Supplement 1 for the manuscript: “Development and application of a
mechanistic pharmacokinetic model for simvastatin and its active
metabolite simvastatin acid using an integrated population PBPK
approach”
Nikolaos Tsamandouras1, Gemma Dickinson2, Yingying Guo2, Stephen Hall2, Amin
Rostami-Hodjegan1,3, Aleksandra Galetin1, Leon Aarons1
1. Centre for Applied Pharmacokinetic Research, Manchester Pharmacy School, University
of Manchester, Manchester, UK.
2. Eli Lilly and Company, Indianapolis, IN, USA
3. Simcyp Limited, Blades Enterprise Centre, Sheffield, UK.
Contents
1. Model structure, assumptions and differential equations .................................................................... 2
2. Figures ................................................................................................................................................ 9
3. Tables ................................................................................................................................................ 11
4. References ......................................................................................................................................... 12
1
1. Model structure, assumptions and differential equations
The model includes small intestinal wall, liver vascular, liver tissue, systemic blood, muscle and rest
of the body (ROB) compartments for both SV and SVA. In order to account for the dissolution and
absorption processes of the orally administered SV, two stomach content and two small intestinal
lumen compartments referring to the solid and dissolved drug have been additionally incorporated for
SV. The dissolution process was modelled according to Hintz and Johnson [1] as exemplified in
Eqs.S1.1-S1.4; solid SV was treated as a powder of monodispersed spherical particles the radius of
which is constant over time. It has been assumed that absorption of SV occurs only in the small
intestine (no colonic absorption) and the small intestinal lumen is treated as a cylinder. SV and SVA
are subject to inter-conversion and this process is modelled with the following assumptions: i) SV SVA inter-conversion in stomach and small intestinal lumen contents is negligible [2]. ii) SV to SVA
hydrolysis takes place in the model compartments representing blood and tissues mediated by plasma
paraoxonases and tissue carboxylesterases respectively in conjunction with chemical (non-enzymatic)
hydrolysis [3]. However, the SV to SVA hydrolysis specifically in the muscle is assumed to be
mediated only chemically without an enzymatic contribution. This is based on the fact that human
carboxylesterases 1 (hCE1) and 2 (hCE2) are not significantly expressed in the muscle, as supported
by a Northern blot analysis of adult tissue [4]. iii) SVA to SV back-transformation takes place in the
liver tissue compartment mainly via an acyl-glucuronide intermediate that undergoes spontaneous
cyclisation to SV at physiological pH [5, 6]. The current model neglects any possible backtransformation in the small intestinal wall due to the absence of any related in vitro information. Both
SV and SVA undergo oxidative metabolism in the small intestinal wall and the liver tissue
compartments, assumed to be mediated exclusively by CYP3A [7, 8]. SVA glucuronidation not
accounted within lactonisation is assumed to be negligible [6]. It is also assumed that renal
elimination of SV and SVA is negligible [9] and that neither SV or SVA are subject to enterohepatic
recirculation [10]. The small intestinal wall is treated as a compartment where no binding (fraction
unbound is 1) [11] or partition (Eq.S1.5) [12] occurs. Due to the complex nature of SV metabolism
(e.g., both chemical and enzymatic hydrolysis), it has been assumed for simplicity that intestinal
2
metabolism is equally possible for both the drug entering the small intestinal wall from the small
intestinal lumen or the systemic compartment.
The structure of the developed model is such that it retains a physiological-mechanistic nature only in
the parts which are relevant to the desired modelling purpose. As specific clinical interest is in the
prediction of concentrations only in plasma, liver (efficacy) and muscle (toxicity) the developed
model is much simpler compared to a typical whole body physiologically based pharmacokinetic
(PBPK) model. In this way any unnecessary additional computational complexity of the system is
avoided which is particularly important as the model will be subject of parameter estimation under a
population pharmacokinetic modelling approach. In particular, the model rather than describing
SV/SVA disposition in the several tissues which are not of clinical interest, includes a rest of body
(ROB) compartment assuming no significant loss of information. It should be clearly highlighted that
this compartment is not the outcome of a “proper lumping” procedure [13]. Although, we
considered starting from a whole-body PBPK model and subsequently reducing it in accordance to
“proper lumping” principles [13], this was not performed due to the increased complexity
added by the SV to SVA conversion inside several tissues and the limited in vitro information for the
quantification of this process in each of them. For example, carboxylesterases (hCE1 or hCE2) are
significantly expressed in several other tissues apart from the liver and small intestinal wall (e.g.
kidney, lungs, heart) [4, 14]. However, although SV to SVA conversion can be assumed to take place
in all these tissues, there is no in vitro information with regard to its magnitude in order to describe
this process in the different model compartments. Therefore, as the available information was not
enough to build a whole-body PBPK model and to subsequently reduce it, we included an empirical
rest of body compartment where SV to SVA conversion is allowed, the magnitude of which is a
parameter upon estimation. As this compartment is not the outcome of a “proper lumping” procedure
it should be interpreted more as an empirical peripheral eliminating compartment rather than an actual
physiological space consisting of specific tissues. However, this rest of body compartment is
associated with a known volume (total body volume minus the sum of volumes related to tissues
explicitly described in the model) and a known blood flow (cardiac output minus the sum of
3
blood flows related to tissues explicitly described in the model). Although a tissue partition
coefficient has been assigned to this rest of body compartment, it is directly estimated from the data
and not from in silico mechanistic equations [15]. Hence, this estimated “rest of body” partition
coefficient is not of physiological interpretation per se as it refers to an empirical peripheral
compartment rather than to an actual tissue. However, the product of the estimated partition
coefficient and the known volume of the “rest of body” compartment will be indicative of the
extent of the compound’s distribution in this empirical peripheral space.
On the contrary to the majority of the tissues where the prediction of concentration profiles is outside
the scope of this model, the SV/SVA distribution in the liver tissue should be very accurately
modelled. As SVA is subject of active uptake into the hepatocytes, the liver has been separated into a
liver vascular and a liver tissue compartment allowing both passive diffusion and active uptake
processes to be described. On the other hand the lipophilic SV is subject of perfusion- and not
permeability-limited distribution into the liver. However the two-compartment liver is maintained for
SV as well to allow differentiation of the SV to SVA hydrolysis rates in liver vasculature (informed
by experiments in plasma) and in liver tissue (informed by experiments in liver S9 fraction). In order
to satisfy perfusion-limited assumptions the permeability surface product for unbound SV influx and
efflux across the hepatic basolateral membrane has been assumed to be 10,000 times greater the
hepatic blood flow [12].
Finally, of specific importance is the treatment of splachnic tissues in the model structure and the
related assumptions. The small intestinal wall has been preserved in the model (Manuscript Figure 1)
due to its crucial importance in first pass CYP3A and hydrolysis metabolism. The rest of the splachnic
tissues (spleen, large intestine, pancreas and stomach) should not be informally lumped in the ROB
compartment as their physiological topology dictates that their efferent blood flows should drain in to
the liver vascular compartment. This is of particular importance for a highly extracted compound as
SV, because the modelling output is sensitive to whether the liver receives the correct total blood flow
(sum of hepatic artery, small intestinal wall and other splachnic tissue blood flows) or not. Therefore,
4
the model presented in Supplementary Figure S1.1 was initially developed, including a “rest of
splachnic tissues” compartment where the spleen, large intestine, pancreas and stomach tissues have
been lumped. SV/SVA inter-conversion in this compartment was for simplicity assumed to be
negligible. This compartment was the result of a “proper lumping” procedure where the tissues are
originally in parallel among each other and in series connected to the liver. The lumping procedure
was performed as in [13] and the volumes and blood flows of the initial non-lumped tissues were
summed to derive the corresponding volume and blood flow of the lumped “rest of splachnic”
compartment. The tissue partition coefficient assigned to this “rest of splachnic” compartment was
predicted in silico [15] for both SV and SVA using the tissue composition parameters of the spleen.
Simulations with this alternative model indicated that the exclusion of the actual “rest of splachnic”
compartment from the model (as in the final model presented in Manuscript Figure 1) did not affect
model predictions on all the compartments of interest (Supplementary Figure S1.2) as long as the liver
receives the correct total blood flow (notice in Manuscript Figure 1 that the “rest of splachnic” blood
flow is retained). The same outcome was observed when the in silico predicted “rest of splachnic”
compartment partition coefficients were varied within a 3-fold error range for both SV and SVA. This
indicates that even an inaccurate prediction of the partition coefficients would not have affected this
observation. Therefore the actual “rest of splachnic” compartment was omitted in the final model
(Manuscript Figure 1) in order to decrease the computational complexity of the differential equations
system. However the blood flow efferent from these tissues (Qspl) is retained in the model to assure
that the liver receives the correct total blood flow. It is acknowledged that the exclusion of the “rest of
splachnic” compartment from the model is a modelling assumption and an oversimplification of
reality. However, this trade-off in order to gain computational efficiency is justifiable given that the
determination of SV/SVA levels in these splachnic tissues is not part of the objectives of this work
and this exclusion does not affect the model predictions in the clinically relevant plasma, liver and
muscle tissues.
The developed mechanistic model can be described with a system of 16 ordinary differential
equations. These mass balance equations for the joint SV-SVA system (Manuscript Figure 1) are
5
described below, where A(n) is the amount in the nth compartment. Abbreviations are defined in
Supplementary Table S1.1.
Eq.S1.1. Compartment 1: Stomach (solid SV)
𝑑𝐴(1)
3∙𝐷
𝐴(2)
= −𝑘𝑔𝑒 ∙ 𝐴(1) −
∙ (𝑆𝑜𝑙𝑠𝑡𝑜𝑚 −
) ∙ 𝐴(1)
𝑑𝑡
𝜌∙𝑟∙ℎ
𝑉𝑠𝑡𝑜𝑚
Eq.S1.2. Compartment 2: Stomach (dissolved SV)
𝑑𝐴(2)
3∙𝐷
𝐴(2)
= −𝑘𝑔𝑒 ∙ 𝐴(2) +
∙ (𝑆𝑜𝑙𝑠𝑡𝑜𝑚 −
) ∙ 𝐴(1)
𝑑𝑡
𝜌∙𝑟∙ℎ
𝑉𝑠𝑡𝑜𝑚
Eq.S1.3. Compartment 3: Small intestinal lumen (solid SV)
𝑑𝐴(3)
3∙𝐷
𝐴(4)
= 𝑘𝑔𝑒 ∙ 𝐴(1) − 𝑘𝑠𝑖𝑡 ∙ 𝐴(3) −
∙ (𝑆𝑜𝑙𝑠𝑖𝑙 −
) ∙ 𝐴(3)
𝑑𝑡
𝜌∙𝑟∙ℎ
𝑉𝑠𝑖𝑙
Eq.S1.4. Compartment 4: Small intestinal lumen (dissolved SV)
𝑑𝐴(4)
3∙𝐷
𝐴(4)
= 𝑘𝑔𝑒 ∙ 𝐴(2) − 𝑘𝑎 ∙ 𝐴(4) − 𝑘𝑠𝑖𝑡 ∙ 𝐴(4) +
∙ (𝑆𝑜𝑙𝑠𝑖𝑙 −
) ∙ 𝐴(3)
𝑑𝑡
𝜌∙𝑟∙ℎ
𝑉𝑠𝑖𝑙
Eq.S1.5. Compartment 5: Small intestinal wall (SV)
𝑑𝐴(5)
𝐴(8)
𝐴(5)
𝐴(5)
= 𝑘𝑎 ∙ 𝐴(4) + 𝑄𝑠𝑖𝑤 ∙
− 𝑄𝑠𝑖𝑤 ∙
− 𝐶𝐿𝑖𝑛𝑡𝐶𝑌𝑃3𝐴,𝑠𝑖𝑤 ∙ 𝑓𝑢𝑠𝑖𝑤 ∙
𝑑𝑡
𝑉𝑏𝑙
𝑉𝑠𝑖𝑤
𝑉𝑠𝑖𝑤
−𝐶𝐿𝑖𝑛𝑡ℎ𝑦𝑑𝑟,𝑠𝑖𝑤 ∙ 𝑓𝑢𝑠𝑖𝑤 ∙
𝐴(5)
𝑉𝑠𝑖𝑤
Eq.S1.6. Compartment 6: Liver vascular (SV)
𝑑𝐴(6)
𝐴(5)
𝐴(7)
𝐴(8)
= 𝑄𝑠𝑖𝑤 ∙
+ 𝑃𝑆𝑢𝑒𝑓𝑓 ∙ 𝑓𝑢𝑙𝑡 ∙
+ (𝑄ℎ𝑎 + 𝑄𝑠𝑝𝑙 ) ∙
𝑑𝑡
𝑉𝑠𝑖𝑤
𝑉𝑙𝑡
𝑉𝑏𝑙
−(𝑄ℎ𝑎 + 𝑄𝑠𝑝𝑙 + 𝑄𝑠𝑖𝑤 ) ∙
𝐴(6)
𝐴(6)
𝐴(6)
− 𝑃𝑆𝑢𝑖𝑛𝑓 ∙ 𝑓𝑢𝑙𝑣 ∙
− 𝐶𝐿𝑖𝑛𝑡ℎ𝑦𝑑𝑟,𝑙𝑣 ∙ 𝑓𝑢𝑙𝑣 ∙
𝑉𝑙𝑣
𝑉𝑙𝑣
𝑉𝑙𝑣
Eq.S1.7. Compartment 7: Liver tissue (SV)
6
𝑑𝐴(7)
𝐴(6)
𝐴(13)
𝐴(7)
= 𝑃𝑆𝑢𝑖𝑛𝑓 ∙ 𝑓𝑢𝑙𝑣 ∙
+ 𝐶𝐿𝑖𝑛𝑡𝑙𝑎𝑐𝑡 ∙ 𝑓𝑢′ 𝑙𝑡 ∙
− 𝑃𝑆𝑢𝑒𝑓𝑓 ∙ 𝑓𝑢𝑙𝑡 ∙
𝑑𝑡
𝑉𝑙𝑣
𝑉𝑙𝑡
𝑉𝑙𝑡
−𝐶𝐿𝑖𝑛𝑡𝐶𝑌𝑃3𝐴,𝑙𝑡 ∙ 𝑓𝑢𝑙𝑡 ∙
𝐴(7)
𝐴(7)
− 𝐶𝐿𝑖𝑛𝑡ℎ𝑦𝑑𝑟,𝑙𝑡 ∙ 𝑓𝑢𝑙𝑡 ∙
𝑉𝑙𝑡
𝑉𝑙𝑡
Eq.S1.8. Compartment 8: Systemic blood (SV)
𝑑𝐴(8)
𝐴(6)
𝐴(10)
𝐴(9)
= (𝑄ℎ𝑎 + 𝑄𝑠𝑝𝑙 + 𝑄𝑠𝑖𝑤 ) ∙
+ 𝑄𝑟𝑜𝑏 ∙
+ 𝑄𝑚 ∙
𝑑𝑡
𝑉𝑙𝑣
𝑉𝑟𝑜𝑏 ∙ 𝐾𝑃𝑇:𝐵,𝑟𝑜𝑏
𝑉𝑚 ∙ 𝐾𝑃𝑇:𝐵,𝑚
−𝑄𝑠𝑖𝑤 ∙
𝐴(8)
𝐴(8)
𝐴(8)
𝐴(8)
− 𝑄𝑟𝑜𝑏 ∙
− 𝑄𝑚 ∙
− (𝑄ℎ𝑎 + 𝑄𝑠𝑝𝑙 ) ∙
𝑉𝑏𝑙
𝑉𝑏𝑙
𝑉𝑏𝑙
𝑉𝑏𝑙
−𝐶𝐿𝑖𝑛𝑡ℎ𝑦𝑑𝑟,𝑏𝑙 ∙ 𝑓𝑢𝑏𝑙 ∙
𝐴(8)
𝑉𝑏𝑙
Eq.S1.9. Compartment 9: Muscle (SV)
𝑑𝐴(9)
𝐴(8)
𝐴(9)
𝐴(9)
= 𝑄𝑚 ∙
− 𝑄𝑚 ∙
− 𝐶𝐿𝑖𝑛𝑡ℎ𝑦𝑑𝑟,𝑚 ∙ 𝑓𝑢𝑚 ∙
𝑑𝑡
𝑉𝑏𝑙
𝑉𝑚 ∙ 𝐾𝑃𝑇:𝐵,𝑚
𝑉𝑚
Eq.S1.10. Compartment 10: Rest of body (SV)
𝑑𝐴(10)
𝐴(8)
𝐴(10)
𝐴(10)
= 𝑄𝑟𝑜𝑏 ∙
− 𝑄𝑟𝑜𝑏 ∙
− 𝐶𝐿𝑖𝑛𝑡ℎ𝑦𝑑𝑟,𝑟𝑜𝑏 ∙ 𝑓𝑢𝑟𝑜𝑏 ∙
𝑑𝑡
𝑉𝑏𝑙
𝑉𝑟𝑜𝑏 ∙ 𝐾𝑃𝑇:𝐵,𝑟𝑜𝑏
𝑉𝑟𝑜𝑏
Eq.S1.11. Compartment 11: Small intestinal wall (SVA)
𝑑𝐴(11)
𝐴(14)
𝐴(11)
𝐴(11)
= 𝑄𝑠𝑖𝑤 ∙
− 𝑄𝑠𝑖𝑤 ∙
− 𝐶𝐿𝑖𝑛𝑡 ′ 𝐶𝑌𝑃3𝐴,𝑠𝑖𝑤 ∙ 𝑓𝑢′ 𝑠𝑖𝑤 ∙
𝑑𝑡
𝑉𝑏𝑙
𝑉𝑠𝑖𝑤
𝑉𝑠𝑖𝑤
+ 𝐶𝐿𝑖𝑛𝑡ℎ𝑦𝑑𝑟,𝑠𝑖𝑤 ∙ 𝑓𝑢𝑠𝑖𝑤 ∙
𝐴(5)
𝑉𝑠𝑖𝑤
Eq.S1.12. Compartment 12: Liver vascular (SVA)
𝑑𝐴(12)
𝐴(11)
𝐴(13)
𝐴(14)
= 𝑄𝑠𝑖𝑤 ∙
+ 𝑃𝑆𝑢𝑑𝑖𝑓 ∙ 𝑓𝑢′ 𝑙𝑡 ∙
+ (𝑄ℎ𝑎 + 𝑄𝑠𝑝𝑙 ) ∙
𝑑𝑡
𝑉𝑠𝑖𝑤
𝑉𝑙𝑡
𝑉𝑏𝑙
7
−(𝑄ℎ𝑎 + 𝑄𝑠𝑝𝑙 + 𝑄𝑠𝑖𝑤 ) ∙
−𝐶𝐿𝑢𝑎𝑐𝑡 ∙ 𝑓𝑢′ 𝑙𝑣 ∙
𝐴(12)
𝐴(12)
− 𝑃𝑆𝑢𝑑𝑖𝑓 ∙ 𝑓𝑢′ 𝑙𝑣 ∙
𝑉𝑙𝑣
𝑉𝑙𝑣
𝐴(12)
𝐴(6)
+ 𝐶𝐿𝑖𝑛𝑡ℎ𝑦𝑑𝑟,𝑙𝑣 ∙ 𝑓𝑢𝑙𝑣 ∙
𝑉𝑙𝑣
𝑉𝑙𝑣
Eq.S1.13. Compartment 13: Liver tissue (SVA)
𝑑𝐴(13)
𝐴(12)
𝐴(12)
𝐴(13)
= 𝑃𝑆𝑢𝑑𝑖𝑓 ∙ 𝑓𝑢′ 𝑙𝑣 ∙
+ 𝐶𝐿𝑢𝑎𝑐𝑡 ∙ 𝑓𝑢′ 𝑙𝑣 ∙
− 𝐶𝐿𝑖𝑛𝑡𝑙𝑎𝑐𝑡 ∙ 𝑓𝑢′ 𝑙𝑡 ∙
𝑑𝑡
𝑉𝑙𝑣
𝑉𝑙𝑣
𝑉𝑙𝑡
−𝑃𝑆𝑢𝑑𝑖𝑓 ∙ 𝑓𝑢′ 𝑙𝑡 ∙
𝐴(13)
𝐴(13)
𝐴(7)
− 𝐶𝐿𝑖𝑛𝑡′𝐶𝑌𝑃3𝐴,𝑙𝑡 ∙ 𝑓𝑢′𝑙𝑡 ∙
+ 𝐶𝐿𝑖𝑛𝑡ℎ𝑦𝑑𝑟,𝑙𝑡 ∙ 𝑓𝑢𝑙𝑡 ∙
𝑉𝑙𝑡
𝑉𝑙𝑡
𝑉𝑙𝑡
Eq.S1.14. Compartment 14: Systemic blood (SVA)
𝑑𝐴(14)
𝐴(12)
𝐴(16)
𝐴(15)
= (𝑄ℎ𝑎 + 𝑄𝑠𝑝𝑙 + 𝑄𝑠𝑖𝑤 ) ∙
+ 𝑄𝑟𝑜𝑏 ∙
+
𝑄
∙
𝑚
𝑑𝑡
𝑉𝑙𝑣
𝑉𝑟𝑜𝑏 ∙ 𝐾𝑃′ 𝑇:𝐵,𝑟𝑜𝑏
𝑉𝑚 ∙ 𝐾𝑃′ 𝑇:𝐵,𝑚
−𝑄𝑠𝑖𝑤 ∙
𝐴(14)
𝐴(14)
𝐴(14)
𝐴(14)
− 𝑄𝑟𝑜𝑏 ∙
− 𝑄𝑚 ∙
− (𝑄ℎ𝑎 + 𝑄𝑠𝑝𝑙 ) ∙
𝑉𝑏𝑙
𝑉𝑏𝑙
𝑉𝑏𝑙
𝑉𝑏𝑙
+𝐶𝐿𝑖𝑛𝑡ℎ𝑦𝑑𝑟,𝑏𝑙 ∙ 𝑓𝑢𝑏𝑙 ∙
𝐴(8)
𝑉𝑏𝑙
Eq.S1.15. Compartment 15: Muscle (SVA)
𝑑𝐴(15)
𝐴(14)
𝐴(15)
𝐴(9)
= 𝑄𝑚 ∙
− 𝑄𝑚 ∙
+ 𝐶𝐿𝑖𝑛𝑡ℎ𝑦𝑑𝑟,𝑚 ∙ 𝑓𝑢𝑚 ∙
𝑑𝑡
𝑉𝑏𝑙
𝑉𝑚 ∙ 𝐾𝑃′ 𝑇:𝐵,𝑚
𝑉𝑚
Eq.S1.16. Compartment 16: Rest of body (SVA)
𝑑𝐴(16)
𝐴(14)
𝐴(16)
𝐴(10)
= 𝑄𝑟𝑜𝑏 ∙
− 𝑄𝑟𝑜𝑏 ∙
+ 𝐶𝐿𝑖𝑛𝑡ℎ𝑦𝑑𝑟,𝑟𝑜𝑏 ∙ 𝑓𝑢𝑟𝑜𝑏 ∙
𝑑𝑡
𝑉𝑏𝑙
𝑉𝑟𝑜𝑏 ∙ 𝐾𝑃′ 𝑇:𝐵,𝑟𝑜𝑏
𝑉𝑟𝑜𝑏
8
2. Figures
Figure S1.1: Alternative SV/SVA mechanistic model that includes an additional lumped “Rest of Splachnic” compartment. Abbreviations are defined in Table S1.1.
9
(a)
(b)
Figure S1.2: Model simulated concentration profiles of SV (a) and SVA (b) in plasma, liver and muscle tissues. Simulations with the full model (Supplementary
Figure S1.1) that includes the “Rest of Splachnic” compartment are represented by the thick red lines. Simulations with the reduced final model (Manuscript
Figure 1) where the “Rest of Splachnic” compartment has been omitted are represented by the blue dashed lines. Simulated profiles are practically identical.
10
3. Tables
Table S1.1: Nomenclature in model schematic representation and mass balance equations
General
CLintCYP3A,i
Intrinsic clearance for CYP3A mediated oxidative metabolism in compartment (i)
CLinthydr,i
Intrinsic clearance for hydrolysis in compartment (i)
CLintlact
Intrinsic clearance for lactonisation in liver tissue
CLuact
Active uptake clearance for unbound SVA across hepatic basolateral membrane
D
Diffusion coefficient
fui
Fraction unbound in compartment (i)
h
Diffusion layer thickness
ka
Absorption rate constant from the intestinal lumen into the epithelium
kdsil
Dissolution rate constant in small intestinal lumen
kdstom
Dissolution rate constant in stomach contents
kge
Gastric emptying rate constant
KPT:B,i
Tissue to blood partition coefficient in compartment (i)
ksit
Small intestinal transit rate constant
PSudif
Passive diffusion clearance across the basolateral membrane for unbound SVA
PSueff
Permeability surface product for unbound SV efflux across basolateral membrane
PSuinf
Permeability surface product for unbound SV influx across basolateral membrane
Qha
Hepatic artery blood flow
Qlv
Blood flow that exits the liver vascular compartment (= Qsiw+ Qha+ Qspl )
Qm
Muscle blood flow
Qrob
“Rest of the body” compartment blood flow
Qsiw
Small intestinal wall blood flow
Qspl
Splachnic organs blood flow excluding small intestinal wall
r
Particle radius
SI lumen
Small intestinal lumen compartment
SI wall
Small intestinal wall compartment
Soli
Solubility in compartment (i)
Stom
Stomach contents compartment
Vi
Volume of compartment (i)
ρ
Particle density
Subscripts (i)
bl
Systemic blood compartment
lt
Liver tissue compartment
lv
Liver vascular compartment
m
Muscle compartment
rob
“Rest of body” compartment
sil
Small intestinal lumen compartment
siw
Small intestinal wall compartment
stom
Stomach content compartment
When any of the above abbreviations is relevant to both SV and SVA, the abbreviation referring to SVA is
followed by a prime.
11
4. References
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Hintz RJ, Johnson KC. The effect of particle size distribution on dissolution rate and oral
absorption. Int J Pharm. 1989;51(1):9-17.
Kaufman MJ. Rate and equilibrium constants for acid-catalyzed lactone hydrolysis of HMGCoA reductase inhibitors. Int J Pharm. 1990;66(1-3):97-106.
Prueksaritanont T, Qiu Y, Mu L, Michel K, Brunner J, Richards KM, et al. Interconversion
pharmacokinetics of simvastatin and its hydroxy acid in dogs: Effects of gemfibrozil. Pharm
Res. 2005;22(7):1101-1109.
Satoh T, Taylor P, Bosron WF, Sanghani SP, Hosokawa M, Du BNL. Current progress on
esterases: From molecular structure to function. Drug Metab Dispos. 2002;30(5):488-493.
Prueksaritanont T, Subramanian R, Fang X, Ma B, Qiu Y, Lin JH, et al. Glucuronidation of
statins in animals and humans: A novel mechanism of statin lactonization. Drug Metab
Dispos. 2002;30(5):505-512.
Prueksaritanont T, Tang C, Qiu Y, Mu L, Subramanian R, Lin JH. Effects of fibrates on
metabolism of statins in human hepatocytes. Drug Metab Dispos. 2002;30(11):1280-1287.
Prueksaritanont T, Gorham LM, Ma B, Liu L, Yu X, Zhao JJ, et al. In vitro metabolism of
simvastatin in humans [SBT]identification of metabolizing enzymes and effect of the drug on
hepatic P450s. Drug Metab Dispos. 1997;25(10):1191-1199.
Prueksaritanont T, Ma B, Yu N. The human hepatic metabolism of simvastatin hydroxy acid is
mediated primarily by CYP3A, and not CYP2D6. Br J Clin Pharmacol. 2003;56(1):120-124.
Mauro VF. Clinical pharmacokinetics and practical applications of simvastatin. Clin
Pharmacokinet. 1993;24(3):195-202.
Cheng H, Schwartz MS, Vickers S, Gilbert JD, Amin RD, Depuy B, et al. Metabolic disposition
of simvastatin in patients with T-tube drainage. Drug Metab Dispos. 1994;22(1):139-142.
Yang J, Jamei M, Yeo KR, Tucker GT, Rostami-Hodjegan A. Prediction of intestinal first-pass
drug metabolism. Curr Drug Metab. 2007;8(7):676-684.
Gertz M, Houston JB, Galetin A. Physiologically based pharmacokinetic modeling of intestinal
first-pass metabolism of CYP3A substrates with high intestinal extraction. Drug Metab
Dispos. 2011;39(9):1633-1642.
Nestorov IA, Aarons LJ, Arundel PA, Rowland M. Lumping of whole-body physiologically
based pharmacokinetic models. J Pharmacokinet Biopharm. 1998;26(1):21-46.
Hosokawa M. Structure and catalytic properties of carboxylesterase isozymes involved in
metabolic activation of prodrugs. Molecules. 2008;13(2):412-431.
Rodgers T, Rowland M. Physiologically based pharmacokinetic modelling 2: Predicting the
tissue distribution of acids, very weak bases, neutrals and zwitterions. J Pharm Sci.
2006;95(6):1238-1257.
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