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Birth-related Brachial Plexus Injuries:
| Type | Nerve Roots | Presentation | Cause |
|---|---|---|---|
| Erb's Palsy | C5, C6 | 'Waiter's tip': arm adducted, internally rotated, elbow extended, wrist pronated, fingers flexed | Shoulder dystocia (excessive lateral neck traction) |
| Klumpke's Palsy | C8, T1 | Claw hand deformity (intrinsic hand muscles paralyzed); Horner's syndrome if T1 root avulsed | Arm hyperabduction during delivery |
| Total Plexus Palsy | C5βT1 | Flail arm, complete paralysis | Severe traction |
'Waiter's tip' = Erb's Palsy (C5βC6). Absent Moro on the affected side (normal Moro requires shoulder abduction/external rotation via C5βC6).
Nursing management:
- Gentle range of motion exercises after 7β10 days
- Proper positioning (avoid abduction)
- Physiotherapy referral
- Most recover spontaneously in 3β6 months
- EMG/nerve conduction at 3 months if no improvement
- Surgical repair (nerve grafting) if no recovery by 3β9 months
Count the total number of $3\times3$ matrices of the form $A=\begin{pmatrix}0&2y&1\\2x&y&-1\\2x&-y&1\end{pmatrix}$ with $x,y\in\mathbb{R},\ x\neq y$, satisfying $A^TA=3I_3$.
Compute $A^TA = 3I_3$ by equating columns to be orthogonal with magnitude $\sqrt{3}$.
Column 1 norm$^2$: $0+(2x)^2+(2x)^2=8x^2=3 \Rightarrow x^2=\frac{3}{8}$: 2 values of $x$.
Column 2 norm$^2$: $4y^2+y^2+y^2=6y^2=3 \Rightarrow y^2=\frac{1}{2}$: 2 values of $y$.
With $x\neq y$: we need to discard cases where $x=y$. Since $x^2=3/8$ and $y^2=1/2$, $x\neq\pm y$ (different magnitudes), so all $2\times2=4$ combinations are valid.
Total $= \mathbf{4}$
Neonatal Respiratory Distress Syndrome (RDS) / Hyaline Membrane Disease
Classic features in a preterm neonate (34 weeks):
- Grunting (auto-PEEP to prevent alveolar collapse)
- Subcostal/intercostal retractions
- Central cyanosis
- Ground glass appearance + air bronchograms on CXR
Pathophysiology:
\[\downarrow \text{Surfactant} \Rightarrow \uparrow \text{Alveolar surface tension} \Rightarrow \text{Alveolar collapse (atelectasis)} \Rightarrow \text{V/Q mismatch} \Rightarrow \text{Hypoxia}\]
Treatment:
- Surfactant replacement therapy (Poractant alfa / Beractant) via ETT β single or multiple doses
- Respiratory support: nCPAP (preferred if breathing spontaneously) or mechanical ventilation
- Oxygen to maintain SpOβ \(91{-}95\%\) (avoid hyperoxia β risk of ROP)
- Caffeine citrate (reduces apnea of prematurity)
Prevention (antenatal): Betamethasone \(12\,\text{mg}\) IM Γ 2 doses (24 hr apart) given to mother before 34 weeks delivery β accelerates fetal surfactant production.
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