Biomedical Engineering Reference
In-Depth Information
Tabl e 4 Comparison
between the values for the
fractal reaction order X
predicted from the slope
X
Dog
Predicted from
γ
Model value
γ
1
2.42 (0.10)
2.56
and obtained from the
model fit
2
3.16 (0.33)
3.35
3
2.68 (0.11)
2.74
4
2.41 (0.22)
2.61
listed in Table 4 . The values agree within error for all but Dog 1. Figure 6 panel (a)
shows the power law tail for Dog 3, and Fig. 6 panel (b) shows the same data fit by
the SSFMM model.
According to Eq. ( 44 ), the existence and onset of the power law tail correlate
with the value of K M , the power law behavior only holds for C
K M .Thevalues
estimated for K M range from 800 ng/mL to 7,000 ng/mL and are between 30 %
and 90 % higher than the maximum plasma concentrations (556.1-1,400 ng/mL).
Therefore, the power law tails are observable because the dose of mibefradil given
to the dogs in this study leads to plasma concentrations well below saturation levels.
Furthermore, Eq. ( 44 ) can be interpreted alternatively in terms of a concentration-
dependent v max of the form v ef max =
v max C X 1 . When the approximate Eq. ( 44 )was
used instead of Eq. ( 42 ), it resulted in similar parameter values as the SSFMM model
but with a poorer fit to the rise of the curve.
3.2
Paclitaxel: Temporally Induced Nonlinearity
One of the biggest challenges in clinical oncology is to estimate the optimum dose
of an anticancer drug for a given patient. Such a calculation normally combines
the physiological characteristics of the patient with the results of preclinical
investigations and clinical trials. Chemotherapeutic drugs offer a unique opportunity
for pharmacokinetic studies. In the early stages of drug development, a drug is
typically administered at high doses and through a wide range of doses in order
to establish toxicity and tolerance. For such experiments to be clinically useful,
we need to be able to take a limited set of measurements and extrapolate from
them an optimum dose for a specific patient. In the simplest case, a doubling of
the dose would result in a doubling of the systemic exposure to the drug. However,
a dose of drugs in a patient is a confined many-body system that can exhibit multiple
degrees of complexity. In many cases, the doubling of a dose produces either less
than or more than double the effect. While we already have the tools to extrapolate
in the linear case, here we strive to develop adequate tools for situations that involve
nonlinearities.
Paclitaxel is a chemotherapeutic drug derived from the European Yew tree
bark. It consists of a taxane nucleus with three rings, and it is poorly water
soluble [ 27 ]. The current formulation is a 6 mg/ml solution in a solvent consisting
 
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