TABLE 1

Summary of Mathematical Models

Model name*Model acronymMathematical expressionParameter
MonoexponentialMEg(t) exp[–t1]τ1
Monoexponential with added constantMECg(t) (w1 exp[–t2] + 1 – w1)w1, τ2
BiexponentialBEg(t) (w2 exp[–t3] + (1 – w2) exp[–t4])w2, τ3, τ4
Stretched exponentialSEg(t) exp[–(t5)γ1]τ5, γ1
Modified stretched exponentialMSEg(t) exp[1 – (1 + t6)γ2]τ6, γ2
Simplified stretched exponentialSSEg(t) exp[–(t7)1/2]τ7
Simplified modified stretched exponentialSMSEg(t) exp[1 – (1 + t8)1/2]τ8
  • * These models were used to analyze antimelanin 188Re-labeled antibody pharmacokinetics in each organ/tissue. Physical decay of 188Re is represented by function g(t) = exp[ –(ln(2)/τ0)t], where τ0 is half-life. All model parameters labeled τ have units of minutes, and all parameters labeled w or γ are unitless.