Local identifiability of a receptor-binding radiopharmacokinetic system having measured parameters of known uncertainty

Local identifiability was determined for a receptor-binding radiopharmacokinetic system that included measured parameters of known uncertainty. Healthy subjects and patients with severe liver disease were studied with [/sup 99m/Tc] galactosylneoglycoalbumin (TcNGA). Measurements during the 30-min dynamic imaging study included the count rate over liver and heart, the quantity of TcNGA injected L/sub 0/, and the fraction-of-injected dose per liter of sampled plasma f~. Typical relative standard deviations for these measurements were 1, 0.2, and 5 percent, respectively. A four-state nonlinear model describing the hepatic and plasma time-activity data was then used to calculate the standard error se(p/sub j/) for model parameters representing receptor concentration [R]/sub 0/, the TcNGA-receptor forward binding rate constant k/sub b/, extrahepatic plasma volume V/sub e/, hepatic plasma volume V/sub h/, and hepatic plasma flow F. Accounting for the measurement uncertainties of L/sub 0/ and f~ did not significantly increase the standard errors for parameters [R]/sub 0/, k/sub b/, V/sub e/, V/sub h/ and F. When the relative errors of L/sub 0/ and f~ were increased to 40%, the change in Se(p/sub j/) ranged from 10 to 100%, with parameter V/sub h/ being the most sensitive. The exception was se(k/sub i/), the increase of which was less than 1%, Imaging studies with reduced [R]/sub 0/, typically associated with patients with liver disease, resulted in greater increases in all estimated parameter errors except se(k/sub b/) which had a lower increase. Lastly, the error propagation introduced by direct measurement of the liver observational coefficients /spl sigma//sub 12/ and /spl sigma//sub 13/ was investigated by simulating changes in the relative standard deviation in parameters /spl sigma//sub 12/ and /spl sigma//sub 13/ from 0 to 40%. Imaging studies from healthy subjects showed no increase in se(p/sub j/). Local identifiability calculations using TcNGA imaging data from patients with liver disease resulted in parameter estimates of lower precision; standard errors increased by a factor of three when the relative standard deviation of /spl sigma//sub 12/ and /spl sigma//sub 1/3 reached 40%.<
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