transit compartment question

Hi all, I was implementing transit compartment for a absorption model for the first time. I could not understand why the relationship between mean transit time and transit rate is MTT=(n+1)/Ktr. Could someone help me understand? Thank you.

Dear Ethan, The analytical solution for the transit model is derived for the chain of n+1 transit compartments. You will notice that the part of analytical solution is factorial function (n!). If the chain had a length of n transit compartments, one would need to use factorial for (n-1). This would require bounding of initial conditions for n (lower boundary at 1). Whichever approach you use, the outcome shall be the same. Clearly, our preferred approach is the one we published. Hope this helps, Rada

Dear Ethan, Perhaps this article is of some help: J Pharm Sci. 1998 Jun;87(6):732-7. Transit compartments versus gamma distribution function to model signal transduction processes in pharmacodynamics. Sun YN, Jusko WJ. Department of Pharmaceutics, School of Pharmacy, State University of New York at Buffalo, Buffalo, New York 14260, USA. Abstract Delayed effects for pharmacodynamic responses can be observed for many signal transduction processes. Three approaches are summarized in this report to describe such effects caused by cascading steps: stochastic process model, gamma distribution function, and transit compartment model. The gamma distribution function, a probability density function of the waiting time for the final step in a stochastic process model, is a function of time with two variables: number of compartments N, and the expected number of compartments occurring per unit time k. The parameter k is equal to 1/tau, where tau is the mean transit time in the stochastic process model. Effects of N and k on the gamma distribution function were examined. The transit compartment model can link the pharmacokinetic profile of the tested compound, receptor occupancy, and cascade steps for the signal transduction process. Time delays are described by numbers of steps, the mean transit time tau, and the amplification or suppression of the process as characterized by a power coefficient gamma. The effects of N, tau, and gamma on signal transduction profiles are shown. The gamma distribution function can be utilized to estimate N and k values when the final response profile is available, but it is less flexible than transit compartments when dose-response relationships, receptor dynamics, and efficiency of the transduction process are of concern. The transit compartment model is useful in pharmacokinetic/pharmacodynamic modeling to describe precursor/product relationships in signal transduction process. PMID: 9607951 [PubMed - indexed for MEDLINE]

Dear Ethan, My few cents... Transit compartment model is generally used to account for delay in the effect (e.g Cell growth; Friberg et al JPCT 2002), (delay in placebo effect ; Mould et al CPT 2007) or (to account for delay in absorption; Savic et al, 2007). It is numerically stable to define the transfer rate constants (Ktr) as mean transit time (MTT) which are larger numbers than rate constant and then let the rate constant be n/MTT. MTT = THETA (1)*EXP(ETA(1)) N= number of transit compartments KTR = N/MTT Best Regards, Venkatesh Pilla Reddy, Phd Student, University of Groningen --- On Tue, 8/3/11, Ethan Wu <[email protected]> wrote:

Dear Ethan, I perhaps shall add that time for molecule to transition between two neighboring compartments is equal to 1/ktr, therefore total time for molecule to reach the absorption site will be sum of times for n+1 compartments, e.g. (n+1/ktr). Rada