Markov chain Monte Carlo analyses of longitudinal biomedical magnetic resonance data

King, Martin David (2004). Markov chain Monte Carlo analyses of longitudinal biomedical magnetic resonance data. PhD thesis The Open University.



Markov chain Monte Carlo simulation was used in an analysis of the data acquired in three longitudinal biomedical magnetic resonance studies. The first of these investigations uses a Bayesian nonlinear hierarchical random coefficients model to examine the longitudinal extracellular direct current (DC) potential and apparent diffusion coefficient (ADC) responses to focal ischaemia in the rat. The purpose is to perform a formal analysis of the temporal relationship between the two responses, and thus to examine the data for compatibility with a common latent (driving) process and, alternatively, the existence of an ADC threshold for anoxic depolarisation. The DC-potential and ADC transition parameter posterior probability distributions were generated, paying particular attention to the within-subject differences between the DC-potential and ADC transition characteristics. The results indicate that the DC-potential and ADC changes are not driven by a common latent process and, in addition, provide no evidence for a consistent ADC threshold associated with anoxic depolarisation.

The second analysis uses data acquired in a nuclear magnetic resonance spectroscopic study into the effects of intestinal ischaemia and subsequent reperfusion on liver metabolism in the rat. The purpose of the analysis is to examine the temporal relationship between energy status [inorganic phosphate to adenosine triphosphate ratio (PAR)] and the pH response, the former of which is an indicator of liver energy failure. The posterior distribution obtained for the PAR-pH onset time difference indicates that the pH response precedes the change in PAR, suggesting that intracellular acidosis cannot be ruled out as a contributing factor to the observed liver failure.

The third dataset was acquired in an electron spin resonance study of the Arrhenius behaviour of the rabbit muscle sarcoplasmic reticulum membrane. An MCMC Arrhenius plot changepoint analysis is used to estimate the order parameter 'transition' temperature.

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