# L

## 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## 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 non*radioactive* 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*.

*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:

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*.

*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.

## 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 ∫*Q*d*t*/*Q* as the ordinate versus ∫*Cp*d*t*/*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 *b*^{log(x)}. Ambiguity in the expression log(*x*) can be avoided if *b* is specified such as log_{10}(*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 log_{10}(*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: 10^{0.3.010} = 2 and *e*^{0.6931} = 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*.