| Download the amazing global Makindo app: Android | Apple | |
|---|---|
| MEDICAL DISCLAIMER: Educational use only. Not for diagnosis or management. See below for full disclaimer. |
Cell → systems → bedside: mechanisms, equations, control loops, and clinical reasoning for high-yield exams. 🔥
| Topic | Equation | Use / Memory Tip |
|---|---|---|
| Nernst | \(E_{ion}=\frac{RT}{zF}\ln\frac{[\text{ion}]_o}{[\text{ion}]_i}\) | At 37 °C, ≈ \(61\,\text{mV}\cdot\frac{1}{z}\log_{10}\frac{o}{i}\). |
| Goldman (GHK) | \(V_m=\frac{RT}{F}\ln\frac{\sum P_i[\text{ion}]_o}{\sum P_i[\text{ion}]_i}\) | Weighted by permeability \(P\). |
| Ohm / driving force | \(I=g(V_m-E_{ion})\) | Sign shows ion entry/exit. |
| Flow | \(Q=\frac{\Delta P}{R}\) | Series ↑R, parallel ↓R. |
| Poiseuille | \(R=\frac{8\eta L}{\pi r^4}\) | Radius rules (×2 radius → 16× flow). |
| MAP | \(\text{MAP}\approx \text{DBP}+\tfrac13(\text{SBP}-\text{DBP})\) | At normal HR; shifts with tachy. |
| Laplace | \(T=\frac{P\cdot r}{2}\) (sphere) | Aneurysm risk ↑ with radius. |
| Alveolar ventilation | \(\dot V_A=(V_T-V_D)f\) | PaCO\(_2\) ∝ \( \frac{\dot V_{CO_2}}{\dot V_A}\). |
| Alveolar gas | \(P_{AO_2}=P_{IO_2}-\frac{P_{aCO_2}}{R}\) | Sea level: \(P_{IO_2}\approx150\) mmHg on air. |
| O\(_2\) content | \(C_{aO_2}=1.34\,\text{Hb} \cdot S_{aO_2}+0.003\,P_{aO_2}\) | Hb dominates O\(_2\) content. |
| Clearance | \(C_x=\frac{U_x V}{P_x}\) | Inulin/Cr ≈ GFR; PAH ≈ RPF. |
| Filtration fraction | \(\text{FF}=\frac{\text{GFR}}{\text{RPF}}\) | Normal ≈ 0.2. |
| Free water clearance | \(C_{H_2O}=\dot V - C_{osm}\) | Sign shows dilute vs concentrated urine. |
| Henderson–Hasselbalch | \(\mathrm{pH}=6.1+\log\frac{[\mathrm{HCO_3^-}]}{0.03\,P_{aCO_2}}\) | Lungs (CO\(_2\)) vs kidneys (HCO\(_3^-\)). |
| Winter’s | \(P_{aCO_2}^{\,\mathrm{exp}}=1.5[\mathrm{HCO_3^-}]+8\pm2\) | Expected compensation in metabolic acidosis. |
| Starling filtration | \(J_v=K_f[(P_c-P_i)-\sigma(\pi_c-\pi_i)]\) | Capillary vs interstitial pressures & oncotic forces. |
| Dose–response | \(E=\frac{E_{max}[A]}{EC_{50}+[A]}\) | Spare receptors shift left. |
| Curve / Diagram | What it shows | Shift / Interpretation |
|---|---|---|
| Left ventricular PV loop | Isovolumic lines, ejection, filling; stroke work = area | ↑Preload → wider loop; ↑Afterload → higher ESP line, lower SV; ↑Contractility → steeper ESPVR, ↑SV at same preload. |
| Starling (ventricular function) | SV/CO vs EDV/RAP | Positive inotropy shifts up; HF shifts down; venoconstriction ↑ preload (moves along curve). |
| Venous return curve | VR vs RAP; intercept = mean systemic filling pressure | ↑Blood volume/venoconstriction → curve up/right; ↑TPR flattens slope. |
| Hb–O\(_2\) dissociation | Sat vs \(P_{O_2}\); sigmoid from cooperativity | Right shift (↑T, ↑H\(^+\), ↑2,3-BPG, ↑CO\(_2\)); Left shift (↓T, ↓H\(^+\), CO, fetal Hb). |
| Compliance curves (lung/chest wall) | Volume vs pressure | Emphysema ↑ compliance; fibrosis ↓. FRC at lung+chest wall equilibrium. |
| Spirometry loops | Obstructive vs restrictive patterns | Obstructive: scooped expiratory limb (↓FEV\(_1\)/FVC); restrictive: small but similar shape (FEV\(_1\)/FVC normal/high). |
| V/Q distribution | Base > apex for both V and Q; V/Q↑ at apex | Dead space (V/Q→∞): PE; shunt (V/Q→0): consolidation/oedema. O\(_2\) fixes dead space better than shunt. |
| Glucose titration (renal) | Filtered, reabsorbed, excreted vs \(P_{glc}\) | Splay between threshold and T\(_m\); glucosuria when filtered load > T\(_m\). |
| Endocrine dose–response | Effect vs ligand concentration | Affinity (EC\(_{50}\)) shifts curve left/right; efficacy alters \(E_{max}\); competitive antagonists shift right. |
🧑🏫 Exam hack: State the axis labels, normal landmarks, then describe a single parameter change (preload/afterload/contractility or compliance) and its effect on the curve.
↑Afterload (narrow valve) → steeper ESP line, higher systolic pressure, ↓SV (narrower loop). Concentric LVH ↑ end-systolic volume; often preserved EF early with elevated pressures → systolic murmur + slow upstroke pulse.
Obstructive: ↓FEV\(_1\) > ↓FVC → ↓FEV\(_1\)/FVC; ↑TLC/RV (air-trapping). Restrictive: ↓FEV\(_1\) & ↓FVC proportionally → normal or ↑ ratio; ↓TLC.
\(A\!-\!a = P_{AO_2}-P_{aO_2}\). Normal increases with age; ↑ in diffusion/VQ mismatch/shunt. 100% O\(_2\) improves V/Q mismatch but not shunt (bypassed alveoli).
| Feature | Pre-renal | Intrinsic (ATN) |
|---|---|---|
| Urine Na\(^+\) | <20 mmol/L | >40 mmol/L |
| FeNa | <1% | >2% |
| Osmolality | >500 mOsm/kg | <350 mOsm/kg |
| Urine sediment | Bland | Granular “muddy brown” casts |
Final thought: Physiology is cause-and-effect. Name the variable, the controller, and the effector, then use the right equation - the answer usually writes itself. 💪