Ratos jovens submetidos à hipóxia crônica intermitente (HCI) por um período de 10 dias apresentam hipertensão arterial e alterações no padrão de acoplamento das atividades simpática e respiratória. A exposição à HCI promove aumento da atividade simpática na fase expiratória final, mas o pico de atividade observado no final da inspiração/pós-inspiração também permanece. Estudos do nosso laboratório realizados em animais acordados mostraram por meio da análise espectral e do bloqueio ganglionar que a atividade simpática total está aumentada após um protocolo de 10 dias de HCI, caracterizando esse como sendo um modelo de hipertensão neurogênica. Em outros estudos voltados para verificar a reversibilidade da hipertensão arterial após o encerramento do protocolo de HCI, foi demonstrado que a pressão arterial desses animais se normaliza dentro de 15 dias em condição de normóxia. No entanto, estudos anteriores do nosso laboratório mostraram que a transmissão sináptica no núcleo do trato solitário permanece alterada mesmo após duas semanas de recuperação do protocolo de HCI. Sendo assim um dos objetivos desse trabalho foi avaliar as respostas cardiovasculares e respiratórias de ratos submetidos a um novo protocolo de HCI depois de 15 dias do encerramento do primeiro protocolo. Adicionalmente, avaliamos se as respostas cardiovasculares e respiratórias induzidas pela HCI seriam ou não influenciadas pelo pré-condicionamento com hipóxia mantida (HM). Assim como na HCI, nos modelos de hipertensão neurogênica a principal causa associada ao aumento de pressão arterial é a hiperatividade simpática. Dentre esses modelos, podemos destacar a hipertensão renovascular 1 rim, 1 clipe (1R, 1C) e os ratos espontaneamente hipertensos (SHR). Nesse contexto, avaliamos também se a pré-exposição à HCI poderia influenciar as respostas cardiovasculares e respiratórias observadas nesses 2 modelos de hipertensão. Os resultados mostraram que o pré-condicionamento com HCI ou com HM não alterou as respostas cardiovasculares promovidas por uma subsequente exposição à HCI. Por outro lado, o nível de hipertensão promovido pelo modelo 1R, 1C foi significativamente menor em animais pré-condicionados com HCI, via inibição do tônus simpático vascular. O procedimento de desnervação renal praticamente eliminou o aumento de pressão arterial associado ao modelo 1R, 1C. Adicionalmente, após a remoção bilateral do corpúsculo carotídeo, o nível de hipertensão decorrente do modelo 1R, 1C foi o mesmo, independente do pré-condicionamento com HCI. Por outro lado, o pré-condicionamento com HCI não alterou o desenvolvimento da hipertensão arterial de ratos SHR. / Juvenile rats submitted to chronic intermittent hypoxia (CIH) during 10 days present hypertension and alterations in the sympathetic and respiratory coupling. Exposure to CIH produces sympathetic overactivity in the late expiratory phase, whereas the peak of activity observed at the end of inspiration/post-inspiration was also maintained. Studies from our laboratory performed in awake animals, using spectral analyses and ganglionic blockade showed that the total sympathetic activity is increased after CIH protocol, characterizing this as a neurogenic model of hypertension. Other studies, designed to verify the reversibility of hypertension at the end of the CIH protocol, showed that the arterial pressure normalizes within 15 days in normoxic conditions. Nevertheless, previous studies from our laboratory showed that the synaptic transmission in the nucleus of the solitary tract continues altered even after two weeks of recovery from the CIH protocol. Thus, one of our goals was to evaluate the cardiovascular and respiratory responses in rats submitted to a new CIH protocol 15 days after the first protocol. Additionally, we evaluated whether or not the cardiovascular and respiratory responses induced by CIH would be influenced by preconditioning with sustained hypoxia (SH). As in CIH, in other models of hypertension the main cause associated with the rise of arterial pressure relies on the sympathetic overactivity. Among those models are the renovascular hypertension 1 kidney, 1 clip (1K, 1C) and the spontaneous hypertensive rats (SHR). In this sense, another goal of this study was to evaluate whether a previous exposure to CIH could affect the cardiovascular and respiratory responses produced by the 1K, 1C and the SHR model. Our results are showing that preconditioning with either CIH or SH did not alter the cardiovascular response produced by a subsequent exposure to CIH. On the other side, the level of hypertension promoted by 1K, 1C was significantly reduced in CIH preconditioned rats, via inhibition of the vascular sympathetic tone. The procedure of renal denervation practically eliminated the rise in arterial pressure associated with 1K, 1C. Additionally, after bilateral carotid body removal, the level of hypertension observed in 1K, 1C rats was the same, regardless CIH preconditioning. However, preconditioning with CIH did not affect the development of hypertension in SHR.

The diploma theses is focused on matrix-free preconditioning of a linear system. It gives a very brief introduction into the area of iterative methods, preconditioning and matrix-free environment. The emphasis is put on a detailed description of a variant of LU factorization which can be computed in a matrix-free manner and on a new technique connected with this factorization for preconditioning by incomplete LU factors in matrix-free environment. Its main features are storage of only one of the two incomplete factors and low memory costs during the computation of the stored factor. The thesis closes with numerical experiments demonstrating the efficiency of the proposed technique.

Nesse estudo investigamos os efeitos da hipóxia tecidual aguda (HA) sobre as propriedades eletrofisiológicas intrínsecas dos neurônios pré-simpáticos bulboespinhais da área rostro-ventrolateral do bulbo (RVLM) de ratos jovens adultos submetidos previamente à hipóxia crônica intermitente (HCI) e os seus respectivos controle. Para marcarmos os neurônios pré-simpáticos bulboespinhais da RVLM, ratos Wistar jovens (P19-P21) anestesiados com ketamina e xilazina, receberam microinjeções bilaterais de rodamina, um traçador fluorescente retrógrado, na coluna intermediolateral da medula espinhal (T3-T6) e 2 dias após a recuperação da cirurgia, os animais foram submetidos ao protocolo de HCI, enquanto que ratos controle foram mantidos em condições de normóxia, durante 10 dias. No décimo primeiro dia, os ratos foram novamente anestesiados para a remoção do cérebro e as fatias do tronco cerebral contendo neurônios pré-simpáticos com marcação positivas foram registrados. Utilizamos a técnica de whole cell patch-clamp para estudo das propriedades eletrofisiológicas desses neurônios. As propriedades eletrofisiológicas intrínsecas foram analisadas antes e após a HA, a qual foi produzida pela perfusão das fatias do tronco cerebral com uma solução hipóxica (95% N2 + 5% CO2) durante 2 minutos na presença de bloqueadores sinápticos excitatórios e inibitórios. Todos os neurônios pré-simpáticos apresentaram característica intrínseca de autodespolarização e a frequência de disparos basal de potenciais de ação (PAs) desses neurônios de ratos do grupo controle e HCI foram similares [Controle= 5,03 ± 0,4 Hz (n=39) vs HCI= 6,31 ± 0,7 Hz (n=31); p > 0,05]. No grupo controle, a HA não alterou a frequência média de disparos de PAs (BS = 5,03 ± 0,4 Hz vs HA = 5,24 ± 0,3 Hz (n=39); p > 0,05], porém revelou diferentes perfis de disparo de PAs após 2 min de exposição à HA: i) 11 neurônios com aumento na frequência de disparos (BS = 5,1 ± 0,7 Hz vs HA = 7 ± 0,7 Hz; p < 0,05]; ii) 21 neurônios sem alteração na frequência de disparos (BS = 4,8 ± 0,5 Hz vs HA = 5,36 ± 0,6 Hz; p > 0,05] e iii) 7 neurônios com diminuição na frequência de disparos (BS = 7,3 ± 1,1 Hz vs HA = 3,6 ± 0,7 Hz; p < 0,05). No grupo HCI, a HA produziu aumento na frequência média de disparos (BS= 6,31 ± 0,7 Hz vs HA= 7,25 ± 0,8 Hz; n=31 - p < 0,05) e na análise do perfil de disparo de PAs, a HA revelou 2 subpopulações: i) 9 neurônios com aumento na frequência de disparos (BS = 4,7 ± 0,8 Hz vs HA = 8,2 ± 1,4 Hz; p < 0,05) e ii) 22 neurônios sem alteração na frequência de disparos (BS = 7,0 ± 1,0 Hz vs HA = 6,8 ± 1,0 Hz; p > 0,05). Esse estudo nos permitiu revelar diferentes subpopulações de neurônios pré-simpáticos que responderam de forma distintas à HA. Os resultados também sugerem que a HCI teria um efeito pré- condicionante na excitabilidade intrínseca dos neurônios pré-simpáticos em resposta à HA / In this study we evaluated the effects of acute hypoxia (AH) on the intrinsic electrophysiological properties of presympathetic neurons from rostro ventrolateral medulla (RVLM) of juvenile rats exposed to chronic intermittent hypoxia (CIH) or normoxic condition (control group). To label the RVLM bulbospinal presympathetic neurons, young Wistar rats (P 19 - 21) anesthetized with ketamine and xylazine, received bilateral microinjections of a fluorescent retrograde tracer (rhodamine retrobeads) were performed into the intermediolateral column of spinal cord (T3-T6) and two days after recovery of the surgery, the animals were submitted to CIH or normoxic protocol, during 10 days. On the 11th day, under anesthesia, brainstem slices were obtained and only the labeled RVLM presympathetic neurons were recorded, using whole-cell patch-clamp approach to study the electrophysiological properties of these neurons. The intrinsic electrophysiological properties were analyzed before and after AH, which was produced by slice perfusion with hypoxic solution (95% N2 and 5% CO2) during 2 min in the presence of excitatory and inhibitory synaptic antagonists. All recorded RVLM presympathetic neurons presented intrinsic pacemaker activity and the baseline firing frequency of these neurons from control and CIH group were similar [Control= 5,03 ± 0,4 Hz (n=39) vs HCI= 6,31 ± 0,7 Hz (n=31); p > 0,05]. In the control group, AH do not change the firing rate (BS = 5,03 ± 0,4 Hz vs HA = 5,24 ± 0,3 Hz (n=39); p > 0,05), but revealed different pattern of firing frequency after 2 min of AH: i) 11 neurons increased the firing frequency (BS = 4,9 ± 0,9 Hz vs HA = 6,9 ± 1,0 Hz; p < 0,05) ; ii) 21 neurons do not change the firing frequency (BS = 4,8 ± 0,5 Hz vs HA = 5,36 ± 0,6 Hz; p > 0,05) and iii) 7 neurons decreased the firing frequency (BS = 7,3 ± 1,1 Hz vs HA = 3,6 ± 0,7 Hz; p < 0,05). In the CIH group, the AH increased the firing rate comparing with basal condition (SB= 6,31 ± 0,7 Hz vs AH= 7,25 ± 0,8 Hz; n=31 - p < 0,05) and analyzing the pattern of action potential, AH revealed 2 subpopulations in this group: i) 9 neurons increased the firing frequency (SB = 4,7 ± 0,8 Hz vs AH = 8,2 ± 1,4 Hz; p < 0,05) and ii) 22 neurons do not change the firing frequency (SB = 7,0 ± 1,0 Hz vs AH = 6,8 ± 1,0 Hz; p > 0,05).. The data shows that AH revealed different subpopulations of presympathetic neurons and suggest that CIH plays a preconditioning in the intrinsic excitability of presympathetic neurons in response to acute hypoxia

The task of choosing a preconditioner M to use when solving a linear system Ax=b with iterative methods is often tedious and most methods remain ad-hoc. This thesis presents a randomized algorithm to make this chore less painful through use of randomized algorithms for estimating traces. In particular, we show that the preconditioner stability || I - M-1A ||F, known to forecast preconditioner quality, can be computed in the time it takes to run a constant number of iterations of conjugate gradients through use of sketching methods. This is in spite of folklore which suggests the quantity is impractical to compute, and a proof we give that ensures the quantity could not possibly be approximated in a useful amount of time by a deterministic algorithm. Using our estimator, we provide a method which can provably select a quality preconditioner among n candidates using floating operations commensurate with running about n log(n) steps of the conjugate gradients algorithm. In the absence of such a preconditioner among the candidates, our method can advise the practitioner to use no preconditioner at all. The algorithm is extremely easy to implement and trivially parallelizable, and along the way we provide theoretical improvements to the literature on trace estimation. In empirical experiments, we show the selection method can be quite helpful. For example, it allows us to create to the best of our knowledge the first preconditioning method for kernel regression which never uses more iterations over the non-preconditioned analog in standard settings.

The development, analysis, and implementation of efficient methods to solve algebraic systems of equations are main research directions in the field of numerical simulation and are the focus of this thesis. Due to their lesser demands for computer resources, iterative solution methods are the choice to make, when very large scale simulations have to be performed. To improve their efficiency, iterative methods are combined with proper techniques to accelerate convergence. A general technique to do this is to use a so-called preconditioner. Constructing and analysing various preconditioning methods has been an active field of research already for decades. Special attention is devoted to the class of the so-called optimal order preconditioners, that possess both optimal convergence rate and optimal computational complexity. The preconditioning techniques, proposed and studied in this thesis, utilise the block structure of the underlying matrices, and lead to methods that are of optimal order. In the first part of the thesis, we construct an Algebraic MultiLevel Iteration (AMLI) method for systems arising from discretizations of parabolic problems, using Crouzeix-Raviart finite elements. The developed AMLI method is based on an approximated block factorization of the original system matrix, where the partitioning is associated with a sequence of nested discretization meshes. In the second part of the thesis we develop solution methods for the numerical simulation of multiphase flow problems, modelled by the Cahn-Hilliard (C-H) equation. We consider the discrete C-H problem, obtained via finite element discretization in space and implicit schemes in time. We propose techniques to precondition the Jacobian of the discrete nonlinear system, based on its natural two-by-two block structure. The preconditioners are used in the framework of inexact Newton methods. We develop two nonlinear solution algorithms for the Cahn-Hilliard problem. Both lead to efficient optimal order methods. One of the main advantages of the proposed methods is that they are implemented using available software toolboxes for both sequential and distributed execution. The theoretical analysis of the solution methods presented in this thesis is combined with numerical studies that confirm their efficiency.

Anoxia is an environmental stress that few air-breathing vertebrates can tolerate for more than a few minutes before extensive neurodegeneration occurs. Some facultative anaerobes, including the freshwater western painted turtle Chrysemys picta bellii, are able to coordinately reduce ATP demand to match reduced ATP availability during anoxia, and thus tolerate prolonged insults without apparent detriment. To reduce metabolic rate, turtle neurons undergo channel arrest and spike arrest to decrease membrane ion permeability and neuronal electrical excitability, respectively. However, although these adaptations have been documented in turtle brain, the mechanisms underlying channel and spike arrest are poorly understood. The aim of my research was to elucidate the cellular mechanisms that underlie channel and spike arrest and the neuroprotection they confer on the anoxic turtle brain. Using electrophysiological and fluorescent imaging techniques, I demonstrate for the first time that: 1) the α-amino-3-hydroxy-5-methyl-4-isoxazole propionic acid receptor (AMPAR) undergoes anoxia-mediated channel arrest; 2) delta opioid receptors (DORs), and 3) mild mitochondrial uncoupling via mitochondrial ATP-sensitive K+ channels result in an increase in cytosolic calcium concentration and subsequent channel arrest of the N-methyl-D-aspartate receptor, preventing excitotoxic calcium entry, and 4) reducing nitric oxide (NO) production; 5) the cellular concentration of reactive oxygen species (ROS) decreases with anoxia and ROS bursts do not occur during reoxygenation; and 6) spike arrest occurs in the anoxic turtle cortex, and that this is regulated by increased neuronal conductance to chloride and potassium ions due to activation of γ–amino-butyric acid receptors (GABAA and GABAB respectively), which create an inhibitory electrical shunt to dampen neuronal excitation during anoxia. These mechanisms are individually critical since blockade of DORs or GABA receptors induce excitotoxic cell death in anoxic turtle neurons. Together, spike and channel arrest significantly reduce neuronal excitability and individually provide key contributions to the turtle’s long-term neuronal survival during anoxia. Since the turtle is the most anoxia-tolerant air-breathing vertebrate identified, these results suggest that multiple mechanisms of metabolic suppression acting in concert are essential to maximizing anoxia-tolerance.

Anoxia is an environmental stress that few air-breathing vertebrates can tolerate for more than a few minutes before extensive neurodegeneration occurs. Some facultative anaerobes, including the freshwater western painted turtle Chrysemys picta bellii, are able to coordinately reduce ATP demand to match reduced ATP availability during anoxia, and thus tolerate prolonged insults without apparent detriment. To reduce metabolic rate, turtle neurons undergo channel arrest and spike arrest to decrease membrane ion permeability and neuronal electrical excitability, respectively. However, although these adaptations have been documented in turtle brain, the mechanisms underlying channel and spike arrest are poorly understood. The aim of my research was to elucidate the cellular mechanisms that underlie channel and spike arrest and the neuroprotection they confer on the anoxic turtle brain. Using electrophysiological and fluorescent imaging techniques, I demonstrate for the first time that: 1) the α-amino-3-hydroxy-5-methyl-4-isoxazole propionic acid receptor (AMPAR) undergoes anoxia-mediated channel arrest; 2) delta opioid receptors (DORs), and 3) mild mitochondrial uncoupling via mitochondrial ATP-sensitive K+ channels result in an increase in cytosolic calcium concentration and subsequent channel arrest of the N-methyl-D-aspartate receptor, preventing excitotoxic calcium entry, and 4) reducing nitric oxide (NO) production; 5) the cellular concentration of reactive oxygen species (ROS) decreases with anoxia and ROS bursts do not occur during reoxygenation; and 6) spike arrest occurs in the anoxic turtle cortex, and that this is regulated by increased neuronal conductance to chloride and potassium ions due to activation of γ–amino-butyric acid receptors (GABAA and GABAB respectively), which create an inhibitory electrical shunt to dampen neuronal excitation during anoxia. These mechanisms are individually critical since blockade of DORs or GABA receptors induce excitotoxic cell death in anoxic turtle neurons. Together, spike and channel arrest significantly reduce neuronal excitability and individually provide key contributions to the turtle’s long-term neuronal survival during anoxia. Since the turtle is the most anoxia-tolerant air-breathing vertebrate identified, these results suggest that multiple mechanisms of metabolic suppression acting in concert are essential to maximizing anoxia-tolerance.

Over the last 25 years, interior-point methods (IPMs) have emerged as a viable class of algorithms for solving various forms of conic optimization problems. Most IPMs use a modified Newton method to determine the search direction at each iteration. The system of equations corresponding to the modified Newton system can often be reduced to the so-called normal equation, a system of equations whose matrix ADA' is positive definite, yet often ill-conditioned. In this thesis, we first investigate the theoretical properties of the maximum weight basis (MWB) preconditioner, and show that when applied to a matrix of the form ADA', where D is positive definite and diagonal, the MWB preconditioner yields a preconditioned matrix whose condition number is uniformly bounded by a constant depending only on A. Next, we incorporate the results regarding the MWB preconditioner into infeasible, long-step, primal-dual, path-following algorithms for linear programming (LP) and convex quadratic programming (CQP). In both LP and CQP, we show that the number of iterative solver iterations of the algorithms can be uniformly bounded by n and a condition number of A, while the algorithmic iterations of the IPMs can be polynomially bounded by n and the logarithm of the desired accuracy. We also expand the scope of the LP and CQP algorithms to incorporate a family of preconditioners, of which MWB is a member, to determine an approximate solution to the normal equation. For the remainder of the thesis, we develop a new preconditioning strategy for solving systems of equations whose associated matrix is positive definite but ill-conditioned. Our so-called adaptive preconditioning strategy allows one to change the preconditioner during the course of the conjugate gradient (CG) algorithm by post-multiplying the current preconditioner by a simple matrix, consisting of the identity matrix plus a rank-one update. Our resulting algorithm, the Adaptive Preconditioned CG (APCG) algorithm, is shown to have polynomial convergence properties. Numerical tests are conducted to compare a variant of the APCG algorithm with the CG algorithm on various matrices.

This study investigated the role of opioid, adenosine, bradykinin, and calcitonin-gene related peptide (CGRP) receptors, and potential ‘cross-talk’ among suspected G-protein coupled receptors in a humoral model of remote ischemic preconditioning (rIPC) cardioprotection. Compared to Control dialysate (from non-preconditioned donor rabbit blood), rIPC dialysate (from remotely preconditioned blood) reduced cell death in rabbit cardiomyocytes following simulated ischemia and reperfusion. Non-selective, δ-, or κ-opioid receptor blockade and non-selective adenosine receptor blockade abolished rIPC dialysate protection; whereas, bradykinin B2 and CGRP receptor blockade had no effect. Non-selective adenosine receptor blockade fully and partially abolished protection by κ- and δ-opioid receptors, respectively. Multiple reaction monitoring mass spectrometry detected low levels of adenosine, and other preconditioning substances, in the dialysate. An increase in extracellular adenosine was not detected during opioid-induced preconditioning to explain this cross-talk. These results suggest that δ-opioid, κ-opioid, adenosine receptors, and opioid-adenosine cross-talk are involved in rIPC of freshly isolated cardiomyocytes.

This study investigated the role of opioid, adenosine, bradykinin, and calcitonin-gene related peptide (CGRP) receptors, and potential ‘cross-talk’ among suspected G-protein coupled receptors in a humoral model of remote ischemic preconditioning (rIPC) cardioprotection. Compared to Control dialysate (from non-preconditioned donor rabbit blood), rIPC dialysate (from remotely preconditioned blood) reduced cell death in rabbit cardiomyocytes following simulated ischemia and reperfusion. Non-selective, δ-, or κ-opioid receptor blockade and non-selective adenosine receptor blockade abolished rIPC dialysate protection; whereas, bradykinin B2 and CGRP receptor blockade had no effect. Non-selective adenosine receptor blockade fully and partially abolished protection by κ- and δ-opioid receptors, respectively. Multiple reaction monitoring mass spectrometry detected low levels of adenosine, and other preconditioning substances, in the dialysate. An increase in extracellular adenosine was not detected during opioid-induced preconditioning to explain this cross-talk. These results suggest that δ-opioid, κ-opioid, adenosine receptors, and opioid-adenosine cross-talk are involved in rIPC of freshly isolated cardiomyocytes.