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 [ ^99mTc] galactosylneoglycoalbumin (TcNGA). Measurements during the 30-min dynamic imaging study included the count rate over liver and heart, the quantity of TcNGA injected L 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 _j) for model parameters representing receptor concentration [R] ₀, the TcNGA-receptor forward binding rate constant k _b, extrahepatic plasma volume V _e, hepatic plasma volume V _h, and hepatic plasma flow F. Accounting for the measurement uncertainties of L ₀ and f~ did not significantly increase the standard errors for parameters [R] ₀, k _b, V _e, V _h and F. When the relative errors of L ₀ and f~ were increased to 40%, the change in Se(p _j) ranged from 10 to 100%, with parameter V _h being the most sensitive. The exception was se(k _i), the increase of which was less than 1%, Imaging studies with reduced [R] ₀, typically associated with patients with liver disease, resulted in greater increases in all estimated parameter errors except se(k _b) which had a lower increase. Lastly, the error propagation introduced by direct measurement of the liver observational coefficients σ ₁₂ and σ ₁₃ was investigated by simulating changes in the relative standard deviation in parameters σ ₁₂ and σ ₁₃ from 0 to 40%. Imaging studies from healthy subjects showed no increase in se(p _j). Local identifiability calculations using TcNGA imaging data from p- - atients with liver disease resulted in parameter estimates of lower precision; standard errors increased by a factor of three when the relative standard deviation of σ ₁₂ and σ ₁3 reached 40%.