Young's Formula for pediatric dosage calculation:

\[\text{Child's dose} = \frac{\text{Age (years)}}{\text{Age (years)} + 12} \times \text{Adult dose}\]

Calculation:

\[\text{Child's dose} = \frac{6}{6 + 12} \times 300\,\text{mg}\]

\[= \frac{6}{18} \times 300\,\text{mg}\]

\[= \frac{1}{3} \times 300\,\text{mg} = 100\,\text{mg}\]

Other pediatric dose formulas:

BSA-based dosing is most precise in clinical practice. Young's formula is used when weight is unavailable.

The circumference formula is $C = \pi d$, where $d$ is the diameter.

$18\pi = \pi d \Rightarrow d = 18$

Column A = 18, Column B = 9.

Since $18 > 9$, Column A is greater.

Stress is defined as $\frac{\text{Force}}{\text{Area}}$.

• Force (Weight) $\propto \text{Volume} \propto L^3$
• Area $\propto L^2$
• $\text{Stress} \propto \frac{L^3}{L^2} \propto L$
• Since $L$ increases by factor $9$, stress increases by factor $9$.

1. Measure serum lactate (re-measure if initial lactate \(> 2 \text{ mmol/L}\))
2. Obtain blood cultures before administering antibiotics
3. Administer broad-spectrum antibiotics
4. Administer \(30 \text{ mL/kg}\) crystalloid (IV fluid bolus) for hypotension or lactate \(\geq 4 \text{ mmol/L}\)
5. Apply vasopressors if patient remains hypotensive during or after fluid resuscitation to maintain \(\text{MAP} \geq 65 \text{ mmHg}\)

• \(< 2 \text{ mmol/L}\): Normal
• \(2 - 4 \text{ mmol/L}\): Elevated — monitor closely
• \(> 4 \text{ mmol/L}\): Severe hypoperfusion — high mortality risk