DƯỢC LÍ Goodman & Gilman's The Pharmacological Basis of Therapeutics 12th, 2010

1368
Absorption compartment (p)
SECTION VII
CHEMOTHERAPY OF MICROBIAL DISEASES
Lung
compartment 2
V L
Transfer
constants
between
lungs and
serum
inhibited, or continued to grow in response to the antibiotic concentration.
For some pathogens such as fungi and bacteria, it is
assumed they are in logarithmic growth phase in the absence of
drug, exhibiting an exponential density-limited growth rate so that
they will reach a stationary phase at a maximal pathogen density,
POPMAX. E is a logistic carrying function, so that
E = 1 – (N/POPMAX) (Equation 48–6)
K a
Input
K 12 K 13
Plasma
compartment 1
V C
Transfer
constants
between
serum and
peripheral
compartment
K 21 K 31
Elimination at rate proportional
to drug concentration
Figure 48–2. Diagrammatic depiction of a multi-compartment model.
Periphery
compartment 3
V p
Elimination at rate proportional
to drug concentration
dN R
/dt = K gmax-R
• (1 − L R
) • N R
• E − K kmax-R
• M R
• NR
(Equation 48–11)
This can be made more complex and predictive adding parameters
describing the effect of inoculum, delay in microbial effect, or
splitting the drug-resistant population to smaller subpopulations based
on molecular mechanism of resistance (Bulitta et al., 2009).
where N is the pathogen burden in a particular compartment. For
replications rates of parasites and viruses, unique models may be
specified. The drug will affect the growth rate either independent of
kill or via killing the pathogen. The drug effect that is independent of
kill is through a saturable Michaelis-Menten-type kinetic event (L).
L = (X 1
/V c
) H /[(X 1
/V c
) H + IC 50H
], where H = H g-s
or H g-r
(Equation 48–7)
where H and IC 50
are as described in Equation 48–1. Microbial kill
is based on the concentrations within the compartment, and is modeled
as a sigmoid E max
effect model M:
M = K kmax
*(X 1
/V c
) H /[(X 1
/V c
) H + IC 50H
],
where H = H k-s
or H k-r
(Equation 48–8)
where K kmax
is the maximal kill rate. Because the microbial density
(N) is in fact a balance between growth (maximal growth rate =
K gmax
) and microbial kill, the change in pathogen density as a function
of time is described by Equation 48–9:
dN/dt = K gmax
• N • E − K kmax
• M • N (Equation 48–9)
The changes in drug-susceptible subpopulation of pathogen
with time and the drug-resistant subpopulation are described by:
dN S
/dt = K gmax-S
• (1 − Ls) • N S
• E − K kmax-S
• MS • N S
(Equation 48–10)
Population Pharmacokinetics and Variability in Drug
Response. The framework for the models central to
population pharmacokinetics evolved from a series of
publications by Lewis Sheiner (Sheiner et al., 1977).
What are population pharmacokinetics? Consider a
simple example. When multiple patients are treated
with the same dose of a drug, each patient will achieve
pharmacokinetic parameters that differ from others.
This is termed between-patient variability. Even when
the same dose is administered to the same patient on
two separate occasions, the patient may achieve a different
concentration-time profile of the drug between
the two occasions. This is termed inter-occasion or
within-patient variability. The variability is reflected at
the level of the compartmental pharmacokinetic parameters
such as k a
, k 12
, k 21
, SCL, V c
, and so on. Even when
a recommended dose is administered, the drug may fail
to reach a therapeutic concentration in some patients.
In other patients, the drug may reach high and toxic
concentrations. Such variability could be due to factors
that can be explained, such as genetic variability. In
addition, anthropometric measures such as weight,
height, and age also lead to variability. Furthermore,
patients may have comorbid conditions such as renal