Lag-Times into the Model

Parameter True values Dense data Sparse data Dense and sparse data Sparse data with normal-inverse Wishart prior (2 df) Sparse data with normal-inverse Wishart prior (13 df) 

Another approach to modeling lag-times is to model the kinetic system using differential equations with the lag-time manifested through a series of intermediate or transit compartments between the absorption compartment and observation compartment (Fig. 8.1). For example, the differential equations for Model A in the figure would be written as 

It should be noted that 1/lag is sometimes referred to as ktr, the transit rate constant. Such a series of differential equations does not have an all-or-none outcome and is more physiologically plausible. Using a differential equation approach to model lag-compartments the rise in concentration to the maximal concentration is more gradual. But, as the number of intermediate lag-compartments increase so does the sharpness in the rate of rise so that an infinite number of transit compartments would appear as an all-or-none function similar to the explicit function approach (Fig. 8.2). Also, as the number of intermediate compartments increase the peakedness around the maximal concentration increases. 

The mean transit time to the absorption compartment is equal to lag(n + 1). Hence, in Model B in Fig. 8.1 the system of differential equations can be reduced to 

The only difficulty in this equation is finding n . NONMEM in particular does not support the factorial function, so instead Stirling s approximation can be used 

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