Modeled PK speed is a PK→PD construct describing how absorption rate, absorption timing, solubility, gastric emptying, distribution loading, distribution geometry, redistribution timing, and clearance shape a concentration-time trajectory for sildenafil and avanafil. “PK speed” refers strictly to modeled PK→PD behavior, not real-world pharmacokinetics. Absorption rate controls rising-phase steepness, absorption timing controls temporal alignment, solubility controls dissolution-driven availability, and gastric emptying controls input arrival. Distribution loading controls early central availability, distribution geometry controls compartmental spread, and redistribution timing controls alignment between central and peripheral compartments. Clearance geometry controls removal dynamics across the modeled trajectory. PD interpretation then converts these PK coordinates into modeled onset and peak geometry: threshold placement defines the onset boundary, binding sensitivity transforms concentration differences, coupling geometry shapes downstream transitions, and PD noise bands widen or narrow interpretation regions. The resulting geometry is a model-space description of timing and shape, not a claim about real-world PK performance. Link to speed overview.
Modeled PK-speed comparison begins with the geometry of the concentration-time curve. Faster modeled absorption steepens the rising phase, earlier absorption timing shifts that phase leftward, solubility determines dissolution-driven availability, and gastric-emptying variability shifts input arrival. Distribution loading determines early central-compartment concentration, distribution geometry determines how rapidly absorbed material spreads across modeled compartments, and redistribution timing determines temporal alignment between them. Clearance geometry determines removal dynamics, while concentration-dependent clearance can alter curvature as concentration changes. These mechanisms interact rather than operating independently: faster modeled absorption can be offset by faster modeled clearance, while broader distribution geometry can offset earlier absorption timing. In this framework, PK geometry supplies the input trajectory that PD parameters subsequently transform. Comparing sildenafil and avanafil therefore means comparing modeled parameter configurations and the resulting trajectory shapes, without assigning those shapes to real-world pharmacokinetic performance or clinical outcomes. See absorption and distribution as separate geometric components. Link to absorption rate and distribution speed.
PD geometry determines how a modeled PK trajectory becomes an interpreted onset-speed or peak-speed trajectory. Threshold placement determines where the PK curve intersects the modeled onset coordinate. Binding sensitivity determines how concentration differences are transformed into binding differences; greater modeled sensitivity can expand separation, whereas lower sensitivity can compress it. Coupling geometry determines how binding is mapped into downstream PD signals; shallow slopes broaden transitions, while steep slopes compress them. PD noise bands widen or narrow the modeled interpretation region around those transitions. Because sildenafil and avanafil can be represented by differing PK parameter sets for absorption rate, solubility, gastric emptying, distribution loading, distribution geometry, clearance geometry, and Tmax/Cmax geometry, the same PD mapping can expand or compress modeled PK-speed differences. Peak geometry likewise depends on where Cmax occurs, how sharply the trajectory approaches it, and how the PD transform responds around that region. This remains model-space interpretation only. Link to peak time.
PK-core geometry starts with the modeled input trajectory. Absorption rate controls the steepness of the rising phase, while absorption timing determines when that rise begins relative to the modeled time axis. Solubility influences the modeled dissolution component that precedes systemic input, and gastric emptying controls the timing of material entering the absorption process. Absorption-window width determines whether input is concentrated into a narrow interval or distributed across a broader interval. Distribution loading then determines how much modeled material appears in the central compartment during the early trajectory. Distribution geometry governs compartmental spread, while redistribution timing determines when movement between compartments changes the central curve. Clearance geometry shapes the descending phase and can alter the apparent separation between rising and falling regions. Together, these parameters create the modeled PK-speed trajectory used for comparison. The construct therefore describes curve geometry and parameter interactions rather than observed pharmacokinetic performance. Link to absorption rate.
PK variability in this framework means variation among modeled parameter sets rather than observed individual behavior. One parameter set can contain rapid absorption, concentrated input timing, strong central loading, limited redistribution delay, and slower clearance; another can contain broader absorption, delayed input, different distribution geometry, and faster removal. Each combination produces a distinct concentration-time trajectory, with changes in slope, curvature, peak position, and persistence. Concentration-dependent clearance can further reshape trajectories when removal changes with concentration, while first-pass metabolism and bioavailability alter the amount of systemic input available to the modeled compartments. Tmax geometry describes the location of the modeled maximum, and Cmax geometry describes its magnitude and local shape. These interacting dimensions create a modeled PK-speed window rather than one fixed speed value. Comparing sildenafil and avanafil therefore involves mapping alternative parameter configurations into trajectory families and examining their geometric separation without implying real-world PK performance. Link to distribution speed.
| PK Domain | PK-Speed Interaction | Link |
|---|---|---|
| Absorption Rate | Steeper rising phase. | absorption rate |
| Distribution Geometry | Compartmental spread. | distribution speed |
| Clearance | Removal geometry. | elimination speed |
Threshold placement determines which portion of a modeled PK trajectory is interpreted as crossing the onset boundary. A threshold positioned closer to the baseline requires less modeled concentration to enter the defined PD region, while a higher threshold requires a later or larger PK trajectory before intersection. The resulting onset coordinate therefore depends on both PK geometry and threshold location. A steep rising phase can cross a threshold over a shorter modeled time interval, whereas a shallow rising phase produces a more extended crossing geometry. Threshold placement can also interact with absorption timing, distribution loading, redistribution timing, and clearance geometry, because each changes the concentration trajectory presented to the PD layer. In this construct, onset speed is therefore not a PK-only coordinate. It is generated by the intersection between a modeled concentration-time curve and a defined PD threshold. The interpretation remains mathematical and mechanistic, with no inference about real-world onset experience or clinical outcomes. Link to PD speed.
Binding sensitivity, coupling geometry, and PD noise bands determine how strongly and how precisely PK differences are expressed in the modeled PD layer. Binding sensitivity controls the concentration-to-binding transformation, so small PK separations can become wider or narrower depending on the modeled response slope. Coupling geometry then maps binding into a downstream PD signal, with nonlinear or steep regions producing different geometric separation from shallow regions. PD noise bands represent modeled uncertainty or dispersion around the transformation and can blur otherwise distinct trajectory intersections. These modifiers do not change the underlying PK curve; they change how that curve is represented after PD transformation. Consequently, two modeled PK trajectories with modest differences in absorption, distribution, or clearance can produce more separated or more overlapping onset-speed and peak-speed coordinates after transformation. The framework therefore distinguishes PK geometry from PD interpretation geometry and treats their interaction as a mathematical mapping rather than a statement about real-world effectiveness or patient outcomes. Link to onset variability comparison.
| PD Domain | PK-Speed Effect | Link |
|---|---|---|
| Threshold Placement | Earlier/later onset. | onset time |
| Binding Sensitivity | Amplification/compression. | onset variability comparison |
| Coupling Geometry | Slope-driven shaping. | peak variability comparison |
Modeled PK-speed differences arise from the parameter configuration used to generate each concentration-time trajectory. Absorption rate and timing establish rising-phase geometry, while solubility, gastric emptying, and absorption-window width shape systemic input. Distribution loading, distribution geometry, and redistribution timing determine early compartmental structure. Clearance geometry and concentration-dependent clearance shape removal and curvature. First-pass metabolism and bioavailability modify modeled systemic input, while Tmax and Cmax geometry describe the location and magnitude of the modeled maximum. These parameters interact, so one change can offset or amplify another. For sildenafil and avanafil, comparison therefore concerns modeled parameter sets and the trajectories they generate. The construct describes mathematical PK geometry only and does not assign trajectory shapes to real-world pharmacokinetic performance within any population or setting.
The principal PK mechanisms are absorption, distribution, and clearance represented as model parameters. Absorption rate controls rising-phase steepness, while absorption timing and gastric emptying control when modeled input enters the trajectory. Solubility and absorption-window width shape the timing and spread of input. Distribution loading controls early central availability, distribution geometry determines compartmental spread, and redistribution timing controls movement between compartments. Clearance geometry determines the descending phase, while concentration-dependent clearance can add curvature. First-pass metabolism and bioavailability modify systemic input available to the modeled compartments. Together, these mechanisms determine trajectory slope, timing, curvature, peak position, and peak magnitude. PK-speed comparison therefore concerns the geometry produced by parameter interactions rather than a single parameter or fixed speed value within the specified model.
PD mechanisms shape PK-speed interpretation by transforming a modeled concentration trajectory into defined PD coordinates. Threshold placement establishes the boundary for a modeled onset transition. Binding sensitivity determines how concentration differences become differences in the binding layer. Coupling geometry determines how binding is transformed into a downstream PD coordinate, including slope and curvature. PD noise bands represent a modeled region around the transformed trajectory and can make coordinate separation appear narrower or broader. These mechanisms act after the PK trajectory is generated, so they do not replace absorption, distribution, or clearance geometry. Instead, they determine how strongly PK differences are expressed in onset-speed and peak-speed space. The interpretation is a mathematical transformation of modeled variables, not a statement about real-world outcomes.
Sildenafil and avanafil differ in modeled PK-speed geometry when their parameter sets use different values or functional forms for absorption, distribution, metabolism, clearance, or related trajectory variables. Differences in absorption rate or timing alter the rising phase; solubility or gastric-emptying parameters alter modeled input timing; and distribution parameters alter early concentration structure. Clearance geometry, first-pass metabolism, bioavailability, and concentration-dependent clearance can further change curvature, Tmax, and Cmax geometry. The PD layer then applies threshold placement, binding sensitivity, coupling geometry, and noise bands to express those PK differences as modeled onset-speed or peak-speed coordinates. Thus, the modeled difference follows from the specified parameterization and its interactions. It is not an inference about real-world PK performance or observed pharmacokinetic behavior in practice.
PK→PD mapping explains PK-speed differences by separating trajectory generation from trajectory interpretation. The PK layer generates a concentration-time curve from absorption rate, timing, solubility, gastric emptying, distribution loading, redistribution, clearance, bioavailability, and related parameters. The curve contains rising-phase slope, Tmax position, Cmax magnitude, curvature, and decline. The PD layer then applies threshold placement, binding sensitivity, coupling geometry, and noise bands to translate those features into modeled onset-speed and peak-speed coordinates. A small PK difference can remain small, become more separated, or become less distinguishable depending on the PD transformation. Similar PK trajectories can also produce different modeled coordinates under different thresholds or sensitivities. PK speed is therefore an emergent model property of the specified trajectory and its PD mapping, not a single intrinsic number or a claim about real-world performance.