definitions of T(lag)
There is the potential for ambiguity as to the meaning of the term lag phase in some of the papers I have read. There appear to be two definitions that are not numerically identical. One refers to the point at which 10% of the test meal has emptied, and the other is related to an inflection point in a graph where time is the x-axis.
Hellmig et al. (2006) wrote, “Integrated software solutions calculated half gastric emptying time (T1/2) and the lag phase (Tlag) as the point of maximum gastric emptying according to Ghoos et al. and Maes et al.14,15 The 13C breath test applied followed a standard protocol used in numerous preceding studies.”
14 Ghoos YF, Maes BD, Geypens BJ et al. Measurement of gastric emptying rate of solids by means of a carbon-labeled octanoic acid breath test. Gastroenterology 1993; 104: 1640–7.
15 Maes BD, Hiele MI, Geypens BJ et al. Pharmacological modulation of gastric emptying rate of solids as measured by the carbon labeled octanoic acid breath test: influence of erythromycin and propantheline. Gut 1994; 35: 333–7.
A paper by Siegel et al., (Gut, 1988, 29, 85-89) uses the following equation: y(t) = 1-(1-e-kt) β. Some papers use b instead of β. The function y(t) is the fraction of the meal remaining at time t. The parameter β is “the extrapolated y-intercept from the terminal [linear] portion of the curve as shown in Figure 1.” These authors wrote, “TLAG, which is numerically equal to ln(β/k) and is the time in minutes when the second derivative of the function is equal to zero (Figure 1). I played around with this equation about a year ago. IIRC TLAG was indeed the inflection point of the curve when the y-axis was presented on linear scale(Figure 1 is shown with a logarithmic scale), hence the title of my previous comment on this subject.
Chen et al. (J. Gastroenterology and Hepatology, 2003, 18, 41-46) used the same formula as Siegel and coworkers: “Scintigraphic GE data were fitted by a modified power exponential formula y(t) =1-(1-e–kt)β, presented by Siegel et al.,16 where y(t) is the fractional meal retention at time t, k is the GE rate per minute, t is the time interval in minutes, and β is the extrapolated y-intercept from the terminal portion of the curve.” They wrote, tlagS “signifies that 10% of the test meal is emptied.” The S indicates data measured by scintillography.
The next paragraph covers the 13C octanoic acid breath test. They use two formulas, the second of which is “y = m(1-e–kt)β (where y is the percentage of cumulative recovery of the dose of 13C in the breath, t is the time in hours, and m, k and β are constants, with m being the total cumulative 13C recovery when time is infinite).” They define tlagB = (-1/k)•ln(1-(0.1)1/β), where the B indicates breath test data.
16 Siegel JA, Urbain JLC, Krevsky B et al. Biphasic nature of gastric emptying. Gut 1988; 29: 85–9.
Nusynowitz and Benedetto (J. Nuclear Medicine, 1995, 35, 1023-1027) implied that the lag phase is a “period of minimal or absent emptying…”. They also wrote, “A power-exponential or modified power exponential function has been proposed and extensively employed (3,8,13), but this empirical fitting procedure is neither necessary nor desirable.” They use something called the starting index (SI) as a measure of the lag phase.
Abell et al. (Am J Gastroenterol 2008;103:753–763) wrote, “The GE curve can be analyzed in several mathematical ways to determine both the emptying rate and the lag phase. A curve fitting procedure such as a dual exponential equation (modified power exponential) has been used, namely, y = 100[1 – (1- e −kt) b] where y is the percent remaining at time t, k is an exponential emptying rate constant (fraction of amount present at time t), and b is the y-intercept of the terminal exponential with slope = −k. The lag time can be then calculated as ln(b)/k. Slope and lag time may be helpful to interpret borderline results.”
