Abstract

An identifying or descriptive marker that is attached to an object. An application in nuclear medicine is where this marker is a tracer having a radioisotope and the object is a blood plasma-carrying substance.

Keywords

Line Source Lookup Table List Mode Dynamic Scan Line Spread Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Label

An identifying or descriptive marker that is attached to an object. An application in nuclear medicine is where this marker is a tracer having a radioisotope and the object is a blood plasma-carrying substance.

Example: Glucose is an important substance that plasma supplies to living tissue. The carbon in its molecule is ordinarily carbon-12, a stable isotope. However, as a label the radioisotope carbon-11 can replace some of its carbon to have a tracer. This positron-emitting tracer, with a 20.38-min half-life, can then be present in small amounts along with the nonradioactive glucose. However, a more popular glucose tracer is FDG, where the more convenient 109.8-min half-life fluorine-18 is used in an almost identical type of glucose molecule.

Lateral

Situated at or extending to the side (as opposed to medial).

Least squares

A popular method involving a cost function, namely, minimizing the sum of the squares of the differences between the data points and the analytical function (often a straight line) desired as a best fit. One use in PET might be fitting a straight line to data of a Patlak plot. See also residual.

Example: The three data points of Fig. P.1 are fit to y  =  mx  +  b, using a general notation for a straight line with a slope m and intercept b. Least squares fitting may readily be accomplished, for example, by using spreadsheet software. The pairs of (x i , y i ) values to be fit are (100, 3.5), (200, 4.5), and (300, 8.5). The result of m  =  0.025 min−1 and b  =  0.5 minimizes a residual, namely, the sum of the squares of fitting errors of the 3 data points:
$${({y}_{1}-m{x}_{1}-b)}^{2}+{({y}_{2}-m{x}_{2}-b)}^{2}+{({y}_{3}-m{x}_{3}-b)}^{2}$$

It can readily be verified that this sum minimizes to a value of 1.5 when m  =  0.025 min−1 and b  =  0.5 since trials of any other values for m and/or b give a larger sum.

Ligand

An ion, molecule, or molecular group that binds to another to form a complex. When the ligand is radioactive, it can serve as a tracer and be imaged. Use of radioactive ligands is popular in dynamic scans of the brain.

Line of response

A line defined by a detector and its collimator in SPECT or by two coincident detectors in PET. Its direction through the subject and associated number of counts are used in reconstruction since it is known that the source of the activity ­concentration being detected must lie somewhere along this line. See also ­sinogram. Acronym is LOR.

Example: In PET, when coincidences occur between any pair of opposing detectors, it is known that the annihilated positron where tissue uptake occurred must be along the defined line of response. These lines are shown in Fig. L.1 for five horizontal and five vertical detector pairs. Values given in the margins of Table F.1 are pro­portional to numbers of coincidences tabulated by the scanner’s computer. These values along with the directions of the lines are then used in reconstruction.
Fig. L.1

Five horizontal and five vertical lines of response terminating at detectors in a depiction of a very simplified PET, such as would be used in acquiring the row and column averages of Table F.1

Line pair

An adjacent black and white pair of parallel lines, having equal widths, in an image within a sequence of such identical pairs of parallel lines. The white space of the pair has the same width as the black line. This uniformly alternating intensity of a test object producing this image can be used to visually assess the resolution of an imaging device. A set of such pairs is imaged as a test object and then imaged again for other line thicknesses. A minimum thickness threshold is eventually found at which the lines merge and cannot be resolved using good ­contrast. The resolution then is customarily stated as this number of line pairs per unit length that can just be resolved. In nuclear medicine scanners, a phantom ­consisting of uniform sequence of hot spots and cold spots as bars of equal width can be imaged for such a test.

Line spread function

A spatial plot showing values in an image that result from an ideal very narrow line activity concentration source. The abscissa of this plot shows relative distance from and perpendicular to the line’s location. This spreading out of the line source is due to the lack of perfect resolution. See also point spread function, partial volume effect, and spillover.

Linear parameter identification

A consequence of a mathematical model in which all parameters appear as separate data coefficients to the first power in the equations used to evaluate these from fitting the model to data. When this occurs, the parameter identification process is quite simple compared to nonlinear parameter identification. See also kinetic analysis and parameter identification.

Example: A straight line model for fitting a set of data points (x i , y i ) has a series of equations, y i  =  mx i  +  b, where it is desired to obtain m and b for the best fit. One approach is least squares fitting of this data to a straight line. The algebraic ­algorithm of this method consists of equations containing the unknown m and b along with all the known data values y i , x i . There are no appearances of m and b in complicated functions. These two parameters only appear separately themselves in combination with data, and they only appear raised to the first power. This is called linear parameter identification, and the equations are relatively easy to solve analytically for these two parameters.

Linear scan

Rectilinear scan.

List mode

A data acquisition approach in which detector counts everywhere are stored sequentially as values, locations, and times. This contrasts with the much more compact storage of time-accumulated counts and locations in defined frames having preselected times and durations. List mode storage of counts, with their locations and times, offers the versatility of being able to reconstruct images later with any desired timing of frames by a rebinning process.

Log

Logarithm.

Logan plot

Plotting integrals of tissue activity concentrations Q versus those of plasma activity concentrations Cp, but these integrals both being tissue-normalized. Using data from dynamic scans, the plot is ∫Qdt/Q as the ordinate versus ∫Cpdt/Q as the abscissa. This type of plot is found useful when at later postinjection times, an equilibrium is being reached between Cp and forms of the radioisotope in tissue that make up Q. Widely used in neurotransmitter studies, slopes of these plots play a role in the determination of binding potentials and distribution volumes. See also multiple-time graphical analysis.

Logarithm

For a specified base b, a function such that its argument results when b is raised to the power given by this function’s value. Thus, for the function, log b (x), the argument x results from the operation blog(x). Ambiguity in the expression log(x) can be avoided if b is specified such as log10(x) or log e (x). The commonly used values for b are 10 and e  =  2.71828. Usage of the latter can be indicated by the term natural logarithm, which is often abbreviated as ln and avoids ambiguity. See also exponential. Abbreviation is log.

Example: It is desired to obtain both log10(x) and log e (x) when x is 2. The results, historically found by accessing mathematical tables, are now conveniently obtained in calculators as 0.3010 and 0.6931. These answers may be checked by raising the base to these powers: 100.3.010  =  2 and e0.6931  =  2.

Long axis

Line through and in the direction of an object’s characteristic feature that is longer than any other feature. One type of long axis is a centered inferior-to-superior line through the human body. In cardiology, however, the long axis would be the line, shown in Fig. H.2, from the apex center to a chosen center of the base. An algorithm fitting a heart model to image data can deduce an exactly defined long axis. See also short axis.

Lookup table

A table in imaging used for interpreting pixels (voxels) to find the correspondence between image intensity values and displayed hues or shades of gray for the particular color scale or gray scale employed. This type of lookup table is a special case of a table being used to map one quantity against another. The table is designed to give a convenient display for interpretation by the viewer.

Example: Fig. G.1 is a simple example of a lookup table. Shades of gray corresponding to 0, 5, and 10 are indicated, and correspondences for other numbers are readily found. Having this table, an image from rounded-off numerical data in this range may readily be constructed. Conversely, any image based on this table may be converted to its underlying numerical values at its pixels (voxels).

LOR

Line of response.

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.University of TennesseeKnoxvilleUSA

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