Over 50 million people worldwide suffer from epilepsy. Of these, nearly a third will be refractory to medical therapy, and many will be poor candidates for surgical resection. Thus there is a need for novel targets and therapies, the former of which will require a greater understanding of neural networks involved in epilepsy, and the latter of which demands the development of novel therapeutic techniques. Seizures are less frequent during periods where theta – a 3-12Hz oscillatory rhythm in the hippocampal local field potential – is present. Theta is thought to originate in the medial septum, a basal forebrain structure that projects to the site of origin for the most common form of intractable epilepsy, the hippocampus. As has been demonstrated with pharmacologic and electrical stimulation, theta generation via the medial septum is consequently an ideal target for intervention. However, of the three neuron populations within the medial septum – cholinergic, GABAergic, and glutamatergic – it is unclear which is responsible for theta, or indeed if a single population is driving the oscillation. Optogenetics, a novel technique that enables activation and inhibition of genetically-defined neurons on a millisecond time-scale, provides the means to functionally dissect this septohippocampal axis and leverage the results for seizure therapy. In this thesis, I detail the current state of deep brain stimulation for epilepsy, and describe our motivation for targeting the medial septum and the importance of the hippocampal theta rhythm. I describe new technologies, software, and adaptations to our electrophysiology platform, NeuroRighter, to enable concurrent optogenetic neuromodulation and electrophysiology in awake and behaving animals, and demonstrate how these technologies and techniques can be used in several experimental approaches. I next use this system to show that both the GABAergic and glutamatergic neurons of the medial septum can drive and pace hippocampal oscillatory rhythms, but only the glutamatergic neurons are necessary to maintain phase relationships between successive theta cycles. I also demonstrate that activating and inhibiting the cholinergic neurons of the medial septum does not alter hippocampal local field potential activity, but does alter single-unit firing rates. These results shed light on the function of the medial septum in generating and modulating theta, and provide clear targets for optogenetic modulation of epilepsy.

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acase@tulane.edu / 1 / Jeremiah Hartner

The medial axis skeleton is a thin line graph that preserves the topology of a region. The skeleton has often been cited as a useful representation for shape description, region interpretation, and object recognition. Unfortunately, the computation of the skeleton is extremely sensitive to variations in the bounding contour. In this paper, we describe a robust method for computing the medial axis skeleton across a variety of scales. The resulting scale-space is parametric with the complexity of the skeleton, where the complexity is defined as the number of branches in the skeleton.

In this thesis we derive some basic properties of graphs G embedded in a surface determining a link diagram D(G), having a specified number μ(D(G)) of components. ( The relationship between the graph and the link diagram comes from the tangle which replaces each edge of the graph). Firstly, we prove that μ (D(G)) ≤ f (G) + 2g, where f (G) is the number of faces in the embedding of G and g is the genus of the surface. Then we focus on the extremal case, where μ (D(G)) = f (G) + 2g. We note that μ (D(G)) does not change when undergoing graph Reidemeister moves or embedded ∆ ↔ Y exchanges. It is also useful that μ(D(G)) changes only very slightly when an edge is added to the graph. We finish with some observations on other possible values of μ(D(G)). We comment on two cases: when μ = 1, and the Petersen and Heawood families of graphs. These two families are obtained from K6 and K7 respectively by using ∆ ↔ Y exchanges.

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Vascular calcification is prevalent in ageing, in atherosclerosis, and especially in patients with Chronic Kidney Disease (CKD), with associated increased morbidity and mortality. The phenotypic transition of Vascular Smooth Muscle Cells (VSMCs) into osteoblastic/chondrogenic-like cells is critical for the development of calcification in CKD patients. Osteocytes, terminally differentiated osteoblasts, have recently emerged as major regulators of calcification in bone. Recently, osteocytelike cells have been observed in human peripheral arteries with medial vascular calcification. However, it remains undetermined as to whether VSMCs can undergo osteocytic differentiation within a calcifying environment and the functional role of osteocyte formation in the development of medial vascular calcification. Initial studies have characterised the ectonucleotide pyrophosphatase/phosphodiesterase 1 knockout (Enpp1-/-) mouse as a valid model of medial vascular calcification, which is employed throughout this thesis. This thesis has compared VSMCs to osteoblasts undergoing osteocytic differentiation in vitro. VSMC in vitro calcification was accompanied by up-regulated expression of osteocyte markers, including Sost, E11, Dmp1, Phex, Mepe and Fgf23. Immunohistochemistry confirmed the appearance of sclerostin and E11 in calcified aortae from the Enpp1-/- mouse. Further studies have identified a direct inhibitory role for the osteocyte specific gene FGF23 in modulating vascular calcification. The inhibitory effect of FGF23 on VSMC calcification was mediated through the MAPK/ERK signalling pathway. This thesis has also determined the role of BMP9, a highly osteogenic bone morphogenic protein, in vascular calcification, which induces VSMC calcification through a Smad signalling mechanism. Furthermore, VSMC expression of the osteocytic marker Sost was markedly increased following BMP9 treatment. Intriguingly, BMP9 was markedly elevated in serum from dialysis patients and a significant correlation was observed between dialysis time and BMP9 concentration in patients receiving haemodialysis. The work described herein has demonstrated that vascular calcification is associated with an osteocyte phenotype, and reports a direct inhibitory effect of the osteocyte specific gene FGF23 on vascular calcification. Furthermore, this thesis has shown that BMP9 induces the expression of the osteocytic marker Sost in VSMCs, and appears to play a critical role in vascular calcification.

Male rat sexual behavior requires aromatization of testosterone (T) to estradiol (E2) in the medial preoptic area (MPO) where estrogen receptors (ER) exist in two isoforms, ERα and ERβ. We hypothesized that E2 acts through estrogen receptor α (ERα) in the MPO to promote male mating behavior. Four groups of male rats were castrated, administered DHT s.c. and bilateral MPO implants delivering either: cholesterol, E2, propyl pyrazole triol (PPT, ERα agonist), diarylpropionitrile (DPN, ER β agonist), or 1-methyl-4-phenyl pyridinium (MPP, ERα antagonist). Additional gonadally intact males received bilateral MPO DPN implants. PPT maintained sexual behavior equally as well as E2, whereas mating was not maintained by cholesterol or DPN MPO implants. Exogenous T did not reinstate mating in animals that received MPP MPO implants. These findings indicate that, in the MPO, ERα is necessary and sufficient to promote copulatory behavior in male rats and ERβ is not sufficient for mating.