title: Modelling the spatial effects of the anaesthetic-induced phase-transition in the cerebral cortex

authors: Whiting, David Robin

subjects: anaesthesia

abstract: In this thesis I investigate the theoretical stochastic behaviour of a one-dimensional model of the cerebral cortex, exposed to varying concentrations of a general anaesthetic agent. The model is that of Steyn-Ross et al. (2003). Theirs is a continuum theory based on the electrical response of a neural mass known as the macrocolum. The model predicts that as anaethetic concentration is increased the cortex will undergo a sudden electrical phase transition corresponding to loss of consciousness (LOC). Similarly, at return of consciousness (ROC) a second distinct phase transition is predicted. Spatial variability is incorporated into the original homogeneous cortical model of Steyn-Ross et al. (1999). This is done by including the possibility of spatial variation in distant excitatory and inhibitory inputs. By modelling the cortex in this way, we hope to gain an understanding of how the cortex functions, and how anaethestic agents “shut-down” the brain.

I simulate the one-dimensional system numerically in order to verify analytical predictions. Both analytical and numerical results show an increase in the coherence (spatial-correlation) of the electrical activity along the one-dimensional rod on approach to both LOC and ROC. Theory and simulations also show that the electrical ﬂuctuations in the unconscious cortex should have a larger correlation length than for the cortex in the conscious state, suggesting that the unconscious state is the more ordered. I derive the theoretical power spectrum and discuss some of its properties.

By expanding the model to include spatial variability, we discover the possibility of self-organized structures forming spontaneously in the one-dimensional cortex. These “Turing” or dissipative structures are stationary in time, showing giant DC voltage variations along the cortical rod. Although the dissipative structures can from a rich variety of pseudo-periodic patterns, the physiological signiﬁcance of such stationary neural structures is not yet clear.

text: Modelling the spatial effects of the anaesthetic-induced phase-transition in the cerebral cortex In this thesis I investigate the theoretical stochastic behaviour of a one-dimensional model of the cerebral cortex, exposed to varying concentrations of a general anaesthetic agent. The model is that of Steyn-Ross et al. (2003). Theirs is a continuum theory based on the electrical response of a neural mass known as the macrocolum. The model predicts that as anaethetic concentration is increased the cortex will undergo a sudden electrical phase transition corresponding to loss of consciousness (LOC). Similarly, at return of consciousness (ROC) a second distinct phase transition is predicted. Spatial variability is incorporated into the original homogeneous cortical model of Steyn-Ross et al. (1999). This is done by including the possibility of spatial variation in distant excitatory and inhibitory inputs. By modelling the cortex in this way, we hope to gain an understanding of how the cortex functions, and how anaethestic agents “shut-down” the brain.

I simulate the one-dimensional system numerically in order to verify analytical predictions. Both analytical and numerical results show an increase in the coherence (spatial-correlation) of the electrical activity along the one-dimensional rod on approach to both LOC and ROC. Theory and simulations also show that the electrical ﬂuctuations in the unconscious cortex should have a larger correlation length than for the cortex in the conscious state, suggesting that the unconscious state is the more ordered. I derive the theoretical power spectrum and discuss some of its properties.

By expanding the model to include spatial variability, we discover the possibility of self-organized structures forming spontaneously in the one-dimensional cortex. These “Turing” or dissipative structures are stationary in time, showing giant DC voltage variations along the cortical rod. Although the dissipative structures can from a rich variety of pseudo-periodic patterns, the physiological signiﬁcance of such stationary neural structures is not yet clear.

year: 2003

title: Towards a Better Understanding of Coastal Cliff Erosion in Waitemata Group Rock; Auckland, New Zealand.

authors: Bell, Jessica Emily

subjects: Waitemata Group

abstract: The soft sedimentary deposits of the Waitemata Group which outcrop on the eastern coastline of the Auckland region are a coastal cliff erosion hazard. The determination of the rate that these cliffs erode for hazard zonation purposes still requires research. A database has been collated of a range of structural, geological, geomorphic and climate parameters from 16 representative cliff sites in order to statistically assess what parameters influence cliff erosion and why erosion rates vary within the relatively uniform geology. 

Four different lithological units have been defined: sandstone beds of turbidites; sandstone beds of densites (contain rip-up clasts); sand to gravel beds of debrites; and siltstone beds. Cliff rock has very weak to weak intact rock strength; apertures of 0.1 to 15 mm; infill types are soft clay and grit, and hard calcite and iron; spacing of discontinuities are smaller in siltstone beds (≥ 5 mm), and up to 5 m in sandstone and debrite beds; bedding and fault planes are continuous, joints are non-continuous; block size is dictated by bed thickness and non-continuous joints. Shore platform widths were used to determine long-term erosion rates which range from 1.2 to 53.0 mm y-1. Platform morphologies are either sloping or horizontal or are a combination of both. Higher platform benches found at some sites are considered to be the result of a higher period of sea-level or are high-tide benches. Intact and rock mass strength increases northwards. Cliff heights are 8 to 38 m; cliff angles are 51 to 79 . Conditions for sporadic planar and wedge failure were determined at some sites; frittered siltstone and low durability sandstone allow smaller-scale, continual erosion. Castor Bay, Army Bay, Waiwera Beach and Leigh Marine Reserve have the lowest rock mass quality. Musick Point, Narrowneck Beach and Waiake Bay have good rock mass quality.

A conceptual model for coastal cliff erosion has been developed for Waitemata Group coastal cliffs, based on the dominant processes that act on the cliffs determined from statistical analysis (student t-test, correlation and regression) and field observations. The primary factor for cliff erosion is bed dip, whereby seaward dipping beds have higher erosion rates than landward dipping beds. The secondary factors for cliff erosion include: the intact and rock mass strength of the rock; the rock mass quality; strength of the siltstone beds; strength and structure of the sandstone beds; and orientation of the bedding planes with respect to the cliff face. Shear stresses are enhanced when beds dip seaward and thus shear failure along continuous surfaces is achievable. When beds dip landward the influence of shear stresses along bedding planes, and their contribution to the removal of individual blocks of rock, is severely inhibited resulting in reduced rates of erosion.  There is no relationship between cliff height and erosion rates and cliff heights are mainly controlled by the pre-existing landscape. Cliff angle is controlled by the proportion of sandstone and siltstone (whereby lower cliff angles are more siltstone-dominated), rock mass strength and weathering.  Erosion rates do vary in Waitemata Group rock of the Auckland region because of the variation in structural and geomorphic conditions of the cliff, most strongly controlled by the dip angle of bedding planes.

text: Towards a Better Understanding of Coastal Cliff Erosion in Waitemata Group Rock; Auckland, New Zealand. The soft sedimentary deposits of the Waitemata Group which outcrop on the eastern coastline of the Auckland region are a coastal cliff erosion hazard. The determination of the rate that these cliffs erode for hazard zonation purposes still requires research. A database has been collated of a range of structural, geological, geomorphic and climate parameters from 16 representative cliff sites in order to statistically assess what parameters influence cliff erosion and why erosion rates vary within the relatively uniform geology. 

Four different lithological units have been defined: sandstone beds of turbidites; sandstone beds of densites (contain rip-up clasts); sand to gravel beds of debrites; and siltstone beds. Cliff rock has very weak to weak intact rock strength; apertures of 0.1 to 15 mm; infill types are soft clay and grit, and hard calcite and iron; spacing of discontinuities are smaller in siltstone beds (≥ 5 mm), and up to 5 m in sandstone and debrite beds; bedding and fault planes are continuous, joints are non-continuous; block size is dictated by bed thickness and non-continuous joints. Shore platform widths were used to determine long-term erosion rates which range from 1.2 to 53.0 mm y-1. Platform morphologies are either sloping or horizontal or are a combination of both. Higher platform benches found at some sites are considered to be the result of a higher period of sea-level or are high-tide benches. Intact and rock mass strength increases northwards. Cliff heights are 8 to 38 m; cliff angles are 51 to 79 . Conditions for sporadic planar and wedge failure were determined at some sites; frittered siltstone and low durability sandstone allow smaller-scale, continual erosion. Castor Bay, Army Bay, Waiwera Beach and Leigh Marine Reserve have the lowest rock mass quality. Musick Point, Narrowneck Beach and Waiake Bay have good rock mass quality.

A conceptual model for coastal cliff erosion has been developed for Waitemata Group coastal cliffs, based on the dominant processes that act on the cliffs determined from statistical analysis (student t-test, correlation and regression) and field observations. The primary factor for cliff erosion is bed dip, whereby seaward dipping beds have higher erosion rates than landward dipping beds. The secondary factors for cliff erosion include: the intact and rock mass strength of the rock; the rock mass quality; strength of the siltstone beds; strength and structure of the sandstone beds; and orientation of the bedding planes with respect to the cliff face. Shear stresses are enhanced when beds dip seaward and thus shear failure along continuous surfaces is achievable. When beds dip landward the influence of shear stresses along bedding planes, and their contribution to the removal of individual blocks of rock, is severely inhibited resulting in reduced rates of erosion.  There is no relationship between cliff height and erosion rates and cliff heights are mainly controlled by the pre-existing landscape. Cliff angle is controlled by the proportion of sandstone and siltstone (whereby lower cliff angles are more siltstone-dominated), rock mass strength and weathering.  Erosion rates do vary in Waitemata Group rock of the Auckland region because of the variation in structural and geomorphic conditions of the cliff, most strongly controlled by the dip angle of bedding planes.

year: 2007

title: Te ahunga atu ki ngā ōhanga oranga Māori: Towards Māori economies of wellbeing - Ngā whānau i te pokapū o te oranga

authors: Spiller, Chellie

abstract: Nau mai ki tēnei kohinga o ngā whakaaro me ngā tikanga e pā ana ki te oranga ohaoha Māori. Ko tō mātou kaupapa matua ko te whānau; e hiahia ana mātou ki te whakaatu i ngā huarahi ki te ora pai mō te whānau i roto i ngā horopaki ohaoha. Ko te ao Māori tō mātou tūāpapa. E whakakao ana tēnei pukapuka i te huhua o ngā reo me ngā tirohanga nō te ao Māori, me ētahi atu wheako e hāngai ana. Kua kotahi mātou ki raro i te taumarumaru o te kaupapa tūturu kotahi: arā, te oranga pai mō ngā whānau. Ko te tūmanako ka tautoko, ka whakaohooho anō hoki tēnei pukapuka i ngā tāngata kia hōhonu atu tā rātou hono ki tēnei kaupapa whaitake, kia whai māramatanga whaihua hoki rātou.

Welcome to this collection of thoughts and practices related to Māori economic life. Our primary focus is the whānau; we want to show ways to live well for the whānau in economic contexts. Our foundation is te ao Māori. This book brings together many voices and perspectives from the Māori world and other relevant experiences. We are united in one true purpose: the good livelihood of whānau. We hope this book will support and inspire people to connect more deeply with this critical topic and gain valuable insights.

text: Te ahunga atu ki ngā ōhanga oranga Māori: Towards Māori economies of wellbeing - Ngā whānau i te pokapū o te oranga Nau mai ki tēnei kohinga o ngā whakaaro me ngā tikanga e pā ana ki te oranga ohaoha Māori. Ko tō mātou kaupapa matua ko te whānau; e hiahia ana mātou ki te whakaatu i ngā huarahi ki te ora pai mō te whānau i roto i ngā horopaki ohaoha. Ko te ao Māori tō mātou tūāpapa. E whakakao ana tēnei pukapuka i te huhua o ngā reo me ngā tirohanga nō te ao Māori, me ētahi atu wheako e hāngai ana. Kua kotahi mātou ki raro i te taumarumaru o te kaupapa tūturu kotahi: arā, te oranga pai mō ngā whānau. Ko te tūmanako ka tautoko, ka whakaohooho anō hoki tēnei pukapuka i ngā tāngata kia hōhonu atu tā rātou hono ki tēnei kaupapa whaitake, kia whai māramatanga whaihua hoki rātou.

Welcome to this collection of thoughts and practices related to Māori economic life. Our primary focus is the whānau; we want to show ways to live well for the whānau in economic contexts. Our foundation is te ao Māori. This book brings together many voices and perspectives from the Māori world and other relevant experiences. We are united in one true purpose: the good livelihood of whānau. We hope this book will support and inspire people to connect more deeply with this critical topic and gain valuable insights.

year: 2025