The range of popular
curvefits include: point to point, straight line, weighted straight line, cubic spline, universal and four parameter logistic (4PL).
Response variables include:
%B/TC, %B/B0, CPM, TC/B, B0/B, 1/CPM, CPM/(standard #), %CPM/ (High Standard), CPM/(TC-CPM) and (TC-CPM)/CPM.
Standard curve axes choices are: Linear-Linear,
semi-Log, Log-Log, Logit-Log, Linear-Log and Log-Linear.
With this variety of choices, even the most demanding applications can be met with ease. A brief description
of each curvefit algorithm follows:
Point to Point:
This curve fit connects adjacent standard points with a straight line. This is a "connect
the dots" approach, and is quite commonly used in older software packages and for connecting particularly difficult data. This curve fit is best used when there are
many standard points within the curve, or when there is a very sharp change in slope. This curvefit minimizes curvature errors.
Straight line:
This
curvefit utilizes a single, straight line to fit all standard points within the curve. This fit, therefore, requires that all points on the curve be first "linearized".
This is most often accomplished by using a Logit-Log or/Bound type of transformation. By first linearizing the data, fitting errors will be minimized.
Weighted
Straight Line:
This curvefit begins as a straight line, then adds "weighting factors" as needed. These weighting factors are particularly helpful to minimize
the effect of stray points which are further from the most stable portion of the curve (mid dose). The weighting factor changes the slope of the curve to maximize the
influence on the mid-dose area of the curve.
Cubic Spline:
The Cubic Spline is actually not a single curve, but rather a series of curvilinear segments,
which are joined together at "knots". These knots are the standard points. Therefore, the overall curve must pass through the mean of each of the standard points exactly.
The cubic spline fit is very commonly used in IRMA assays, where a larger number of standard points is typical. Due to the nature of the cubic spline equation, the
standard curve must contain at least 4 points in order to fill the equation.
Universal Curve:
The Universal Curve found in the Genesys 5000 series
gamma counter is an extension of the basic cubic spline with some very unique differences. The Universal Curve utilizes the statistical uncertainties of each standard
point in the curve to allow a "range" into which to fit the curve, rather than force it through the mean.
Because of this statistical "smoothing" function, the
Universal Curve has the ability to fulfill a much wider range of data than the standard cubic spline. The Universal Curve can be specifically useful in IRMA assays
which involve very low count standard points at low dose. Since the uncertainty is greatest near the extremities of the curve and particularly the area of lowest count
rate, this region logically should impact the shape of the overall curve the least. Thus, the Universal Curve compensates for these inaccuracies by extending the range
through which the curve is fit, thereby greatly improving the overall performance of the assay as a whole.
Four Parameter Logistic:
The four parameter
logistic curve fit is based upon the "All Fit" program originally developed at NIH. It is basically an extension of the two parameter Logit-Log method. By its nature,
the 4PL, like the cubic spline must have at least four standard points in order to plot a curve. The four parameter is the most "robust" of all the curve fits, and
is the most widely suitable for a variety of applications from sigmoidal or J-shaped RIA's to high sensitivity IRMAs.
The nature of the 4PL equation requires
that the GENESYS 5000 SERIES gamma counters perform many iterations of highly complex calculations in order to achieve the best fitting curve. It is therefore common
to wait A second or two for the curve to calculate.
A brief summary of the curvefits and the best instances to use them: