Article Figures & Data
Figures
- Fig. 1.
The concept of calculation for hybrid automata with multiple beats. (A) Time t is expressed by m and u in each beat. (B) By overlaying multiple beats on the t-axis, a hybrid automaton alternates continuous changes and discrete transitions.
- Fig. 2.
Model structures of hybrid automata. (A) The three-compartment model for PAH is composed of the central, distribution, and renal blood compartments. (B) The four-compartment model for propranolol is composed of the central, two distribution, and hepatic blood compartments. (C) The one-dimensional tube flow considering convection. (D) The one-dimensional tube flow considering convection and diffusion. (E) Body fluid as a drug container is constructed by connecting the liver, kidney, and gut with the cardiovascular compartments. The circulatory blood flows every interval τcb, leaving and returning to the heart via the artery, other, and vein or via the lung.
- Fig. 3.
Blood concentration–time profile of PAH after intravenous administration. The observed data from Fagan et al. (1982) (open circle) and the simulated result obtained using the two-compartmental hybrid automaton (solid line) are shown.
- Fig. 4.
Blood concentration–time profile of propranolol after intravenous administration. The observed data from Prescott et al. (1993) (open circle) and the simulated result obtained using the three-compartmental hybrid automaton (solid line) are shown.
- Fig. 5.
The simulated fluid volume–time profiles in the body on a virtual day, simulating the changes in the fluid volume in the body. For upper jejunum, lower jejunum, upper ileum, and lower ileum, the sums of the volume in each region are plotted. asc, ascending colon; bduct, bile duct; dsc, descending colon; duo, duodenum; fhb, flowing volume of hepatic blood; gbd, gallbladder; glm, glomerulus; hb-inlet, hepatic blood inlet; hb-outlet, hepatic blood outlet; if, interstitial fluid; lw-ile, lower ileum; lw-jej, lower jejunum; pv, portal vein; rb, renal blood; rec, rectum; ru, renal urine; stm, stomach; tsc, transverse colon; ubd, urinary bladder; up-ile, upper ileum; up-jej, upper jejunum.
Additional Files
Data Supplement
Supplemental Data
- Supplemental Data -
Supplemental Figure 1 - The flow expressions based on (A) a first-order kinetics in an ODE and (B) one-dimensional convection in a PDE.
Supplemental Figure 2- Nonlinear blood concentration–time profile of a virtual drug after intravenous administration when the dosing amount is escalated from 0.3–30 mmol.
Supplemental Figure 3 - Blood concentration–time profile of a virtual drug (victim) coadministered with a virtual inhibitor (perpetrator).
Supplemental Figure 4 - Hybrid automata of hepatic flow.
Supplemental Figure 5 - Hepatic availability based on the various models.
Supplemental Figure 6 - Hybrid automata of renal flow.
Supplemental Figure 7 - Gastric emptying model.
Supplemental Figure 8 - Gastric emptying after drinking water.
Supplemental Figure 9 - Gallbladder emptying model and hepatic flow with variable volume.
Supplemental Figure 10 - Gallbladder emptying after eating a meal.
Supplemental Figure 11 - Hybrid automata of gastrointestinal transit.
Supplemental Figure 12 - Calculation of steady state of body fluid during virtual days.
Supplemental Figure 13 - Blood concentration–time profiles of 5-ASA and Ac-5-ASA after oral administration.
Supplemental Figure 14 - The plotting position of gut regions in heatmap animation of Movie 4 and 5.
Supplemental Table 1 - Parameters for hybrid automata of hepatic flow.
Supplemental Table 2 - Parameters for hybrid automata of renal flow.
Supplemental Table 3 - Parameters for gastric emptying model.
Supplemental Table 4 - Parameters for gallbladder emptying model and altered hepatic flow model.
Supplemental Table 5 - Parameters for hybrid automata of gastrointestinal transit.
Supplemental Table 6 - Gut length and blood allocation to gut regions.
Supplemental Table 7 - Parameters for hybrid automata of cardiovascular system and water balance.
Supplemental Table 8 - Schedule of action on virtual day and in clinical study.
Supplemental Table 9 - Compound-dependent parameters for 5-ASA and Ac-5-ASA.
Supplemental Table 10 - Formulation-dependent parameters.
Supplemental Table 11 - Ratio of regional maximum concentration within one-dimensional tube in Movie 1.
Supplemental Table 12 - Ratio of regional cleared amount within one-dimensional tube in Movie 1.
Supplemental Table 13 - Parameters of systemic 5-ASA and Ac-5-ASA.
Supplemental Movies
Supplemental References
- Supplemental Movie 1 -
Movie 1. Simulation of concentrations of a virtual drug in the one-dimensional tube flow models after instantaneous
injection. - Supplemental Movie 2 -
Movie 2. Transit of fluid and residue through the gut on a virtual day.
- Supplemental Movie 3 -
Movie 3. Transit of 5-ASA through the gut after administration.
- Supplemental Movie 4 -
Movie 4. Heatmap animation of 5-ASA amount in the gut during absorption and transit.
- Supplemental Movie 5 -
Movie 5. Simulation of a virtual drug disposition affected by enterohepatic circulation.
- Supplemental Model File 1
- Supplemental Model File 2
- Supplemental Model File 3
- Supplemental Model File 4
- Supplemental Model File 5
- Supplemental Model File 6
- Supplemental Model File 7
- Supplemental Data -
In this issue
Flow Modeling Using Hybrid Automata
