approach 2 based on exceeding a pre defined hu threshold this additional potential mechanism for auto triggering requires the creation of a function to fit the data points of hu values acquired during the scan in most cases the equation is a cubic function but it could also be expressed as any polynomial expression when the enhancement is reaching the peak the slope of the curve begins to decrease thus the derivative of this enhancement function will generally be increasing for early time points and then begin to decrease several seconds before the peak is reached see fig3 fig4 illustrates that the trigger could be initiated from consecutive declines in the value of the derivative function this analysis could be used in conjunction with the slope measure as an additional check in other words the slope of the derivative should be decreasing as the enhancement approaches peak fig5 illustrates an example of the derivative function for a given time intensity curve this analysis also has the potential for predicting the onset of the peak enhancement without requiring a desired threshold user input moreover the desired threshold could be estimated on anatomy to be scanned protocol prescribed patient parameters weight sex age cardiac rate etc approach 3 based on the slope at the time a given hu threshold is reached this alternative method would make the delay to start the scanning phase inversely proportional to the slope at the time a threshold is reached fig6 illustrates that this threshold could be at a user specified value or an empirically defined value as mentioned in method 2 i e approach 2 an additional application is imaging of the carotid and circle of willis vasculature in the neck and head regions in many vascular imaging.