Markov Chain Decomposition and Characterization of Hypertensive Blood Pressure with Applications to Linkage Analysis
Date of Award
Dissertation - Restricted
Doctor of Philosophy (PhD)
Mathematics, Statistics and Computer Science
This thesis uses Markov chain decomposition techniques to extract informative traits from arterial pressure recordings of hypertensive rats and humans. The feedback mechanisms, such as baroreceptor and renin angiotensin system, acting on blood pressure are quantified by the Cheeger ratios of specific levels and patterns of blood pressure. Statistical properties of Cheeger ratios and related quantities are established in a central limit theorem. The results show the dependence of the error on the spectral gap, length of recordings and relative frequencies of the estimated sets. These quantities are shown to be statistically different between normal and hypertensive rats, and heritable for the human population. New lower and upper bounds for the convergence rate (spectral gap) of the chain are derived via decomposition techniques. Linkage analysis and multi-trait linkage are used to find QTL for the estimated Cheeger ratios. Principal components are used to reduce the number of tests and increase the linkage power. Conditions for maximizing the power are derived and applied for humans.