Influence of Collimation and Detector length on CT exposures measured in   a 60cm long body phantom
  Background: Data fitting approaches to modeling allow for parametric formulae that may not reveal the physical quantities involved and their influence on the function being studied. In this paper the author models the approach to equilibrium function by a method that allows the physical quantities to be defined beforehand, allows their influence to be studied, and can be used to predict how each physical quantity affects approach to equilibrium. Methods: An ordinary differential equation (ODE) is used to model the approach to equilibrium function for the case where collimation is changed at fixed detector size. A parallel model is used to study the approach to equilibrium as a function of detector size for fixed collimation. Both models are validated by experimental measurements in a 60cm body phantom. Influence of detector size is simulated by using leaded sleeves of varying sizes wrapped around a 100mm pencil chamber. This creates sleeve gaps of 10 - 60mm around the chamber. A 100mm detector size is the pencil chamber without a leaded sleeve. Results: Model accurately describes the experimental data for the cases studied. Except for the smallest collimation of 5mm, linear regression analysis shows good correlation between data and model according to the R^2 values at all collimations. Further analysis of the model reveals minimum detector size that will integrate 98% of the signal for a given collimation is, d=4.95L. Additional analysis shows the minimum collimation at which a given detector will collect 98% of the signal is, L=5.49d. Conclusion: Modeling by differential equations is an accurate method for the approach to equilibrium function, and has advantages over curve fitting methods. 
Victor J Weir
physics.med-ph