We begin by injecting contrast into the arm usually as a tight bolus. And by that I mean that the injection is performed at high rates, so that all the contrast enters the circulation in only a few seconds. By the time it has worked its way up the arm, through the right side of the heart, through the lung back to the heart and finally up to the brain however, it has been diluted somewhat by non-contrast containing blood from elsewhere in the body and has spread out.
Therefore, when we examine the concentration time curve of the terminal internal carotid artery, we get a slightly elongated curve, and this is essentially what the tissue will receive. We call this curve the arterial input function or AIF, and having a normal curve is essential if the rest of the perfusion study is to be adequate. Anything that impairs this process, such as occlusions or long collaterals or shunts etc... will potentially make the examination uninterpretable.
A similar process occurs within the brain's microcirculation. The number and size of these small vessels affects the speed at which contrast traverses the capillary bed and how much of it remains within them. This in turn changes the shape of the bolus that we can see both within the tissue, which we call the tissue concentration curve as well as on the venous end, for example, the superior sagital sinus, and we call this the venous output function.
The effect of the microcirculation on the arterial input function to change it into the tissue concentration curve we directly observe is what we are interested in. This is what will vary from region to region and give us insight into what is happening at a microscopic level.
How the arterial input function is changed into the tissue concentration curve we observe, we call the residual tissue function. Although we can not directly measure it, since we can measure the tissue concentration curve of the tissue brain as well as the AIF, we can calculate the residual tissue function by a process called deconvolution.
Convolution is a mathematical operation on two functions that produces a a third function that expresses how the shape of one is modified by the other. The process can be reversed and this we call deconvolution, the details of which are entirely tangential to what we need to know. Anyway, we now have these three curves; two of them measured and one calculated. And from these we can derive all our other parameters.
Directly from the residual tissue function, we can obtain cerebral blood flow and T-Max.