coupled with the Smoluchowski equation yields the ER membrane nanoporation for calcium outflow based on a numerical simulation. This is combined with the continuum Li-Rinzel model and drift- diffusion for calcium dynamics. The results are shown to be in agreement with reported calcium release data. A modest increase (rough doubling) of the cellular calcium is predicted in the absence of extra-cellular calcium. In particular, the applied field of 15k V/cm with 60 ns pulse duration makes for a strong comparison. No oscillations are predicted and the net recovery period of about 5 minutes are both in agreement with published experimental results. A quantitative explanation for the lack of such oscillatory behavior, based on the density dependent calcium fluxes is also provided.

A discrete stochastic intracellular calcium model coupled with lower electric field (1kV/cm) is to be studied as a first step to providing a more descriptive intracellular calcium model in response to external electrical fields. While a deterministic continuum intracellular calcium model is implemented in 1-D, discrete stochastic model is a 2-D simulation. Thus, this model can be used as a valuable visualization tool for better understanding of interactions between intracellular calcium and an external electric field.

In the context of multiple high-intensity ultrashort electric field pulses, simplified version of intracellular calcium coupled with an external model provides a suitable curve fitting that will be utilized to better match the simulation results with experimental data and to extract practical parameters of interest. The intracellular pore's closing time is one such parameter.

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DOI

10.25777/5nbx-5n50

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