🩺 Medicine — TFT_3Pack Example Suite

Problem 1 — Drug Resonance Half-Life

t₁/₂ = ln(2) / (ΛΘ)

If \( Θ \) decreases by 10%, how does the half-life change?

Problem 2 — Heart Rhythm Resonance

R = T_f D₃

If \( T_f \) increases by 8%, what is the percent change in R?

Problem 3 — Dose-Response Resonance

S = X / (1 + e^{-τ_r})

If \( τ_r \) increases, how does S change qualitatively?

Solution 1 — Half-Life

\( t_{1/2}' = t_{1/2} / 0.9 \). Half-life increases by 11.1%.

Solution 2 — Heart Rhythm

Rhythm increases by 8%.

Solution 3 — Dose-Response

As \( τ_r \) increases, the exponential term shrinks → S increases.

Problem 4 — Metabolic Clearance

C = T_f / (D₆ + τ_r)

Describe how increasing τ_r and T_f affect clearance.

Problem 5 — Neural Firing Threshold

Θ_f = D₉ - X √τ_r

Describe how quadrupling τ_r affects Θ_f.

Problem 6 — Immune Response

I = X ln(1 + D₃ τ_r)

Describe how increasing τ_r affects I.

Problem 7 — Pharmacodynamic Saturation

S_sat = (ΛΘ + T_f) / (1 + e^{-D₆ τ_r})

Analyze effects of increasing τ_r and ΛΘ.

Problem 8 — Blood Flow Resonance

F = F₃ τ_r² / (D₃ + ΛΘ)

Describe how changes in τ_r and ΛΘ affect flow.

Diagram 1 — Drug Half-Life

Λ + Θ → ΛΘ → ln(2)/ΛΘ → t₁/₂
        

Diagram 2 — Heart Rhythm

T_f × D₃ → R
        

Diagram 3 — Dose-Response

τ_r → e^{-τ_r} → 1 + e^{-τ_r} → X ÷ (...) → S