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: Evaluation of composite laminates interleaved with nanofibre and microfibre veils.

authors: Collins-Gargan, Rosalie

abstract: The research covered in this thesis aimed to investigate the use of nanofibre and microfibre veils in carbon fibre reinforced composites and assessed the potential of the veils to improve damage resistance during impact and fatigue loading. It was hypothesised that the interleavings would increase the amount of energy required for crack propagation because of toughening due to fibre reinforcement mechanisms such as crack deflection, fibre pull out and fibre breakage. The work was undertaken as a combined project between the University of Waikato (Hamilton, New Zealand) and Revolution Fibres Ltd (Auckland, New Zealand). 
During this investigation, six thermoplastic polymers were chosen (acrylonitrile butadiene styrene (ABS), acrylonitrile styrene acrylate (ASA), polystyrene (PS), chlorinated polyvinyl chloride (CPVC), polymethyl methacrylate (PMMA) and polycarbonate (PC)) that could potentially be used for the electrospinning of polymer nanofibre veils. Nanofibre veils were successfully produced from PMMA, and a polymer blend of polyamide 6,6 (PA6,6) and PMMA, (referred to as 'nanoNyplex'). These veils, along with three other nanofibre veils (nanoPA6,6, poly vinyl butyral (nanoPVB), and poly ether sulfone (nanoPES)), three microfibre veils (polyphenylene sulfide (microPPS), polyetherimide (microPEI), and woven polyamide 6 (microtricot)) procured from other manufacturers, and three veils combining one of the nanofibre veils with each of the microfibre veils (microPPSnanoPA6,6, microPEInanoPA6,6, and microtricotnanoPA6,6) were then used as interleaves in the manufacture of carbon fibre reinforced epoxy composite panels. Interleaves were placed between every ply of prepreg. After curing the panels, test specimens were created to assess fatigue, vibration damping and compression after impact performance.
From the vibration damping study, it was found that the nanoNyplex interleaving improved damping the most. It was thought that energy dissipation was due friction brought about by the movement of the interleaving fibres in the matrix, resulting in friction due to weak adhesion between the nanoNyplex fibres and the epoxy matrix.
From the compression after impact (CAI) section of this study, it was found that specimens interleaved with nanoPA6,6, microPPS and microPPSnanoPA6,6 had the highest CAI strengths. From optical inspection, it appeared (in general) that as the CAI strength of the specimen increased, the length of the damage region also increased. However, those identified with the highest CAI strengths had shorter damage regions.
From the fatigue section of this study, it was found that the use of most interleavings, (apart from microtricot) increased the number of cycles to failure. Post fatigue test scanning electron microscopy confirmed that crack deflection was present for most interleaved specimens. Some evidence of pull out and breakage of the interleaving fibres was seen on the fracture surfaces of the nanoPA6,6, microPPS, microPEI, microPEInanoPA6,6 and microPPSnanoPA6,6 interleaved specimens.
For both CAI and fatigue, it was found that improvement was generally greater with veils that had a large number of fibres per unit area and high adhesion strength with the matrix. However, for CAI it seems that high fracture toughness was also desirable.

text: Evaluation of composite laminates interleaved with nanofibre and microfibre veils. The research covered in this thesis aimed to investigate the use of nanofibre and microfibre veils in carbon fibre reinforced composites and assessed the potential of the veils to improve damage resistance during impact and fatigue loading. It was hypothesised that the interleavings would increase the amount of energy required for crack propagation because of toughening due to fibre reinforcement mechanisms such as crack deflection, fibre pull out and fibre breakage. The work was undertaken as a combined project between the University of Waikato (Hamilton, New Zealand) and Revolution Fibres Ltd (Auckland, New Zealand). 
During this investigation, six thermoplastic polymers were chosen (acrylonitrile butadiene styrene (ABS), acrylonitrile styrene acrylate (ASA), polystyrene (PS), chlorinated polyvinyl chloride (CPVC), polymethyl methacrylate (PMMA) and polycarbonate (PC)) that could potentially be used for the electrospinning of polymer nanofibre veils. Nanofibre veils were successfully produced from PMMA, and a polymer blend of polyamide 6,6 (PA6,6) and PMMA, (referred to as 'nanoNyplex'). These veils, along with three other nanofibre veils (nanoPA6,6, poly vinyl butyral (nanoPVB), and poly ether sulfone (nanoPES)), three microfibre veils (polyphenylene sulfide (microPPS), polyetherimide (microPEI), and woven polyamide 6 (microtricot)) procured from other manufacturers, and three veils combining one of the nanofibre veils with each of the microfibre veils (microPPSnanoPA6,6, microPEInanoPA6,6, and microtricotnanoPA6,6) were then used as interleaves in the manufacture of carbon fibre reinforced epoxy composite panels. Interleaves were placed between every ply of prepreg. After curing the panels, test specimens were created to assess fatigue, vibration damping and compression after impact performance.
From the vibration damping study, it was found that the nanoNyplex interleaving improved damping the most. It was thought that energy dissipation was due friction brought about by the movement of the interleaving fibres in the matrix, resulting in friction due to weak adhesion between the nanoNyplex fibres and the epoxy matrix.
From the compression after impact (CAI) section of this study, it was found that specimens interleaved with nanoPA6,6, microPPS and microPPSnanoPA6,6 had the highest CAI strengths. From optical inspection, it appeared (in general) that as the CAI strength of the specimen increased, the length of the damage region also increased. However, those identified with the highest CAI strengths had shorter damage regions.
From the fatigue section of this study, it was found that the use of most interleavings, (apart from microtricot) increased the number of cycles to failure. Post fatigue test scanning electron microscopy confirmed that crack deflection was present for most interleaved specimens. Some evidence of pull out and breakage of the interleaving fibres was seen on the fracture surfaces of the nanoPA6,6, microPPS, microPEI, microPEInanoPA6,6 and microPPSnanoPA6,6 interleaved specimens.
For both CAI and fatigue, it was found that improvement was generally greater with veils that had a large number of fibres per unit area and high adhesion strength with the matrix. However, for CAI it seems that high fracture toughness was also desirable.

year: 2015

title: Proposing an indigenous power of veto in Aotearoa New Zealand

authors: Te Aho, Linda

abstract: Tom Fookes was an architect of New Zealand's Resource Management Act passed in 1991 (RMA). When interviewed about his life's work, Tom responded that he had sought to create a 'fair, integrated consideration of the decisions and policy to do with the social, economic and environmental conditions of our people'. I am told that he worked hard to provide a fair opportunity for all people to have a voice in decisions that affect them and places they care about. Processes were included in the RMA to allow this to occur, with particular provisions for a distinctive Maori voice. Because of these provisions, and the Act's lodestar of sustainable resource management, the RMA was promoted as one of the 'world's finest national environmental policies'.

text: Proposing an indigenous power of veto in Aotearoa New Zealand Tom Fookes was an architect of New Zealand's Resource Management Act passed in 1991 (RMA). When interviewed about his life's work, Tom responded that he had sought to create a 'fair, integrated consideration of the decisions and policy to do with the social, economic and environmental conditions of our people'. I am told that he worked hard to provide a fair opportunity for all people to have a voice in decisions that affect them and places they care about. Processes were included in the RMA to allow this to occur, with particular provisions for a distinctive Maori voice. Because of these provisions, and the Act's lodestar of sustainable resource management, the RMA was promoted as one of the 'world's finest national environmental policies'.

year: 2015