Simulate drug concentration-time profiles with 1- and 2-compartment models. Visualize multiple-dose accumulation, steady state, and therapeutic window in real time.
Parameters
Dosing Model
Dose
mg
Body Weight
kg
Volume of Distribution Vd
L/kg
Clearance CL
L/h
Absorption Rate ka
/h
Bioavailability F
Number of Doses
Dosing Interval τ
h
Min Effective Conc. MEC
μg/mL
Max Safe Conc. MSC
μg/mL
Results
—
Cmax [μg/mL]
—
Tmax [h]
—
t₁/₂ [h]
—
AUC₀→∞ [μg·h/mL]
—
Css_avg [μg/mL]
—
Therapeutic Index MSC/MEC
Drug Concentration C(t) — Multiple Dosing (semi-log)
Theory & Key Formulas
1-Compartment IV Bolus: $C(t) = \dfrac{D}{V_d}e^{-k_{el} t}$, $k_{el}= \dfrac{CL}{V_d}$
What exactly is a "compartment" in these models? It sounds like a physical box inside the body.
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Basically, it's not a physical box. It's a conceptual "space" where the drug is assumed to mix instantly and uniformly. In practice, the 1-compartment model treats your whole body as one well-mixed bucket. Try selecting the "1-Compartment IV Bolus" model in the simulator above. You'll see the concentration drops in a single, smooth curve because we're ignoring details like tissue distribution.
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Wait, really? So when would you need a second compartment? And what do the "ka" and "CL" sliders actually control?
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Good question! You need a second compartment when the drug distributes into tissues like fat or muscle at a different rate than the blood. The "ka" slider controls the absorption rate from the gut into the bloodstream—a higher `ka` makes the curve spike faster. "CL" (Clearance) is how fast the kidneys/liver remove the drug. Increase CL in the simulator, and you'll see the entire curve drops faster because the drug is eliminated more quickly.
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That makes sense. But what about the "MEC" line and giving multiple doses? How do we use the model to design a safe dosing schedule?
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Excellent! That's the core of therapy. The MEC (Minimum Effective Concentration) is the target. You want the drug level to stay above it for effect but below toxic levels. Now, try increasing the "Number of Doses" to 4 or 5. See how the peaks and troughs accumulate until they level off at "steady state"? The goal is to adjust the "Dose" and "Dosing Interval τ" so that at steady state, the troughs stay above MEC and the peaks stay safe. This simulator lets you visually design that!
Physical Model & Key Equations
The simplest model is a 1-compartment intravenous (IV) bolus. The body is a single volume (Vd), and drug is eliminated proportionally to its concentration, characterized by the elimination rate constant (k_el).
C(t): Plasma concentration at time t. D: Administered dose. Vd: Volume of Distribution - the apparent volume the drug disperses into. CL: Clearance - the volume of plasma cleared of drug per unit time. k_el: Elimination rate constant.
For oral dosing, we add an absorption phase from the gut into the central compartment. This is governed by a first-order absorption rate constant (ka) and bioavailability (F), the fraction of dose that reaches circulation.
F: Bioavailability (0 to 1). k_a: Absorption rate constant. A larger k_a means faster absorption, leading to a sharper, earlier peak.
The equation shows the superposition of the rising absorption process (e^{-k_a t}term) and the declining elimination process (e^{-k_{el} t} term).
Frequently Asked Questions
The time to reach steady state depends on the drug's elimination half-life (t1/2). Generally, steady state is approached after approximately 4 to 5 times the half-life. For example, if the half-life is 6 hours, steady state is nearly achieved after about 24 to 30 hours (4 to 5 doses). In the simulator, this is automatically calculated based on the dosing interval and elimination rate constant, and can be verified on the graph.
A one-compartment model is suitable when the drug distributes rapidly in the body and exhibits a single elimination process (e.g., many small molecule drugs). A two-compartment model is used for drugs with distinct distribution and elimination phases (e.g., some antibiotics and anesthetics). By switching between the two in the simulator and comparing the shape of the blood concentration curve, you can select the appropriate model.
In the 'Therapeutic Window Settings' item on the screen, directly enter the values for the minimum effective concentration (MEC) and maximum toxic concentration (MTC). After setting, a light-colored band will be displayed on the graph, allowing you to check in real time whether the blood concentration is maintained within this range. An alert can also be displayed if the range is exceeded.
Yes, it is possible. For a one-compartment model, you can visually read the time at which the blood concentration is halved on the graph. More precisely, the elimination rate constant k_el can be determined from the slope of the linear portion of the elimination phase (when displayed on a semi-logarithmic graph), and t1/2 is calculated as ln(2)/k_el. The simulator also has a feature that automatically displays the half-life in the numerical display panel.
Real-World Applications
Vancomycin/Aminoglycoside Therapeutic Drug Monitoring (TDM): These antibiotics have narrow therapeutic windows—too low is ineffective, too high causes kidney toxicity. Pharmacokinetic models, exactly like this simulator, are used to predict trough and peak levels based on a patient's weight, renal function (which affects CL), and chosen dose/interval to individualize therapy safely.
Anticancer Drug Dosing Schedule Design: Chemotherapy drugs are often highly toxic. PK modeling helps design schedules (like continuous infusion vs. bolus) that maintain tumor-killing concentrations while minimizing time spent at concentrations that cause severe side effects, improving the therapeutic index.
Personalized Medicine & Renal Function Correction: A patient's drug clearance (CL) is directly tied to organ function, especially kidney function. Clinicians estimate a patient's CL from their creatinine clearance, input it into a PK model (using the CL slider here), and calculate a personalized dose to achieve the same target concentration as a healthy person.
Population PK Model Pre-Validation: Before running costly clinical trials, drug developers use simulation tools to test how different population characteristics (e.g., ranges of Vd and CL) will affect drug exposure. This helps design smarter trials and anticipate dosing strategies for sub-populations like the elderly or obese.
Common Misconceptions and Points to Note
First, understand that "the volume of distribution (Vd) is not a physical volume." For example, even if Vd calculates to 500L, many newcomers get confused thinking, "That's an impossibly large volume!" This is merely an "apparent value indicating how diluted the drug is within the body." Drugs with high lipophilicity that are readily taken up by tissues tend to have a larger Vd. In practice, you use this value to roughly predict the "initial blood concentration" after administration.
Next, don't overlook the "interdependence" of parameters. For instance, clearance (CL) and half-life (t1/2) are not determined independently. If the volume of distribution (Vd) changes, the half-life changes even if CL remains the same. The relationship is given by $$t_{1/2} = \frac{0.693 \times V_d}{CL}$$. Try using the simulator to double Vd and confirm that the half-life also doubles. Cases where edema (swelling) in a patient increases Vd, thereby prolonging the half-life, are quite common.
Finally, never forget the fundamental principle that "models are only approximations of reality." The one-compartment model is useful for simple initial assessments, such as when liver or kidney function changes abruptly, but actual blood concentration curves are far more complex. Pay particular attention to the assumption that the "absorption rate constant (ka)" is constant, especially for oral administration. Absorption fluctuates due to stomach contents or interactions with other drugs. Consider simulation results as merely "one indicator for observing trends," and always cross-verify them with actual TDM (Therapeutic Drug Monitoring) data.