**Parametric images**

There are several times when the physician is interested in the behavior of many parts of an organ. According to our former knowledge, in this case many small ROIs should be marked and numerous curves should be generated, but their display at the same time is rather chaotic.

Lots of times there is only one part of the curves which is of interest for the physician.

In an extreme case, each pixel can be regarded as a different ROI, curves are fitted for each ROI and the required parameter of the curve is determined, usually by some function fitting. Plotting the typical parameter values with color coding at the places of the pixels, one gets a parametric image showing important characteristics of details projected into the field of view.

If a characteristic cannot be calculated than its value is set to 0 or another special value.

Examples for parametric images created from sequence of images made during dynamic examinations:

PMax: maximal value of sequence of images per a pixel.

Parametric image is “cleared” many times. This clearing can be the concealment of a parameter at an area with too low activity, or the usage only of a certain part of the image sequence to calculate the parametric image.

For the top left picture (Max) the first few images were not used, because at the beginning the activity of the hearth and the large vessels is high, although the purpose of examination is the liver’s function to excrete bile. The pictures at the top right and bottom left show the parameters only at that areas where Max has an activity large enough.

**TMax**: time of reaching the maximum for each pixel (maybe the index of image
**T _{1/2}**: T half maximum (based on linear/exponential fitting). If the value of a pixel does not not decrease, then

**T**can be 0 or extremely high.

_{1/2}**MTT**: (Mean Transit Time).

#### Phase and amplitude image

In the case of ECG gated examination, each pixel value changes periodically, thus they can be written as a Fourier series expansion.

The F_{k} is the image of kth /kth element (1 < k < n) in the sequence and φ_{k} = (2k - 1)π/n. Then

is the cosine image,

is the sine image,

is the average image,

is the phase image,

is the amplitude image, and

The amplitude image illustrates the strength of pulses in each pixel, and the phase image demonstrates the time of contractions.

A positive result can be seen in figure 37. The paradox movement can be clearly seen in amplitude, phase and on the phase histogram. All of these can be compared against the qualitative analysis of the movement of the hearth.