Vascular Function in Chronic Kidney Disease and in Renovascular Disease

Cardiovascular mortality is 15 to 30 times higher in patients with chronic kidney disease than in the age-adjusted general population. Even minor renal dysfunction predicts cardiovascular events and death in the general population. In patients with atherosclerotic renovascular disease the annual cardiovascular event and death rate is even higher. The abnormalities in coronary and peripheral artery function in the different stages of chronic kidney disease and in renovascular disease are still poorly understood, nor have the cardiac effects of renal artery revascularization been well characterized, although considered to be beneficial. This study was conducted to characterize myocardial perfusion and peripheral endothelial function in patients with chronic kidney disease and in patients with atherosclerotic renovascular disease. Myocardial perfusion was measured with positron emission tomography (PET) and peripheral endothelial function with brachial artery flow-mediated dilatation. It has been suggested that the poor renal outcomes after the renal artery revascularization could be due to damage in the stenotic kidney parenchyma; especially the reduction in the microvascular density, changes mainly evident at the cortical level which controls almost 80% of the total renal blood flow. This study was also performed to measure the effect of renal artery stenosis revascularization on renal perfusion in patients with renovascular disease. In order to do that a PET-based method for quantification of renal perfusion was developed. The coronary flow reserve of patients with chronic kidney disease was similar to the coronary flow reserve of healthy controls. In renovascular disease the coronary flow reserve was, however, markedly reduced. Flow-mediated dilatation of brachial artery was decreased in patients with chronic kidney disease compared to healthy controls, and even more so in patients with renovascular disease. After renal artery stenosis revascularization, coronary vascular function and renal perfusion did not improve in patients with atherosclerotic renovascular disease, but in patients with bilateral renal artery stenosis, flow-mediated dilatation improved. Chronic kidney disease does not significantly affect coronary vascular function. On the contrary, coronary vascular function was severely deteriorated in patients with atherosclerotic renovascular disease, possibly because of diffuse coronary artery disease and/or diffuse microvascular disease. The peripheral endothelial function was disturbed in patients with chronic kidney disease and even more so in patient with atherosclerotic renovascular disease. Renal artery stenosis dilatation does not seem to offer any benefits over medical treatment in patients with renovascular disease, since revascularization does not improve coronary vascular function or renal perfusion.

Mathematical modeling and optimal control of malaria

Malaria continues to infect millions and kill hundreds of thousands of people worldwide each year, despite over a century of research and attempts to control and eliminate this infectious disease. Challenges such as the development and spread of drug resistant malaria parasites, insecticide resistance to mosquitoes, climate change, the presence of individuals with subpatent malaria infections which normally are asymptomatic and behavioral plasticity in the mosquito hinder the prospects of malaria control and elimination. In this thesis, mathematical models of malaria transmission and control that address the role of drug resistance, immunity, iron supplementation and anemia, immigration and visitation, and the presence of asymptomatic carriers in malaria transmission are developed. A within-host mathematical model of severe Plasmodium falciparum malaria is also developed. First, a deterministic mathematical model for transmission of antimalarial drug resistance parasites with superinfection is developed and analyzed. The possibility of increase in the risk of superinfection due to iron supplementation and fortification in malaria endemic areas is discussed. The model results calls upon stakeholders to weigh the pros and cons of iron supplementation to individuals living in malaria endemic regions. Second, a deterministic model of transmission of drug resistant malaria parasites, including the inflow of infective immigrants, is presented and analyzed. The optimal control theory is applied to this model to study the impact of various malaria and vector control strategies, such as screening of immigrants, treatment of drug-sensitive infections, treatment of drug-resistant infections, and the use of insecticide-treated bed nets and indoor spraying of mosquitoes. The results of the model emphasize the importance of using a combination of all four controls tools for effective malaria intervention. Next, a two-age-class mathematical model for malaria transmission with asymptomatic carriers is developed and analyzed. In development of this model, four possible control measures are analyzed: the use of long-lasting treated mosquito nets, indoor residual spraying, screening and treatment of symptomatic, and screening and treatment of asymptomatic individuals. The numerical results show that a disease-free equilibrium can be attained if all four control measures are used. A common pitfall for most epidemiological models is the absence of real data; model-based conclusions have to be drawn based on uncertain parameter values. In this thesis, an approach to study the robustness of optimal control solutions under such parameter uncertainty is presented. Numerical analysis of the optimal control problem in the presence of parameter uncertainty demonstrate the robustness of the optimal control approach that: when a comprehensive control strategy is used the main conclusions of the optimal control remain unchanged, even if inevitable variability remains in the control profiles. The results provide a promising framework for the design of cost-effective strategies for disease control with multiple interventions, even under considerable uncertainty of model parameters. Finally, a separate work modeling the within-host Plasmodium falciparum infection in humans is presented. The developed model allows re-infection of already-infected red blood cells. The model hypothesizes that in severe malaria due to parasite quest for survival and rapid multiplication, the Plasmodium falciparum can be absorbed in the already-infected red blood cells which accelerates the rupture rate and consequently cause anemia. Analysis of the model and parameter identifiability using Markov chain Monte Carlo methods is presented.