Two-Drug Pharmacodynamic Interaction & Combination Index

Drug Pair Preset

Doses (× each drug's own EC₅₀)

Drug A dose 1.50 × EC₅₀ᴬ

Drug B dose 1.50 × EC₅₀ᴮ

Interaction index α 0.00

Effect & Interaction

Set both doses > 0

Drug A alone

0.0%

Drug B alone

0.0%

Combined effect (observed)

0.0%

Combination Index (CI)

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How it works

Each drug alone follows a Hill / E_max dose-response curve, doses expressed as a ratio r = D / EC₅₀ so both drugs share one scale:

E(r) = 100 · r^n / (1 + r^n),  n = 1.5 (Hill slope)

The two drugs are combined into one effective potency C using a Loewe-additivity model with an interaction term α:

C = a + b + α·√(a·b)
E_combined = 100 · C^n / (1 + C^n)

where a, b are the Drug A / Drug B dose ratios. α = 0 reproduces pure Loewe additivity (the two drugs simply add up). α > 0 means the pair boosts each other beyond addition (synergy — e.g. an opioid's respiratory depression amplified by a benzodiazepine). α < 0 means one blunts the other (antagonism — e.g. naloxone displacing an opioid from its receptor).

The Combination Index follows the Chou–Talalay definition: CI = (a + b) / C. Because additivity makes C = a + b exactly, CI = 1 at α = 0 by construction. CI < 1 = synergism, CI = 1 = additivity, CI > 1 = antagonism — the standard clinical-pharmacology yardstick for reading drug-combination studies.

The 3D surface is the full effect landscape E(a,b): its height at every (Drug A, Drug B) dose pair is the combined effect. The white ring is the 50%-effect isobole — every dose pair sitting on that ring produces the same half-maximal effect, which is exactly what a real isobologram plots in 2D.

Current dose marker 50% isobole

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