Clinical Pharmacokinetics PK/PD Simulator

Interactive 1-Compartment mathematical model for simulating steady-state concentrations and custom patient clearances.

Parameters Panel

Select Preset Scenario

Narrow Therapeutic Index (NTI) Drugs:
These drugs have a very small difference between safe effective doses and life-threatening toxicity. Active Therapeutic Drug Monitoring (TDM) is clinically mandatory to adjust doses in real-time.

Administration Route

Dose (D) 160 mg

Dosing Interval (τ) 8 h

Vol. of Distribution (V_d) 20 L

Baseline Clearance (Cl) 6.0 L/h

Glomerular Filtration (GFR) 120 mL/min

Lowering GFR reduces kidney drug clearance.

Absorption Rate (k_a) 1.0 h⁻¹

Infusion Duration (T_inf) 0.5 h

Concentration-Time Curve Plot Hover on graph for exact coordinates

Half Life (t_½)

2.3 h

Peak Concentration (C_max)

8.0 mg/L

Trough Concentration (C_min)

1.8 mg/L

Therapeutic Assessment

✅ Safe Therapeutic

Steady-state concentrations are well inside the target therapeutic limits.

1. Creatinine Clearance & Kidney Adjustments

Calculated using the Cockcroft-Gault linear equation to adjust baseline drug clearance dynamically:

                    CrCl (mL/min) = [(140 - Age) × Wt (kg)] / [72 × SCr (mg/dL)]
                

*Multiply output by 0.85 for female patients.
Clearance adjustment multiplier:
CL_adj = CL_base × [0.2 + 0.8 × (GFR / 120)]

Cockcroft-Gault Weight Rules:

- IBW (Male): 50 kg + 2.3 kg × (Height inches - 60)
- IBW (Female): 45.5 kg + 2.3 kg × (Height inches - 60)
- AdjBW (Obese / Wt > 120% IBW): IBW + 0.4 × (Actual Weight - IBW)

2. Elimination Rate & Half-Life

Determines the clearance rate constant (k_e) and biological half-life (t_½):

                    ke = CLadj / Vd

                    t½ = 0.693 / ke

- V_d: Apparent volume of distribution (L).
- CL_adj: GFR-adjusted clearance (L/h).

3. Steady State Equations by Route

Models steady-state concentration curves under superposition:

IV Bolus (Instant distribution):

                    Cmax, ss = (Dose / Vd) / (1 - e-ke·τ)

                    C(t) = Cmax, ss × e-ke·t

IV Infusion (Continuous input rate R₀):

                    R0 = Dose / tinf

                    Cmax, ss = (R0/CL) × (1 - e-ke·tinf) / (1 - e-ke·τ)

                    Cmin, ss = Cmax, ss × e-ke·(τ - tinf)

Oral (1-Compartment First-Order Absorption):

                    C(t) = [F·Dose·ka / Vd(ka - ke)] ×

                    [ e-ke·t / (1-e-ke·τ) - e-ka·t / (1-e-ka·τ) ]

- τ (Tau): Dosing interval (hours).
- t_inf: Infusion duration (hours).
- k_a: Absorption rate constant (h⁻¹).
- F: Bioavailability fraction (assumed at 90% or F=0.9).

4. Loading & Maintenance Doses

Clinical target dose calculations for initiating and maintaining therapy:

Loading Dose (LD):

Rapidly achieves target peak concentration (C_target) in the patient's distribution volume.

                    LD = Ctarget × Vd / F
                

Maintenance Dose (MD):

Maintains steady-state average concentration (C_{ss, avg}) by replacing cleared drug.

                    MD = Css, avg × CL × τ / F
                

*For IV routes (Bolus/Infusion), Bioavailability fraction F = 1.0.
*For Oral routes, Bioavailability fraction F = 0.9.

5. TDM Clinical Reference Ranges

Therapeutic windows (MEC to MTC) for all 12 monitored NTI drugs:

Drug	Range	Admin Type
Gentamicin	2.0 - 10.0 mg/L	IV Infusion
Amikacin	5.0 - 30.0 mg/L	IV Infusion
Tobramycin	1.5 - 8.0 mg/L	IV Infusion
Lidocaine	1.5 - 5.0 mg/L	IV Infusion
Vancomycin	10.0 - 20.0 mg/L	IV Bolus
Digoxin	0.8 - 2.0 mcg/L	IV Bolus
Theophylline	8.0 - 20.0 mg/L	Oral
Lithium	0.6 - 1.2 mEq/L	Oral
Phenytoin	10.0 - 20.0 mg/L	Oral
Valproic Acid	50.0 - 100.0 mg/L	Oral
Carbamazepine	4.0 - 12.0 mg/L	Oral
Tacrolimus	5.0 - 15.0 ng/mL	Oral