Brain microbleeds are increased in chronic kidney disease (CKD) and their presence increases risk of cognitive decline and stroke. We examined the interaction between CKD and brain microhemorrhages (the neuropathological substrate of microbleeds) in mouse and cell culture models and studied progression of microbleed burden on serial brain imaging from humans. Mouse studies: Two CKD models were investigated: adenine-induced tubulointerstitial nephritis and surgical 5/6 nephrectomy. Cell culture studies: bEnd.3 mouse brain endothelial cells were grown to confluence, and monolayer integrity was measured after exposure to 5-15% human uremic serum or increasing concentrations of urea. Human studies: Progression of brain microbleeds was evaluated on serial MRI from control, pre-dialysis CKD, and dialysis patients. Microhemorrhages were increased 2-2.5-fold in mice with CKD independent of higher blood pressure in the 5/6 nephrectomy model. IgG staining was increased in CKD animals, consistent with increased blood-brain barrier permeability. Incubation of bEnd.3 cells with uremic serum or elevated urea produced a dose-dependent drop in trans-endothelial electrical resistance. Elevated urea induced actin cytoskeleton derangements and decreased claudin-5 expression. In human subjects, prevalence of microbleeds was 50% in both CKD cohorts compared with 10% in agematched controls. More patients in the dialysis cohort had increased microbleeds on follow-up MRI after 1.5 years. CKD disrupts the blood-brain barrier and increases brain microhemorrhages in mice and microbleeds in humans. Elevated urea alters the actin cytoskeleton and tight junction proteins in cultured endothelial cells, suggesting that these mechanisms explain (at least in part) the microhemorrhages and microbleeds observed in the animal and human studies.

In reliability theory, Cox's proportional hazard model is quite popular and widely used. In many situations, it is observed that failure rates under consideration are not proportional, rather they cross each other. In such situations, an alternative to Cox's proportional hazard model may be monotone hazard ratio model (provided the ratio exists). A notion of relative aging based on increasing hazard ratio was introduced by Kalashnikov and Rachev [19]. Sengupta and Deshpande [40] further explored this model and posited two other notions of relative aging based on increasing reversed failure rate ratio and increasing mean residual life ratio. In this study, for two life distributions, we derive sufficient conditions under which a life distribution ages faster than the other with respect to notions of relative aging described above. These sufficient conditions are easy to verify and can be used in practical applications where one is interested in studying relative aging of two life distributions. Applications of these results to relative aging of weighted distributions have also been illustrated. We also introduce a new relative aging ordering in terms of mean inactivity time order and study its fundamental properties.

The residual life of a random variable X at random time is defined to be a random variable X having the same distribution as the conditional distribution of X − given X > (denoted by X = (X − |X >)). Let (X, 1 ) and (Y, 2 ) be two pairs of jointly distributed random variables, where X and 1 (and, Y and 2 ) are not necessarily independent. In this paper, we compare random variables X 1 and Y 2 by providing sufficient conditions under which X 1 and Y 2 are stochastically ordered with respect to various stochastic orderings. These comparisons have been made with respect to hazard rate, likelihood ratio and mean residual life orders. We also study various ageing properties of random variable X 1 . By considering this generalized model, we generalize and unify several results in the literature on stochastic properties of residual lifetimes at random times. Some examples to illustrate the application of the results derived in the paper are also presented.

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