title: Compact nonlinear model of an implantable electrode array for spinal cord stimulation (SCS)

authors: Scott, Jonathan B.

subjects: electrical stimulation

abstract: We describe the construction of a model of the electrode-electrolyte interface and surrounding electrolyte in the case of a platinum-electrode array intended for spinal-cord stimulation (SCS) application. We show that a finite, two dimensional, resistor array provides a satisfactory model of the bulk electrolyte, and we identify the complexity required of that resistor array. The electrode-electrolyte interface is modelled in a fashion suitable for commonly-available, compact simulators using a nonlinear extension of the model of Franks et al. that incorporates diodes and a memristor. The electrode-electrolyte interface model accounts for the nonlinear current-overpotential characteristic and diffusion-limiting effects. We characterise a commercial, implantable, electrode array, fit the model to it, and show that the model successfully predicts subtle operational characteristics.

text: Compact nonlinear model of an implantable electrode array for spinal cord stimulation (SCS) We describe the construction of a model of the electrode-electrolyte interface and surrounding electrolyte in the case of a platinum-electrode array intended for spinal-cord stimulation (SCS) application. We show that a finite, two dimensional, resistor array provides a satisfactory model of the bulk electrolyte, and we identify the complexity required of that resistor array. The electrode-electrolyte interface is modelled in a fashion suitable for commonly-available, compact simulators using a nonlinear extension of the model of Franks et al. that incorporates diodes and a memristor. The electrode-electrolyte interface model accounts for the nonlinear current-overpotential characteristic and diffusion-limiting effects. We characterise a commercial, implantable, electrode array, fit the model to it, and show that the model successfully predicts subtle operational characteristics.

year: 2013

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: Wrestling with Biculturalism in Social Work Education

authors: Glubb-Smith, Kelly J.

subjects: Bicultural social work

abstract: When approached to write a piece on Donna Awatere’s (1984) book Māori Sovereignty from a social work perspective we seized the opportunity to reconsider her work. Revisiting the text after a 30-year-plus hiatus sparked a series of reflective conversations about how we wrestle with teaching biculturalism and our efficacy in preparing students for bicultural practice realities. This article draws upon our co-constructed narratives about what it means to be a social work educator in a bicultural practice landscape. Social work students graduate into an exceedingly complex practice environment fraught with tension about how to resolve inequities across the micro-to-macro continuum. The focus of this article is how Donna Awatere’s work is reflected in the tensions and responsibilities experienced when socialising students into the bicultural mission of social work practice in Aotearoa (New Zealand).

text: Wrestling with Biculturalism in Social Work Education When approached to write a piece on Donna Awatere’s (1984) book Māori Sovereignty from a social work perspective we seized the opportunity to reconsider her work. Revisiting the text after a 30-year-plus hiatus sparked a series of reflective conversations about how we wrestle with teaching biculturalism and our efficacy in preparing students for bicultural practice realities. This article draws upon our co-constructed narratives about what it means to be a social work educator in a bicultural practice landscape. Social work students graduate into an exceedingly complex practice environment fraught with tension about how to resolve inequities across the micro-to-macro continuum. The focus of this article is how Donna Awatere’s work is reflected in the tensions and responsibilities experienced when socialising students into the bicultural mission of social work practice in Aotearoa (New Zealand).

year: 2023-07-27