Medicine extended problems (resonance framework)

Problem 4 – Resonant metabolic clearance#

Metabolic clearance is modeled as

$$ C = \frac{T_f}{D_6 + τ_r}. $$

1. If $$τ_r$$ increases, how does clearance change?
2. If $$T_f$$ increases, what is the qualitative effect?

Problem 5 – Neural firing threshold#

A neuron’s firing threshold is modeled as

$$ Θ_f = D_9 - X \sqrt{τ_r}. $$

1. If $$τ_r$$ quadruples, how does the second term change?
2. Does the firing threshold increase or decrease?

Problem 6 – Resonant immune response#

An immune activation index is

$$ I = X \ln(1 + D_3 τ_r). $$

If $$τ_r$$ increases by 20%, how does $$I$$ change qualitatively?

Problem 7 – Pharmacodynamic saturation#

A saturation model is

$$ S_{\text{sat}} = \frac{ΛΘ + T_f}{1 + e^{-D_6 τ_r}}. $$

1. If $$τ_r$$ increases, does saturation increase or decrease?
2. If $$ΛΘ$$ increases, what is the effect?

Problem 8 – Resonant blood flow#

Blood flow through a vessel is modeled as

$$ F = \frac{F_3 τ_r^2}{D_3 + ΛΘ}. $$

1. If $$τ_r$$ increases by 10%, how does the numerator change?
2. If $$ΛΘ$$ increases due to stress, how does the denominator change?
3. What is the qualitative net effect on $$F$$?