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. 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 back-transformation 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 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 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, 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 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)dt=-kge∙A1-3∙Dρ∙r∙h∙Solstom-A2Vstom∙A1
Eq.S1.2. Compartment 2: Stomach (dissolved SV)
dA(2)dt=-kge∙A(2)+ 3∙Dρ∙r∙h∙Solstom-A2Vstom∙A(1)
Eq.S1.3. Compartment 3: Small intestinal lumen (solid SV)
dA(3)dt=kge∙A(1)-ksit∙A(3)-3∙Dρ∙r∙h∙Solsil-A(4)Vsil∙A(3)
Eq.S1.4. Compartment 4: Small intestinal lumen (dissolved SV)
dA(4)dt=kge∙A(2)-ka∙A(4)-ksit∙A(4)+3∙Dρ∙r∙h∙Solsil-A(4)Vsil∙A(3)
Eq.S1.5. Compartment 5: Small intestinal wall (SV)
dA5dt=ka∙A4+Qsiw∙A8Vbl-Qsiw∙A5Vsiw-CLintCYP3A,siw∙fusiw∙A5Vsiw
-CLinthydr,siw∙fusiw∙A(5)Vsiw
Eq.S1.6. Compartment 6: Liver vascular (SV)
dA6dt=Qsiw∙A5Vsiw+PSueff∙fult∙A7Vlt+Qha+Qspl∙A8Vbl
-Qha+Qspl+Qsiw ∙A(6)Vlv-PSuinf∙fulv∙A(6)Vlv-CLinthydr,lv∙fulv∙A(6)Vlv
Eq.S1.7. Compartment 7: Liver tissue (SV)
dA7dt=PSuinf∙fulv∙A6Vlv+CLintlact∙fu'lt∙A13Vlt-PSueff∙fult∙A7Vlt
-CLintCYP3A,lt ∙fult ∙A(7)Vlt-CLinthydr,lt∙fult∙A(7)Vlt
Eq.S1.8. Compartment 8: Systemic blood (SV)
dA8dt=Qha+Qspl+Qsiw∙A6Vlv+Qrob∙A10Vrob∙KPT:B,rob+Qm∙A9Vm∙KPT:B,m
-Qsiw∙A8Vbl-Qrob∙A8Vbl-Qm∙A8Vbl-Qha+Qspl∙A8Vbl
-CLinthydr,bl∙fubl∙A(8)Vbl
Eq.S1.9. Compartment 9: Muscle (SV)
dA9dt=Qm∙A8Vbl-Qm∙A9Vm∙KPT:B,m-CLinthydr,m∙fum∙A(9)Vm
Eq.S1.10. Compartment 10: Rest of body (SV)
dA10dt=Qrob∙A8Vbl-Qrob∙A10Vrob∙KPT:B,rob-CLinthydr,rob∙furob∙A(10)Vrob
Eq.S1.11. Compartment 11: Small intestinal wall (SVA)
dA11dt=Qsiw∙A14Vbl-Qsiw∙A11Vsiw-CLint'CYP3A,siw∙fu'siw∙A11Vsiw
+ CLinthydr,siw∙fusiw∙A(5)Vsiw
Eq.S1.12. Compartment 12: Liver vascular (SVA)
dA12dt=Qsiw∙A11Vsiw+PSudif∙fu'lt∙A13Vlt+Qha+Qspl∙A14Vbl
-Qha+Qspl+Qsiw ∙A12Vlv-PSudif∙fu'lv∙A12Vlv
-CLuact∙fu'lv ∙A12Vlv+CLinthydr,lv∙fulv∙A6Vlv
Eq.S1.13. Compartment 13: Liver tissue (SVA)
dA13dt=PSudif∙fu'lv∙A12Vlv+CLuact∙fu'lv∙A12Vlv-CLintlact∙fu'lt∙A13Vlt
-PSudif ∙fu'lt∙A13Vlt-CLint'CYP3A,lt∙fu'lt∙A(13)Vlt+CLinthydr,lt∙fult∙A(7)Vlt
Eq.S1.14. Compartment 14: Systemic blood (SVA)
dA14dt=Qha+Qspl+Qsiw∙A12Vlv+Qrob∙A16Vrob∙KP'T:B,rob+Qm∙A15Vm∙KP'T:B,m
-Qsiw∙A14Vbl-Qrob∙A14Vbl-Qm∙A14Vbl-Qha+Qspl∙A14Vbl
+CLinthydr,bl ∙fubl∙A(8)Vbl
Eq.S1.15. Compartment 15: Muscle (SVA)
dA15dt=Qm∙A14Vbl-Qm∙A15Vm∙KP'T:B,m+CLinthydr,m∙fum∙A(9)Vm
Eq.S1.16. Compartment 16: Rest of body (SVA)
dA16dt=Qrob∙A14Vbl-Qrob∙A16Vrob∙KP'T:B,rob+CLinthydr,rob∙furob∙A(10)Vrob
12
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.
12
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.
12
3. Tables
Table S1.1: Nomenclature in model schematic representation and mass balance equations
GeneralCLintCYP3A,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.
4. References
1. Hintz RJ, Johnson KC. The effect of particle size distribution on dissolution rate and oral absorption. Int J Pharm. 1989;51(1):9-17.
2. Kaufman MJ. Rate and equilibrium constants for acid-catalyzed lactone hydrolysis of HMG-CoA reductase inhibitors. Int J Pharm. 1990;66(1-3):97-106.