Hybrid method for monitoring large Fabry-Pérot cavity displacements with nanometer precision.

The change in length of an optical fiber-based Fabry-Pérot cavity (FPC) can be precisely measured using phase tracking, but the displacement range is limited by phase ambiguity. Period tracking techniques determine the absolute FPC length, but with larger uncertainties from tracking the spacing between multiple peaks. A hybrid method is demonstrated that identifies appropriate peaks for phase tracking using a coarse estimate obtained from the free spectral range to effectively maintain the high precision (∼1 nm) of phase tracking techniques to measure ∼24 µm displacements, well beyond the range limitations (typically <1 µm) of phase tracking methods.

Expanding the range of the resolvable strain from distributed fiber optic sensors using a local adaptive reference approach.

Optical frequency domain reflectometry (OFDR) is a spectral measurement technique in which shifts in the local Rayleigh backscatter spectra can be used to perform distributed temperature or strain measurements relative to a reference measurement using ordinary single-mode optical fibers. This work demonstrates a data processing methodology for improving the resolvable range of temperature and strain by adaptively varying the reference measurement position by position, based on the time evolution of the local optical intensities and the correlation between the reference and active measurements. These methods nearly double the resolvable range of temperature and strain compared with that achieved using the traditional static reference approach.

Graphical Optimization of Spectral Shift Reconstructions for Optical Backscatter Reflectometry.

Optical backscatter reflectometry (OBR) is an interferometric technique that can be used to measure local changes in temperature and mechanical strain based on spectral analyses of backscattered light from a singlemode optical fiber. The technique uses Fourier analyses to resolve spectra resulting from reflections occurring over a discrete region along the fiber. These spectra are cross-correlated with reference spectra to calculate the relative spectral shifts between measurements. The maximum of the cross-correlated spectra-termed quality-is a metric that quantifies the degree of correlation between the two measurements. Recently, this quality metric was incorporated into an adaptive algorithm to (1) selectively vary the reference measurement until the quality exceeds a predefined threshold and (2) calculate incremental spectral shifts that can be summed to determine the spectral shift relative to the initial reference. Using a graphical (network) framework, this effort demonstrated the optimal reconstruction of distributed OBR measurements for all sensing locations using a maximum spanning tree (MST). By allowing the reference to vary as a function of both time and sensing location, the MST and other adaptive algorithms could resolve spectral shifts at some locations, even if others can no longer be resolved.

Quantification of cell membrane permeability induced by monopolar and high-frequency bipolar bursts of electrical pulses.

High-frequency bipolar electric pulses have been shown to mitigate undesirable muscle contraction during irreversible electroporation (IRE) therapy. Here, we evaluate the potential applicability of such pulses for introducing exogenous molecules into cells, such as in electrochemotherapy (ECT). For this purpose we develop a method for calculating the time course of the effective permeability of an electroporated cell membrane based on real-time imaging of propidium transport into single cells that allows a quantitative comparison between different pulsing schemes. We calculate the effective permeability for several pulsed electric field treatments including trains of 100µs monopolar pulses, conventionally used in IRE and ECT, and pulse trains containing bursts or evenly-spaced 1µs bipolar pulses. We show that shorter bipolar pulses induce lower effective membrane permeability than longer monopolar pulses with equivalent treatment times. This lower efficiency can be attributed to incomplete membrane charging. Nevertheless, bipolar pulses could be used for increasing the uptake of small molecules into cells more symmetrically, but at the expense of higher applied voltages. These data indicate that high-frequency bipolar bursts of electrical pulses may be designed to electroporate cells as effectively as and more homogeneously than conventional monopolar pulses.

A feasibility study for enrichment of highly aggressive cancer subpopulations by their biophysical properties via dielectrophoresis enhanced with synergistic fluid flow.

A common problem with cancer treatment is the development of treatment resistance and tumor recurrence that result from treatments that kill most tumor cells yet leave behind aggressive cells to repopulate. Presented here is a microfluidic device that can be used to isolate tumor subpopulations to optimize treatment selection. Dielectrophoresis (DEP) is a phenomenon where particles are polarized by an electric field and move along the electric field gradient. Different cell subpopulations have different DEP responses depending on their bioelectrical phenotype, which, we hypothesize, correlate with aggressiveness. We have designed a microfluidic device in which a region containing posts locally distorts the electric field created by an AC voltage and forces cells toward the posts through DEP. This force is balanced with a simultaneous drag force from fluid motion that pulls cells away from the posts. We have shown that by adjusting the drag force, cells with aggressive phenotypes are influenced more by the DEP force and trap on posts while others flow through the chip unaffected. Utilizing single-cell trapping via cell-sized posts coupled with a drag-DEP force balance, we show that separation of similar cell subpopulations may be achieved, a result that was previously impossible with DEP alone. Separated subpopulations maintain high viability downstream, and remain in a native state, without fluorescent labeling. These cells can then be cultured to help select a therapy that kills aggressive subpopulations equally or better than the bulk of the tumor, mitigating resistance and recurrence.

Modeling of Transmembrane Potential in Realistic Multicellular Structures before Electroporation.

Many approaches for studying the transmembrane potential (TMP) induced during the treatment of biological cells with pulsed electric fields have been reported. From the simple analytical models to more complex numerical models requiring significant computational resources, a gamut of methods have been used to recapitulate multicellular environments in silico. Cells have been modeled as simple shapes in two dimensions as well as more complex geometries attempting to replicate realistic cell shapes. In this study, we describe a method for extracting realistic cell morphologies from fluorescence microscopy images to generate the piecewise continuous mesh used to develop a finite element model in two dimensions. The preelectroporation TMP induced in tightly packed cells is analyzed for two sets of pulse parameters inspired by clinical irreversible electroporation treatments. We show that high-frequency bipolar pulse trains are better, and more homogeneously raise the TMP of tightly packed cells to a simulated electroporation threshold than conventional irreversible electroporation pulse trains, at the expense of larger applied potentials. Our results demonstrate the viability of our method and emphasize the importance of considering multicellular effects in the numerical models used for studying the response of biological tissues exposed to electric fields.

Mitigation of impedance changes due to electroporation therapy using bursts of high-frequency bipolar pulses.

BACKGROUND: For electroporation-based therapies, accurate modeling of the electric field distribution within the target tissue is important for predicting the treatment volume. In response to conventional, unipolar pulses, the electrical impedance of a tissue varies as a function of the local electric field, leading to a redistribution of the field. These dynamic impedance changes, which depend on the tissue type and the applied electric field, need to be quantified a priori, making mathematical modeling complicated. Here, it is shown that the impedance changes during high-frequency, bipolar electroporation therapy are reduced, and the electric field distribution can be approximated using the analytical solution to Laplace's equation that is valid for a homogeneous medium of constant conductivity. METHODS: Two methods were used to examine the agreement between the analytical solution to Laplace's equation and the electric fields generated by 100 µs unipolar pulses and bursts of 1 µs bipolar pulses. First, pulses were applied to potato tuber tissue while an infrared camera was used to monitor the temperature distribution in real-time as a corollary to the electric field distribution. The analytical solution was overlaid on the thermal images for a qualitative assessment of the electric fields. Second, potato ablations were performed and the lesion size was measured along the x- and y-axes. These values were compared to the analytical solution to quantify its ability to predict treatment outcomes. To analyze the dynamic impedance changes due to electroporation at different frequencies, electrical impedance measurements (1 Hz to 1 MHz) were made before and after the treatment of potato tissue. RESULTS: For high-frequency bipolar burst treatment, the thermal images closely mirrored the constant electric field contours. The potato tissue lesions differed from the analytical solution by 39.7 ± 1.3 % (x-axis) and 6.87 ± 6.26 % (y-axis) for conventional unipolar pulses, and 15.46 ± 1.37 % (x-axis) and 3.63 ± 5.9 % (y-axis) for high- frequency bipolar pulses. CONCLUSIONS: The electric field distributions due to high-frequency, bipolar electroporation pulses can be closely approximated with the homogeneous analytical solution. This paves way for modeling fields without prior characterization of non-linear tissue properties, and thereby simplifying electroporation procedures.

Characterization of sequentially-staged cancer cells using electrorotation.

The identification and separation of cells from heterogeneous populations is critical to the diagnosis of diseases. Label-free methodologies in particular have been developed to manipulate individual cells using properties such as density and morphology. The electrical properties of malignant cells, including the membrane capacitance and cytoplasmic conductivity, have been demonstrated to be altered compared to non-malignant cells of similar origin. Here, we exploit these changes to characterize individual cells in a sequentially-staged in vitro cancer model using electrorotation (EROT)-the rotation of a cell induced by a rotating electric field. Using a microfabricated device, a dielectrophoretic force to suspend cells while measuring their angular velocity resulting from an EROT force applied at frequencies between 3 kHz to 10 MHz. We experimentally determine the EROT response for cells at three stages of malignancy and analyze the resultant spectra by considering models that include the effect of the cell membrane alone (single-shell model) and the combined effect of the cell membrane and nucleus (double-shell model). We find that the cell membrane is largely responsible for a given cell's EROT response between 3 kHz and 10 MHz. Our results also indicate that membrane capacitance, membrane conductance, and cytoplasmic conductivity increase with an increasingly malignant phenotype. Our results demonstrate the potential of using electrorotation as a means making of non-invasive measurements to characterize the dielectric properties of cancer cells.

Discontinuous Galerkin Model of Cellular Electroporation.

Electroporation (EP) is a phenomenon involving both nonlinear biophysical processes and complex geometries. When exposed to strong electric fields, the formation of pores within a cell membrane increases the membrane permeability. Discontinuous Galerkin (DG) finite element methods can directly enforce these flux jumps across the thin cell membrane interface. We implement a DG finite element method to model the electric field, pore formation, and transmembrane flux of charged solutes during EP. Our model is readily extensible for parallel computation on high performance clusters and agrees with previous reports.

Characterization of Cell Membrane Permeability In Vitro Part II: Computational Model of Electroporation-Mediated Membrane Transport.

Electroporation is the process by which applied electric fields generate nanoscale defects in biological membranes to more efficiently deliver drugs and other small molecules into the cells. Due to the complexity of the process, computational models of cellular electroporation are difficult to validate against quantitative molecular uptake data. In part I of this two-part report, we describe a novel method for quantitatively determining cell membrane permeability and molecular membrane transport using fluorescence microscopy. Here, in part II, we use the data from part I to develop a two-stage ordinary differential equation model of cellular electroporation. We fit our model using experimental data from cells immersed in three buffer solutions and exposed to electric field strengths of 170 to 400 kV/m and pulse durations of 1 to 1000 µs. We report that a low-conductivity 4-(2-hydroxyethyl)-1 piperazineethanesulfonic acid buffer enables molecular transport into the cell to increase more rapidly than with phosphate-buffered saline or culture medium-based buffer. For multipulse schemes, our model suggests that the interpulse delay between two opposite polarity electric field pulses does not play an appreciable role in the resultant molecular uptake for delays up to 100 µs. Our model also predicts the per-pulse permeability enhancement decreases as a function of the pulse number. This is the first report of an ordinary differential equation model of electroporation to be validated with quantitative molecular uptake data and consider both membrane permeability and charging.

Characterization of Cell Membrane Permeability In Vitro Part I: Transport Behavior Induced by Single-Pulse Electric Fields.

Most experimental studies of electroporation focus on permeabilization of the outer cell membrane. Some experiments address delivery of ions and molecules into cells that should survive; others focus on efficient killing of the cells with minimal temperature rise. A basic method for quantifying electroporation effectiveness is measuring the membrane's diffusive permeability. More specifically, comparisons of membrane permeability between electroporation protocols often rely on relative fluorescence measurements, which are not able to be directly connected to theoretical calculations and complicate comparisons between studies. Here we present part I of a 2-part study: a research method for quantitatively determining the membrane diffusive permeability for individual cells using fluorescence microscopy. We determine diffusive permeabilities of cell membranes to propidium for electric field pulses with durations of 1 to 1000 µs and strengths of 170 to 400 kV/m and show that diffusive permeabilities can reach 1.3±0.4×10-8 m/s. This leads to a correlation between increased membrane permeability and eventual propidium uptake. We also identify a subpopulation of cells that exhibit a delayed and significant propidium uptake for relatively small single pulses. Our results provide evidence that cells, especially those that uptake propidium more slowly, can achieve large permeabilities with a single electrical pulse that may be quantitatively measured using standard fluorescence microscopy equipment and techniques.