title: Dynamic Electroporation Modelling

authors: Talele, Sadhana

subjects: electroporation

abstract: In this thesis, modelling and simulation of the effects of electric fields on a single spherical cell are undertaken. Of interest is the effect that different electric field waveforms have on the induced transmembrane potential of the cell and by consequence the electropermeabilization of the cell membrane in terms of pore density or the fraction of the cell area that the pores occupy. Conventional biotechnology processes of electroporation make use of unipolar electric field pulses, which are known to generate undesirable conditions such as asymmetrical electropermeabilization. These electrical protocols also contribute to lower efficiencies in electroporation based applications (in terms of uptake of molecules in the cell) by being sensitive to cell radii.

Until recently, theoretical models of electroporation have lagged behind the experimental research. In order to optimize the efficiency of electroporation, it is important to consider as many biological and physical aspects as possible and it is a necessity that a variety of electric pulse parameters be tested. Thus a comprehensive model which can predict electropermeabilization as a result of any form of applied electric field and other important electroporation parameters is necessary. None of the existing theoretical modelling studies present simulations of dynamic electroporation modelling as a cell response to bipolar electric field wave-shapes. Developing such a model is the aim of this thesis.

In this thesis two numerical models are developed. These models consider electroporation as a dynamic process and include the non-linear dynamic effects of membrane electropermeabilization. The first model assumes all pores are identical and small (0.76~nm radius) and is capable of simulating transmembrane potential and pore density temporally and spatially, given any form of applied electric field and other important electroporation system parameters such as external medium, membrane, and cytoplasm complex dielectric properties. The piece-wise step response model presented here is used to simulate cell response to several different applied electric field wave-shape pulses.% including a unipolar square wave, bipolar square wave, bipolar sine wave, bipolar rectangular wave (rectangular pulse train), and a bipolar triangular wave.

Additional results from the first model demonstrate how the efficiency of electroporation related applications can be significantly improved by appropriately adjusting the parameters of the applied electric field and the  extracellular conductivity. Emphasis is given on the normalization of the degree of electroporation (in terms of pore density) for  two  cell radii (7.5~$\mu$m and 15~$\mu$m).

Although, these results gave a fair indication of the extent of electroporation in terms of pore density, the approximation that all pores have the same size, and do not change with time, may not be  appropriate. There is a need to model electroporation so as to reflect the growth or shrinkage of pores with time, as well as efficiently handle arbitrary waveshapes of electric fields. The additional information about pore radius evolution  gives a more realistic picture of the extent of electroporation, especially if one is to model for longer time (longer than 1~$\mu$s) or if an application necessarily required existence of larger pores (radius lager than 1~nm) rather than just the total pore area. Pore radius and pore numbers  affect the transmembrane potential, which in turn  affects pore density and pore radius.
Literature includes information on spatial and temporal aspects of pore radius evolution. However, the electric fields used in these models were limited to unipolar DC pulses and details of temporal and spatial evolution of transmembrane potential and pore radius have not been reported.
 
The second model developed in this thesis   simulates  spatial and temporal aspects of pore radius as an effect of  any given form  of applied electric field (including unipolar or bipolar), and other important electroporation system parameters.   The transmembrane potential and pore radii as function of time and angular position about the cell membrane   are presented. The results show that pore  radii    tend to be more normalized when an AC (bipolar)    field is used when compared to a  DC (unipolar) field (pore radii ranging from 1~nm to 8~nm for DC protocol compared with 1~nm to 3.4~nm for AC protocol when  the pulse amplitude used in both  cases is such as to give a similar fractional pore area at the end of 2~$\mu$s).
 
Additional simulation results from this model are  used to  compare the extent of electroporation   in response to sinusoidal AC (bipolar) electric field pulses of two different frequencies in a range of extracellular conductivity for two different cell radii (7.5~$\mu$m and 15~$\mu$m). 
It is   observed that  a higher frequency (1~MHz) bipolar sinusoidal applied electric field pulse reduces the relative difference in fractional pore area   for the two cell sizes compared to a lower frequency  (100~kHz) pulse. Nevertheless for the high frequency, a significantly higher amplitude is required to create the same level of average fractional pore area. Asymmetry of fractional pore area between the two hemispheres of the cell is observed for both field protocols.

text: Dynamic Electroporation Modelling In this thesis, modelling and simulation of the effects of electric fields on a single spherical cell are undertaken. Of interest is the effect that different electric field waveforms have on the induced transmembrane potential of the cell and by consequence the electropermeabilization of the cell membrane in terms of pore density or the fraction of the cell area that the pores occupy. Conventional biotechnology processes of electroporation make use of unipolar electric field pulses, which are known to generate undesirable conditions such as asymmetrical electropermeabilization. These electrical protocols also contribute to lower efficiencies in electroporation based applications (in terms of uptake of molecules in the cell) by being sensitive to cell radii.

Until recently, theoretical models of electroporation have lagged behind the experimental research. In order to optimize the efficiency of electroporation, it is important to consider as many biological and physical aspects as possible and it is a necessity that a variety of electric pulse parameters be tested. Thus a comprehensive model which can predict electropermeabilization as a result of any form of applied electric field and other important electroporation parameters is necessary. None of the existing theoretical modelling studies present simulations of dynamic electroporation modelling as a cell response to bipolar electric field wave-shapes. Developing such a model is the aim of this thesis.

In this thesis two numerical models are developed. These models consider electroporation as a dynamic process and include the non-linear dynamic effects of membrane electropermeabilization. The first model assumes all pores are identical and small (0.76~nm radius) and is capable of simulating transmembrane potential and pore density temporally and spatially, given any form of applied electric field and other important electroporation system parameters such as external medium, membrane, and cytoplasm complex dielectric properties. The piece-wise step response model presented here is used to simulate cell response to several different applied electric field wave-shape pulses.% including a unipolar square wave, bipolar square wave, bipolar sine wave, bipolar rectangular wave (rectangular pulse train), and a bipolar triangular wave.

Additional results from the first model demonstrate how the efficiency of electroporation related applications can be significantly improved by appropriately adjusting the parameters of the applied electric field and the  extracellular conductivity. Emphasis is given on the normalization of the degree of electroporation (in terms of pore density) for  two  cell radii (7.5~$\mu$m and 15~$\mu$m).

Although, these results gave a fair indication of the extent of electroporation in terms of pore density, the approximation that all pores have the same size, and do not change with time, may not be  appropriate. There is a need to model electroporation so as to reflect the growth or shrinkage of pores with time, as well as efficiently handle arbitrary waveshapes of electric fields. The additional information about pore radius evolution  gives a more realistic picture of the extent of electroporation, especially if one is to model for longer time (longer than 1~$\mu$s) or if an application necessarily required existence of larger pores (radius lager than 1~nm) rather than just the total pore area. Pore radius and pore numbers  affect the transmembrane potential, which in turn  affects pore density and pore radius.
Literature includes information on spatial and temporal aspects of pore radius evolution. However, the electric fields used in these models were limited to unipolar DC pulses and details of temporal and spatial evolution of transmembrane potential and pore radius have not been reported.
 
The second model developed in this thesis   simulates  spatial and temporal aspects of pore radius as an effect of  any given form  of applied electric field (including unipolar or bipolar), and other important electroporation system parameters.   The transmembrane potential and pore radii as function of time and angular position about the cell membrane   are presented. The results show that pore  radii    tend to be more normalized when an AC (bipolar)    field is used when compared to a  DC (unipolar) field (pore radii ranging from 1~nm to 8~nm for DC protocol compared with 1~nm to 3.4~nm for AC protocol when  the pulse amplitude used in both  cases is such as to give a similar fractional pore area at the end of 2~$\mu$s).
 
Additional simulation results from this model are  used to  compare the extent of electroporation   in response to sinusoidal AC (bipolar) electric field pulses of two different frequencies in a range of extracellular conductivity for two different cell radii (7.5~$\mu$m and 15~$\mu$m). 
It is   observed that  a higher frequency (1~MHz) bipolar sinusoidal applied electric field pulse reduces the relative difference in fractional pore area   for the two cell sizes compared to a lower frequency  (100~kHz) pulse. Nevertheless for the high frequency, a significantly higher amplitude is required to create the same level of average fractional pore area. Asymmetry of fractional pore area between the two hemispheres of the cell is observed for both field protocols.

year: 2009

title: IntCal09 and Marine09 radiocarbon age calibration curves, 0-50,000yeats cal BP

authors: Reimer, Paula J.

subjects: radiocarbon

abstract: The IntCal04 and Marine04 radiocarbon calibration curves have been updated from 12 cal kBP (cal kBP is here defined as thousands of calibrated years before AD 1950), and extended to 50 cal kBP, utilizing newly available data sets that meet the IntCal Working Group criteria for pristine corals and other carbonates and for quantification of uncertainty in both the 14C and calendar timescales as established in 2002. No change was made to the curves from 0–12 cal kBP. The curves were constructed using a Markov chain Monte Carlo (MCMC) implementation of the random walk model used for IntCal04 and Marine04. The new curves were ratified at the 20th International Radiocarbon Conference in June 2009 and are available in the Supplemental Material at www.radiocarbon.org.

text: IntCal09 and Marine09 radiocarbon age calibration curves, 0-50,000yeats cal BP The IntCal04 and Marine04 radiocarbon calibration curves have been updated from 12 cal kBP (cal kBP is here defined as thousands of calibrated years before AD 1950), and extended to 50 cal kBP, utilizing newly available data sets that meet the IntCal Working Group criteria for pristine corals and other carbonates and for quantification of uncertainty in both the 14C and calendar timescales as established in 2002. No change was made to the curves from 0–12 cal kBP. The curves were constructed using a Markov chain Monte Carlo (MCMC) implementation of the random walk model used for IntCal04 and Marine04. The new curves were ratified at the 20th International Radiocarbon Conference in June 2009 and are available in the Supplemental Material at www.radiocarbon.org.

year: 2009

title: What’s in a title? The use of honorifics in media coverage

authors: Nikora, Linda Waimarie

subjects: Maori

abstract: On the 15th August 2006, Te Arikinui Dame Te Atairangikaahu (referred to in this paper as Te Arikinui) passed away at the age of 75 years old after serving the Kingitanga movement for forty years. Her passing heralded the movement of large numbers of people to Turangawaewae marae where she lay in state. Intensive media coverage played a significant role in representing who Te Arikinui was, in profiling the Kingitanga movement and activities associated with the tangi as it progressed from the 15th to the 21st August 2006.  While we may be able to identify a “correct” honorific for Te Arikinui, our findings suggest that its understanding and use by mainstream television news media presenters, reporters and interviewees is a matter influenced by ethnic and cultural politics. The preferred use of titles by Maori and non-Maori sets up a process where representations of Te Ariki are contested. To non-Maori she is a “Dame”. To Maori, she is Te Arikinui. Through further analysis and theorising we will endeavour to further discuss the nature of these politics and the differences between Maori and non-Maori representations of Te Arikinui.

text: What’s in a title? The use of honorifics in media coverage On the 15th August 2006, Te Arikinui Dame Te Atairangikaahu (referred to in this paper as Te Arikinui) passed away at the age of 75 years old after serving the Kingitanga movement for forty years. Her passing heralded the movement of large numbers of people to Turangawaewae marae where she lay in state. Intensive media coverage played a significant role in representing who Te Arikinui was, in profiling the Kingitanga movement and activities associated with the tangi as it progressed from the 15th to the 21st August 2006.  While we may be able to identify a “correct” honorific for Te Arikinui, our findings suggest that its understanding and use by mainstream television news media presenters, reporters and interviewees is a matter influenced by ethnic and cultural politics. The preferred use of titles by Maori and non-Maori sets up a process where representations of Te Ariki are contested. To non-Maori she is a “Dame”. To Maori, she is Te Arikinui. Through further analysis and theorising we will endeavour to further discuss the nature of these politics and the differences between Maori and non-Maori representations of Te Arikinui.

year: 2008