A New Diffusion Model to Estimate the Triiodothyronine Repletion in Infants During Cardiopulmonary Bypass For Congenital Heart Disease Using Stochastic Analysis

Abstract :

Cardiopulmonary bypass suppresses circulating thyroid hormone levels. We hypothesized that triiodothyronine deficiency in the developing heart after bypass may adversely affect cardiac function reserve postoperatively. We consider two identical, parallel M/M/1 queues. Both queues are fed by a Poisson arrival stream of rate ? and have service rates equal to ?. When both queues are non empty, the two systems behave independently of each other. However, when one of the queues becomes empty, the corresponding server helps in the other queue. This is called head of the line processor sharing. We study this model in the heavy traffic limit, where ?=??→1 . For, Cardiopulmonary bypass we use the formula that the heavy traffic diffusion approximation and the time dependent probability of the diffusion approximation to the joint queue length process.

Author Name : R. Vijayakumar, Dr. A. Muthaiyan & G. Vijayaprabha

Keywords: Cardiopulmonary Bypass, Diffusion Model, Congenital Heart Disease, Stochastic Analysis & Normal Distribution.