Biomedical Engineering - Theses
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ItemModeling electrical properties of neural tissue using a cellular composite approach( 2017)This research develops a framework for modeling the electrical properties of neu- ral tissue based on its cellular constituents. This has application to modeling of electrical stimulation of neural tissue, including for therapeutic purposes. It also has application to the modeling and interpretation of intrinsic electrical signals in the brain such as spiking, multi-unit activity, local field potential and electroencephalogram (EEG). Standard volume conductor models of neural tissue approximate the electrical properties of tissue with a locally homogeneous conductivity. This is despite the fact that realistic neural tissue is composed of cells with different geometries, orientations and electrical properties. The framework presented here suggests that these cellular level properties have a profound effect on the bulk electrical properties of tissue that cannot be captured by a simple conductivity. The membrane lipid bilayer structure behaves as a capacitance that relates the applied current density to the extracellular potential at previous times. Also, the cells within tissue are tightly packed causing higher resistance in the extracellular space compared with the wider intracellular space, which creates different current paths for the passage of electrical current flow in these spaces. In this mathematical and computational study, we replace the conductivity of tissue in the standard volume conductor approach with an admittivity which depends on spatial and temporal frequencies. Our expressions for bulk tissue admittivity, are derived from single cell properties by using a mean-field approach. The temporal frequency dependence arises through the capacitance of the membrane lipid bilayer and is related to the membrane time constant. The spatial frequency arises due to the passage of current from the highly confined extracellular space into the less confined intracellular space of a neuron and is related to the electrotonic length constant of neurites. Expressions for the admittivity are calculated for tissue consisting of a variety of morphological cell types. These include fiber bundles, layered structures in which the dendrites are confined to a plane and tissue composed of cells with a stellate morphology. Finally, these morphological types are combined in model of cortical grey matter that include the effect of glia as well as neurons on the tissue admittivity. The results show that the effective admittivity changes depending on whether tissue is in the near-, intermediate- or far-field regions relative to a stimulating electrode. The definition of the limits of these regions depends on both spatial and temporal frequencies being applied. The magnitude of the admittivity is smaller in the near-field than the far-field. It is also shown how anisotropic tissue responds to the electrical stimulation depending on the distance of fibers from an electrode. Anisotropic behavior is more prevalent in the far-field region compared to the near-field range in cases where the distribution of fiber orientations shows a bias. The effect of pulse width on tissue response is also investigated and our results demonstrate that for longer pulse widths the transition between near-field to far-field is displaced away from the electrode compared to shorter pulse widths. These results are all explained in details in Chapters 3 and 4 of the thesis. The glia influence on shaping the admittivity response of tissue based on their population is considered in Chapter 5. The new, more realistic model will facilitate a more accurate application of electrical stimulation to any neural tissue and specifically the brain. More accurate stimulation will improve emerging neurological therapies, such as deep brain stimulation for epilepsy and Parkinson’s disease.