Fig 1.
Biological scales and modeling modalities.
Length scales (left) of biological processes (center) and the corresponding modeling modalities (right).
Fig 2.
Description of modular structure of the model.
Whole body uptake, distribution and clearance (1a) is represented as a PBPK model (1b) in SBML. The rectangular compartments represent tissues or blood compartments with blood flows between compartments indicated by black arrows. The compartment labeled “Rest” is the remainder of the body. The blue arrows and ovals represent non-blood borne transfer between compartments and organ lumens or, in the case of liver metabolism, an unspecified location external to the PBPK model. The tissue scale model of the liver (2a) is represented in CC3D as a single sinusoid modeled as a linear pipe lined with hepatocytes (green) (2b). Blood flow within the sinusoid consists of RBCs (red) and portions of serum (blue). Portions of serum are modeled as generalized cells. The hepatocyte (3a) metabolic pathways (3b) are model as a set of chemical reactions expressed in SBML.
Table 1.
Whole-body PBPK Model Rate Equations.
Table 2.
PBPK Parameter Set REFSIM.
Fig 3.
The diffusion model for the multicell scale sinusoid model.
Transfer between each of the three cell, or pseudo-cell, types is described by this transfer map. Subscripts indicate that there are multiple cells of each of the types and transfer is calculated between all pairs of cells that are in contact at a particular instant. The paired arrows represent passive transport that equilibrates across pairs of cell types if they are in contact. Looped arrows represent passive transport between adjacent cells of the same type. The single arrow labeled “Active Transport” represents the Michaelis-Menten modeled import of APAP from the serum into hepatocytes.
Table 3.
Intercellular Molecule Transfer Rate Equations.
Table 4.
CC3D Parameters.
Table 5.
Subcellular Reaction Kinetics Rate Equations.
Table 6.
Subcellular Reaction Kinetic Parameters.
Fig 4.
Standalone simulation of the PBPK module using the REFSIM parameters.
This simulation is for a 1.4g oral APAP dose in a 70Kg male. The open symbols are in vivo data [58] and the line is the model output.
Fig 5.
Time course of a standalone simulation of the sinusoid model in CC3D using the parameters set REFSIM.
A simulated 3 second square pulse of APAP was pushed into the left end of the vessel lumen for three seconds starting one second into the simulation. The concentration of APAP in the blood and hepatocytes is given by the heat map scale at left and time progresses from top to bottom. Blood components are created at the periportal (left) end and a constant force is exerted on the blood components to induce blood flow through the simulated sinusoid. The temporal scales was adjusted so that the blood speed in the simulation was equivalent to 200 μm/s, giving a transit time of a blood component through the sinusoid of one second.
Fig 6.
Standalone simulation of sub-cellular model.
Results of the standalone run of the sub-cellular model using parameter set REFSIM and an initial concentration of APAP of 0.1mM (15μg/ml).
Fig 7.
Plasma concentrations versus time for APAP and metabolites for REFSIM.
Plasma concentrations versus time for APAP and metabolites simulated with the complete multiscale model using parameter set REFSIM (lines). Open symbols are in vivo average values from nine Caucasian subjects given a 1.4g oral dose of APAP [58].
Fig 8.
Plasma concentrations versus time for APAP and metabolites for HMPCsim6.
Plasma concentrations versus time for APAP and metabolites simulated with the complete multiscale model using the best fit parameter set HMPCsim6. Symbols are as described in Fig 7.
Fig 9.
Plasma concentrations calculated using parameter set LNsim8.
This parameter set represents a hypothetical chemical species with ADME behavior significantly different than APAP. Symbols are as described in Fig 7 and the APAP in vivo data is included for comparison.
Fig 10.
Plasma concentrations calculated using parameter set LNsim23.
This parameter set represents a hypothetical chemical species with ADME behavior significantly different than APAP or the hypothetical species in Fig 9. Symbols are as described in Fig 7 and the APAP in vivo data is included for comparison.
Fig 11.
Subcellular concentration of APAP and Phase I metabolites in REFSIM simulation.
Four cells were monitored in each of the three regions; (A), periportal (PP), midzonal (MZ) and perivenous (PV), and the average concentration in each group is plotted. (B) APAP, (C) GSH, (D) NAPQI, (E) NAPQI-GSH, (E) APAP-Glucuronide, and (E) APAP-Sulfate. Error bars are the standard deviation of the four cells in a region.
Fig 12.
Sinusoid chemical concentration time course.
Time course snapshots of the chemical field for the multi-cell scale of the complete model using parameter set REFSIM. Concentrations of APAP (left), APAPG (middle) and APAPS (right) are indicated by the color scale. This time course spans 8 simulated hours top to bottom.
Fig 13.
Fixed point sensitivity of model outputs to single parameter variations.
The horizontal axis lists the model’s parameters grouped by the sub-model. Parameters for the PBPK model start with “pbpk_”, the sinusoid models with “cc3d_” and the subcellular model with “sc_”. The vertical axis lists the model’s outputs duplicated for each of the input parameter sets. The “Average” row is the average of all the sensitivities in the column for the particular parameter set. Each square in the heat map is the relative change of a model output divided by the relative change of the model parameter in single-parameter-variation simulation. Dark space indicates little influence of a parameter on the model outputs, bright regions reflect strong influence of a parameter and white regions represent sensitivities greater than one.
Table 7.
Correlation Coefficients and R2 values between sensitivities for the four parameter sets.
Fig 14.
Compound-independent parameters sensitivity comparison.
Comparison of the sensitivities for the compound-independent parameters in the whole-body PBPK model about the fixed point REFSIM. Axis are as described in Fig 13.
Fig 15.
Sensitivity comparisons for formation of NAPQI-GSH.
Comparison of the sensitivities for the formation of NAPQI-GSH (NAPQIGSH_Sum) versus the average parameter sensitivities about the fixed point REFSIM. Axis are as described in Fig 13.
Fig 16.
Nonlinear sensitivity of model outputs to PPV.
Pairwise parameter interactions for model output RMSEsum. Each square in the heat map is the difference between the relative changes in model output (RMSEsum) for two individual single-parameter-variation simulations compared with the pairwise-parameter-variation simulation. White space indicates little interaction between a pair of parameters, red or blue regions reflect strong, non-linear parameter interactions. Horizontal and vertical lines separate the parameters of the three model scales with rectangular regions showing interactions that cross model scales and triangular regions for interactions within a model scale. Parameter variations are about the fixed point REFSIM.
Fig 17.
Population variability based on 1000 simulated individuals.
The population was generated by assuming that for each in silico individual, each parameter was within a truncated normal distribution with coefficient of variation of 25% around the base parameter from the parameter set REFSIM. (A) Average serum concentrations of APAP and Phase II metabolites for the simulated population. Open symbols are human in vivo data, closed symbols simulation results. (B) Average urinary excretion of APAP and Phase II metabolites for the simulated population. (C) Average cellular NAPQI-GSH for the population (zones as defined in Fig 11A). (D) Comparison of the average response (closed symbols with error bars) of the simulated population with the simulated individuals that deviate the most, high and low, from the population average (symbols without error bars). Error bars are standard deviations.