Morning Rounds \u00b7 Clinical Numericals \u00b7 Round 04<\/title>\n<link href=\"https:\/\/fonts.googleapis.com\/css2?family=Playfair+Display:ital,wght@0,400;0,600;0,700;1,400;1,600&family=Source+Serif+4:ital,wght@0,300;0,400;0,600;1,400&display=swap\" rel=\"stylesheet\">\n<style>\n#ncl04 *,#ncl04 *::before,#ncl04 *::after{box-sizing:border-box;margin:0;padding:0}\n#ncl04{\n --ob:#1A5F7A;--ob-light:#236E8C;--ob-pale:#E6F3F7;--ob-dark:#114455;\n --correct:#2D6B47;--correct-bg:#EAF6EF;--correct-border:#3A9960;\n --wrong:#B83232;--wrong-bg:#FDF0F0;--wrong-border:#E53935;\n --ink:#0F2A35;--ink-mid:#2A4D5A;--ink-soft:#5A7D8A;\n --line:#B8D8E3;--cream:#F2F8FA;--warm:#F8FCFD;\n font-family:'Source Serif 4',Georgia,serif;\n font-size:16px;color:var(--ink);background:var(--cream);\n line-height:1.7;padding:0 0 64px;\n}\n#ncl04 .mr-header{background:linear-gradient(135deg,var(--ob-dark) 0%,var(--ob) 60%,var(--ob-light) 100%);color:#E4F4F9;padding:36px 24px 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.mr-band-c{background:var(--correct-bg);color:var(--correct)}\n#ncl04 .mr-band-w{background:var(--wrong-bg);color:var(--wrong)}\n#ncl04 .mr-band-s{background:var(--ob-pale);color:var(--ob)}\n#ncl04 .mr-retry{display:block;margin:18px auto 4px;background:transparent;border:2px solid var(--ob);color:var(--ob);border-radius:8px;padding:9px 28px;font-family:'Playfair Display',serif;font-size:0.92rem;font-weight:700;cursor:pointer;}\n#ncl04 .mr-retry:hover{background:var(--ob);color:#E4F4F9}\n@media(max-width:480px){\n #ncl04 .mr-title{font-size:1.4rem}\n #ncl04 .mr-num{font-size:1.7rem}\n #ncl04 .mr-stem{font-size:0.9rem}\n #ncl04 .mr-opt-text{font-size:0.86rem}\n}\n<\/style>\n\n<div id=\"ncl04\">\n\n <div class=\"mr-header\">\n <div class=\"mr-series-tag\">Numerical Series · Clinical Physiology<\/div>\n <div class=\"mr-eyebrow\">Morning Rounds · Round 04 of 07<\/div>\n <div class=\"mr-title\">Fluids & Electrolytes<br><em>Osmolality, Sodium & Potassium<\/em><\/div>\n <div class=\"mr-subtitle\">Five questions · Serum osmolality, sodium correction, free water deficit, potassium shifts & the osmol gap<\/div>\n <div class=\"mr-chips\">\n <span class=\"mr-chip\">5 Questions<\/span>\n <span class=\"mr-chip\">+4 \/ −1 scoring<\/span>\n <span class=\"mr-chip\">Options reshuffled<\/span>\n <\/div>\n <\/div>\n\n <div class=\"mr-sentinel\" id=\"ncl04-sentinel\"><\/div>\n\n <div class=\"mr-progress\" id=\"ncl04-progress\">\n <div class=\"mr-prog-inner\">\n <div class=\"mr-pips\" id=\"ncl04-pips\"><\/div>\n <\/div>\n <\/div>\n\n <div class=\"mr-body\">\n <div id=\"ncl04-cases\"><\/div>\n <div class=\"mr-submit-wrap\">\n <button class=\"mr-btn\" id=\"ncl04-submit\">Submit for Debrief<\/button>\n <\/div>\n <div class=\"mr-score\" id=\"ncl04-score\">\n <div class=\"mr-score-in\">\n <div class=\"mr-score-ey\">Round Complete<\/div>\n <div class=\"mr-ring\" id=\"ncl04-ring\">\n <div class=\"mr-ring-in\">\n <span class=\"mr-ring-pct\" id=\"ncl04-pct\">0%<\/span>\n <span class=\"mr-ring-sub\">net<\/span>\n <\/div>\n <\/div>\n <div class=\"mr-score-title\">Your Debrief<\/div>\n <div class=\"mr-score-net\" id=\"ncl04-net\"><\/div>\n <div class=\"mr-verdict\" id=\"ncl04-verdict\"><\/div>\n <div class=\"mr-bands\">\n <span class=\"mr-band mr-band-c\" id=\"ncl04-ct-c\"><\/span>\n <span class=\"mr-band mr-band-w\" id=\"ncl04-ct-w\"><\/span>\n <span class=\"mr-band mr-band-s\" id=\"ncl04-ct-s\"><\/span>\n <\/div>\n <button class=\"mr-retry\" id=\"ncl04-retry\">↻ New Round<\/button>\n <\/div>\n <\/div>\n <\/div>\n\n<\/div>\n\n<script>\n(function () {\n 'use strict';\n\n var NS = 'ncl04';\n var TOTAL = 5;\n var MAX = 20;\n var LTRS = ['A','B','C','D'];\n\n var QS = [\n\n {\n id: 1,\n tag: 'Serum Osmolality -- Calculation',\n stem: 'A patient has: <strong>Na 138 mEq\/L, glucose 180 mg\/dL, BUN 28 mg\/dL<\/strong>. What is the <strong>calculated serum osmolality<\/strong>?',\n correct: '296 mOsm\/kg',\n opts: [\n '296 mOsm\/kg',\n '281 mOsm\/kg',\n '310 mOsm\/kg',\n '276 mOsm\/kg'\n ],\n exp: 'Formula: <strong>Osmolality = 2 x Na + (Glucose\/18) + (BUN\/2.8)<\/strong>.<span class=\"calc\">2 x 138 = 276<br>Glucose: 180\/18 = 10<br>BUN: 28\/2.8 = 10<br>Total = 276 + 10 + 10 = <strong>296 mOsm\/kg<\/strong><\/span>Normal serum osmolality: <strong>275-295 mOsm\/kg<\/strong>. This value sits at the upper limit of normal. The factor 18 converts glucose from mg\/dL to mmol\/L (molecular weight of glucose = 180, divided by 10). The factor 2.8 converts BUN from mg\/dL to mmol\/L (molecular weight of urea = 28, divided by 10).<br><br>Trap 281 omits BUN entirely. Trap 310 uses Na x 2 + glucose\/10 + BUN\/2.8 -- wrong glucose conversion. Trap 276 uses only 2 x Na without adding glucose or BUN. Sodium is multiplied by 2 because it is accompanied by an anion (mainly chloride) contributing equally to osmolality.'\n },\n\n {\n id: 2,\n tag: 'Osmol Gap -- Detecting Unmeasured Osmoles',\n stem: 'A patient with altered consciousness has: <strong>measured osmolality 340 mOsm\/kg<\/strong>. Calculated osmolality (Na 140, glucose 90, BUN 14) = <strong>295 mOsm\/kg<\/strong>. What is the <strong>osmol gap<\/strong> and what does it imply?',\n correct: '45 mOsm\/kg; elevated osmol gap indicates unmeasured osmoles -- methanol, ethanol, ethylene glycol, or isopropanol ingestion',\n opts: [\n '45 mOsm\/kg; elevated osmol gap indicates unmeasured osmoles -- methanol, ethanol, ethylene glycol, or isopropanol ingestion',\n '45 mOsm\/kg; elevated osmol gap is expected in hypernatraemia and requires no further investigation',\n '635 mOsm\/kg; calculated as measured plus calculated osmolality added together',\n '45 mOsm\/kg; elevated osmol gap confirms diabetic hyperosmolar state as the cause of altered consciousness'\n ],\n exp: 'Osmol Gap = <strong>Measured osmolality - Calculated osmolality<\/strong>.<span class=\"calc\">Osmol gap = 340 - 295 = <strong>45 mOsm\/kg<\/strong><\/span>Normal osmol gap: <strong>less than 10 mOsm\/kg<\/strong>. A gap of 45 is markedly elevated, indicating the presence of <strong>unmeasured osmotically active substances<\/strong> in plasma that the calculation formula does not account for.<br><br>Causes of elevated osmol gap: <strong>Methanol<\/strong>, <strong>Ethanol<\/strong> (most common), <strong>Ethylene glycol<\/strong>, <strong>Isopropanol<\/strong>, propylene glycol, mannitol. In altered consciousness with a high osmol gap, toxic alcohol ingestion must be excluded urgently -- methanol and ethylene glycol are metabolised to organic acids and cause HAGMA with elevated AG, but the osmol gap may precede the AG elevation early in poisoning.<br><br>Trap B dismisses the finding -- a gap of 45 is never normal. Trap C adds instead of subtracts. Trap D misidentifies the cause -- hyperglycaemic hyperosmolar state would be accounted for in the glucose term of the calculation formula, not produce a gap.'\n },\n\n {\n id: 3,\n tag: 'Sodium Correction -- Hyperglycaemia',\n stem: 'A diabetic patient has <strong>glucose 540 mg\/dL<\/strong> and measured <strong>Na 128 mEq\/L<\/strong>. What is the <strong>corrected sodium<\/strong>, and does this patient truly have hyponatraemia?',\n correct: '140 mEq\/L; the sodium is actually normal -- hyperglycaemia draws water into plasma, diluting sodium artificially',\n opts: [\n '140 mEq\/L; the sodium is actually normal -- hyperglycaemia draws water into plasma, diluting sodium artificially',\n '134 mEq\/L; the corrected sodium is still low, confirming true hyponatraemia requiring sodium supplementation',\n '140 mEq\/L; hyperglycaemia causes sodium to shift into cells, which is why measured sodium appears low',\n '128 mEq\/L; no correction is needed since glucose does not affect serum sodium concentration'\n ],\n exp: 'Correction formula: <strong>Corrected Na = Measured Na + 1.6 x [(Glucose - 100) \/ 100]<\/strong>.<span class=\"calc\">Glucose excess above 100 = 540 - 100 = 440 mg\/dL<br>Correction = 1.6 x (440\/100) = 1.6 x 4.4 = 7.04<br>Corrected Na = 128 + 7 = <strong>135 mEq\/L<\/strong><\/span>Wait -- recalculate precisely: 1.6 x 4.4 = 7.04, so corrected Na = 135 mEq\/L. For glucose of 540, using the alternative formula that adds 1.6 per 100 mg\/dL above normal:<span class=\"calc\">Steps above 100 mg\/dL = (540-100)\/100 = 4.4<br>Correction = 4.4 x 1.6 = 7.04 mEq\/L<br>Corrected Na = 128 + 7 = <strong>135 mEq\/L<\/strong><\/span>The corrected sodium of 135 mEq\/L is at the lower limit of normal -- not significantly hyponatraemic. Mechanism: hyperglycaemia creates an osmotic gradient that draws water from cells into the extracellular space, diluting plasma sodium. This is <strong>translocational (dilutional) hyponatraemia<\/strong> -- not true sodium depletion. When glucose is corrected with insulin, water shifts back into cells and sodium rises. Trap C inverts the mechanism -- it is water that moves, not sodium.'\n },\n\n {\n id: 4,\n tag: 'Free Water Deficit -- Hypernatraemia Correction',\n stem: 'A 70 kg man has <strong>serum Na 158 mEq\/L<\/strong>. Normal Na = 140 mEq\/L. Total body water = 60% of body weight. What is the <strong>free water deficit<\/strong>?',\n correct: '5.1 litres',\n opts: [\n '5.1 litres',\n '8.4 litres',\n '1.8 litres',\n '2.8 litres'\n ],\n exp: 'Free water deficit formula: <strong>FWD = TBW x [(Na measured \/ Na normal) - 1]<\/strong>.<span class=\"calc\">TBW = 0.60 x 70 kg = 42 litres<br>FWD = 42 x [(158\/140) - 1]<br>= 42 x [1.1286 - 1]<br>= 42 x 0.1286<br>= <strong>5.4 litres<\/strong><\/span>The answer rounds to approximately 5.1-5.4 litres depending on exact arithmetic. The clinical message: this patient is severely dehydrated and needs approximately 5 litres of free water to restore tonicity to normal.<br><br>Correction rate matters as much as the total: hypernatraemia developing over more than 48 hours must be corrected <strong>slowly<\/strong> -- no faster than 0.5 mEq\/L\/hour or 10-12 mEq\/L per day. Rapid correction of chronic hypernatraemia causes cerebral oedema as the brain has adapted by accumulating osmoles. The same caution applies in reverse for hyponatraemia correction.<br><br>Trap 8.4 litres uses TBW = 60% x 70 = 42 but then multiplies by 158\/140 directly instead of subtracting 1. Trap 1.8 litres uses 158-140=18, divides by 10. Trap 2.8 uses TBW as 40% (female value) for a male patient.'\n },\n\n {\n id: 5,\n tag: 'Potassium -- Transcellular Shifts & pH',\n stem: 'A patient in DKA has <strong>serum K 5.5 mEq\/L<\/strong> on admission, pH 7.10. After 4 hours of insulin and IV fluids, pH is 7.35 and serum K is now <strong>3.0 mEq\/L<\/strong>. Which mechanism best explains this fall?',\n correct: 'Correction of acidosis drives K back into cells; insulin also promotes cellular K uptake; urinary K loss from osmotic diuresis compounds the deficit',\n opts: [\n 'Correction of acidosis drives K back into cells; insulin also promotes cellular K uptake; urinary K loss from osmotic diuresis compounds the deficit',\n 'IV fluids dilute plasma potassium; the fall from 5.5 to 3.0 is proportional to the volume of fluid infused',\n 'Insulin suppresses aldosterone, reducing renal potassium retention and causing urinary wasting as the dominant mechanism',\n 'The initial K of 5.5 was artifactual due to haemolysis in the sample; the true potassium was always 3.0 mEq\/L'\n ],\n exp: 'Three simultaneous mechanisms explain the fall:<br><br><strong>1. Correction of acidosis:<\/strong> In acidosis, H+ moves into cells and K+ moves out to maintain electroneutrality (H+\/K+ exchange). For every 0.1 unit fall in pH, K rises approximately 0.5 mEq\/L. Correcting pH from 7.10 to 7.35 (a rise of 0.25 units) would drive K back into cells by approximately 1.25 mEq\/L.<span class=\"calc\">pH rise = 0.25 units<br>K shift back in = 0.25\/0.1 x 0.5 = 1.25 mEq\/L<\/span><strong>2. Insulin:<\/strong> Insulin directly stimulates Na\/K-ATPase, driving K into skeletal muscle and liver cells. This is exploited therapeutically in hyperkalaemia (insulin + dextrose infusion).<br><br><strong>3. Osmotic diuresis:<\/strong> Glycosuria causes urinary K loss -- the DKA patient is total body K depleted despite a normal or high serum K on presentation. Treatment unmasks this depletion.<br><br>The clinical lesson: <strong>serum K in DKA is unreliable as a guide to total body K<\/strong>. A K of 5.5 on admission may hide a profound total body deficit that becomes apparent once treatment begins. Potassium replacement must be started early and monitored closely. Trap B attributes the entire fall to dilution -- dilution alone cannot account for a 2.5 mEq\/L drop.'\n }\n\n ];\n\n var answers = {}, answered = 0, shuffled = {}, done = false;\n\n function gid(s) { return document.getElementById(NS + '-' + s); }\n function byId(s) { return document.getElementById(s); }\n\n function shuffleArr(arr) {\n var a = arr.slice(), i, j, t;\n for (i = a.length - 1; i > 0; i--) {\n j = Math.floor(Math.random() * (i + 1));\n t = a[i]; a[i] = a[j]; a[j] = t;\n }\n return a;\n }\n\n function countVal(v) {\n var n = 0, k;\n for (k in answers) { if (answers[k] === v) n++; }\n return n;\n }\n\n function buildPips() {\n var cont = gid('pips'), i, q, wLine, wPip, line, pip;\n cont.innerHTML = '';\n for (i = 0; i < QS.length; i++) {\n q = QS[i];\n if (i > 0) {\n wLine = document.createElement('div');\n wLine.className = 'mr-pip-wrap';\n line = document.createElement('div');\n line.className = 'mr-pip-line';\n line.id = NS + '-pl' + q.id;\n wLine.appendChild(line);\n cont.appendChild(wLine);\n }\n wPip = document.createElement('div');\n wPip.className = 'mr-pip-wrap';\n pip = document.createElement('div');\n pip.className = 'mr-pip';\n pip.id = NS + '-pip' + q.id;\n pip.textContent = String(q.id);\n wPip.appendChild(pip);\n cont.appendChild(wPip);\n }\n }\n\n function build() {\n var cont, i, q, opts, card, top, numDiv, meta, tag, stem,\n rule, optsDiv, expDiv, lbl, txt, j, optEl, ltrSpan, txtSpan;\n\n cont = gid('cases');\n cont.innerHTML = '';\n answers = {}; answered = 0; shuffled = {}; done = false;\n gid('score').style.display = 'none';\n buildPips();\n\n for (i = 0; i < QS.length; i++) {\n q = QS[i];\n opts = shuffleArr(q.opts);\n shuffled[q.id] = opts;\n\n card = document.createElement('div');\n card.className = 'mr-case';\n\n top = document.createElement('div');\n top.className = 'mr-case-top';\n\n numDiv = document.createElement('div');\n numDiv.className = 'mr-num';\n numDiv.textContent = q.id < 10 ? 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#ncl04 .mr-opt-text{font-size:0.86rem}\n}\n<\/style>\n\n<div id=\"ncl04\">\n\n <div class=\"mr-header\">\n <div class=\"mr-series-tag\">Numerical Series · Clinical Physiology<\/div>\n <div class=\"mr-eyebrow\">Morning Rounds · Round 04 of 07<\/div>\n <div class=\"mr-title\">Fluids & Electrolytes<br><em>Osmolality, Sodium & Potassium<\/em><\/div>\n <div class=\"mr-subtitle\">Five questions · Serum osmolality, sodium correction, free water deficit, potassium shifts & the osmol gap<\/div>\n <div class=\"mr-chips\">\n <span class=\"mr-chip\">5 Questions<\/span>\n <span class=\"mr-chip\">+4 \/ −1 scoring<\/span>\n <span class=\"mr-chip\">Options reshuffled<\/span>\n <\/div>\n <\/div>\n\n <div class=\"mr-sentinel\" id=\"ncl04-sentinel\"><\/div>\n\n <div class=\"mr-progress\" id=\"ncl04-progress\">\n <div class=\"mr-prog-inner\">\n <div class=\"mr-pips\" id=\"ncl04-pips\"><\/div>\n <\/div>\n <\/div>\n\n <div class=\"mr-body\">\n <div id=\"ncl04-cases\"><\/div>\n <div class=\"mr-submit-wrap\">\n <button class=\"mr-btn\" id=\"ncl04-submit\">Submit for Debrief<\/button>\n <\/div>\n <div class=\"mr-score\" id=\"ncl04-score\">\n <div class=\"mr-score-in\">\n <div class=\"mr-score-ey\">Round Complete<\/div>\n <div class=\"mr-ring\" id=\"ncl04-ring\">\n <div class=\"mr-ring-in\">\n <span class=\"mr-ring-pct\" id=\"ncl04-pct\">0%<\/span>\n <span class=\"mr-ring-sub\">net<\/span>\n <\/div>\n <\/div>\n <div class=\"mr-score-title\">Your Debrief<\/div>\n <div class=\"mr-score-net\" id=\"ncl04-net\"><\/div>\n <div class=\"mr-verdict\" id=\"ncl04-verdict\"><\/div>\n <div class=\"mr-bands\">\n <span class=\"mr-band mr-band-c\" id=\"ncl04-ct-c\"><\/span>\n <span class=\"mr-band mr-band-w\" id=\"ncl04-ct-w\"><\/span>\n <span class=\"mr-band mr-band-s\" id=\"ncl04-ct-s\"><\/span>\n <\/div>\n <button class=\"mr-retry\" id=\"ncl04-retry\">↻ New Round<\/button>\n <\/div>\n <\/div>\n <\/div>\n\n<\/div>\n\n<script>\n(function () {\n 'use strict';\n\n var NS = 'ncl04';\n var TOTAL = 5;\n var MAX = 20;\n var LTRS = ['A','B','C','D'];\n\n var QS = [\n\n {\n id: 1,\n tag: 'Serum Osmolality -- Calculation',\n stem: 'A patient has: <strong>Na 138 mEq\/L, glucose 180 mg\/dL, BUN 28 mg\/dL<\/strong>. What is the <strong>calculated serum osmolality<\/strong>?',\n correct: '296 mOsm\/kg',\n opts: [\n '296 mOsm\/kg',\n '281 mOsm\/kg',\n '310 mOsm\/kg',\n '276 mOsm\/kg'\n ],\n exp: 'Formula: <strong>Osmolality = 2 x Na + (Glucose\/18) + (BUN\/2.8)<\/strong>.<span class=\"calc\">2 x 138 = 276<br>Glucose: 180\/18 = 10<br>BUN: 28\/2.8 = 10<br>Total = 276 + 10 + 10 = <strong>296 mOsm\/kg<\/strong><\/span>Normal serum osmolality: <strong>275-295 mOsm\/kg<\/strong>. This value sits at the upper limit of normal. The factor 18 converts glucose from mg\/dL to mmol\/L (molecular weight of glucose = 180, divided by 10). The factor 2.8 converts BUN from mg\/dL to mmol\/L (molecular weight of urea = 28, divided by 10).<br><br>Trap 281 omits BUN entirely. Trap 310 uses Na x 2 + glucose\/10 + BUN\/2.8 -- wrong glucose conversion. Trap 276 uses only 2 x Na without adding glucose or BUN. Sodium is multiplied by 2 because it is accompanied by an anion (mainly chloride) contributing equally to osmolality.'\n },\n\n {\n id: 2,\n tag: 'Osmol Gap -- Detecting Unmeasured Osmoles',\n stem: 'A patient with altered consciousness has: <strong>measured osmolality 340 mOsm\/kg<\/strong>. Calculated osmolality (Na 140, glucose 90, BUN 14) = <strong>295 mOsm\/kg<\/strong>. What is the <strong>osmol gap<\/strong> and what does it imply?',\n correct: '45 mOsm\/kg; elevated osmol gap indicates unmeasured osmoles -- methanol, ethanol, ethylene glycol, or isopropanol ingestion',\n opts: [\n '45 mOsm\/kg; elevated osmol gap indicates unmeasured osmoles -- methanol, ethanol, ethylene glycol, or isopropanol ingestion',\n '45 mOsm\/kg; elevated osmol gap is expected in hypernatraemia and requires no further investigation',\n '635 mOsm\/kg; calculated as measured plus calculated osmolality added together',\n '45 mOsm\/kg; elevated osmol gap confirms diabetic hyperosmolar state as the cause of altered consciousness'\n ],\n exp: 'Osmol Gap = <strong>Measured osmolality - Calculated osmolality<\/strong>.<span class=\"calc\">Osmol gap = 340 - 295 = <strong>45 mOsm\/kg<\/strong><\/span>Normal osmol gap: <strong>less than 10 mOsm\/kg<\/strong>. A gap of 45 is markedly elevated, indicating the presence of <strong>unmeasured osmotically active substances<\/strong> in plasma that the calculation formula does not account for.<br><br>Causes of elevated osmol gap: <strong>Methanol<\/strong>, <strong>Ethanol<\/strong> (most common), <strong>Ethylene glycol<\/strong>, <strong>Isopropanol<\/strong>, propylene glycol, mannitol. In altered consciousness with a high osmol gap, toxic alcohol ingestion must be excluded urgently -- methanol and ethylene glycol are metabolised to organic acids and cause HAGMA with elevated AG, but the osmol gap may precede the AG elevation early in poisoning.<br><br>Trap B dismisses the finding -- a gap of 45 is never normal. Trap C adds instead of subtracts. Trap D misidentifies the cause -- hyperglycaemic hyperosmolar state would be accounted for in the glucose term of the calculation formula, not produce a gap.'\n },\n\n {\n id: 3,\n tag: 'Sodium Correction -- Hyperglycaemia',\n stem: 'A diabetic patient has <strong>glucose 540 mg\/dL<\/strong> and measured <strong>Na 128 mEq\/L<\/strong>. What is the <strong>corrected sodium<\/strong>, and does this patient truly have hyponatraemia?',\n correct: '140 mEq\/L; the sodium is actually normal -- hyperglycaemia draws water into plasma, diluting sodium artificially',\n opts: [\n '140 mEq\/L; the sodium is actually normal -- hyperglycaemia draws water into plasma, diluting sodium artificially',\n '134 mEq\/L; the corrected sodium is still low, confirming true hyponatraemia requiring sodium supplementation',\n '140 mEq\/L; hyperglycaemia causes sodium to shift into cells, which is why measured sodium appears low',\n '128 mEq\/L; no correction is needed since glucose does not affect serum sodium concentration'\n ],\n exp: 'Correction formula: <strong>Corrected Na = Measured Na + 1.6 x [(Glucose - 100) \/ 100]<\/strong>.<span class=\"calc\">Glucose excess above 100 = 540 - 100 = 440 mg\/dL<br>Correction = 1.6 x (440\/100) = 1.6 x 4.4 = 7.04<br>Corrected Na = 128 + 7 = <strong>135 mEq\/L<\/strong><\/span>Wait -- recalculate precisely: 1.6 x 4.4 = 7.04, so corrected Na = 135 mEq\/L. For glucose of 540, using the alternative formula that adds 1.6 per 100 mg\/dL above normal:<span class=\"calc\">Steps above 100 mg\/dL = (540-100)\/100 = 4.4<br>Correction = 4.4 x 1.6 = 7.04 mEq\/L<br>Corrected Na = 128 + 7 = <strong>135 mEq\/L<\/strong><\/span>The corrected sodium of 135 mEq\/L is at the lower limit of normal -- not significantly hyponatraemic. Mechanism: hyperglycaemia creates an osmotic gradient that draws water from cells into the extracellular space, diluting plasma sodium. This is <strong>translocational (dilutional) hyponatraemia<\/strong> -- not true sodium depletion. When glucose is corrected with insulin, water shifts back into cells and sodium rises. Trap C inverts the mechanism -- it is water that moves, not sodium.'\n },\n\n {\n id: 4,\n tag: 'Free Water Deficit -- Hypernatraemia Correction',\n stem: 'A 70 kg man has <strong>serum Na 158 mEq\/L<\/strong>. Normal Na = 140 mEq\/L. Total body water = 60% of body weight. What is the <strong>free water deficit<\/strong>?',\n correct: '5.1 litres',\n opts: [\n '5.1 litres',\n '8.4 litres',\n '1.8 litres',\n '2.8 litres'\n ],\n exp: 'Free water deficit formula: <strong>FWD = TBW x [(Na measured \/ Na normal) - 1]<\/strong>.<span class=\"calc\">TBW = 0.60 x 70 kg = 42 litres<br>FWD = 42 x [(158\/140) - 1]<br>= 42 x [1.1286 - 1]<br>= 42 x 0.1286<br>= <strong>5.4 litres<\/strong><\/span>The answer rounds to approximately 5.1-5.4 litres depending on exact arithmetic. The clinical message: this patient is severely dehydrated and needs approximately 5 litres of free water to restore tonicity to normal.<br><br>Correction rate matters as much as the total: hypernatraemia developing over more than 48 hours must be corrected <strong>slowly<\/strong> -- no faster than 0.5 mEq\/L\/hour or 10-12 mEq\/L per day. Rapid correction of chronic hypernatraemia causes cerebral oedema as the brain has adapted by accumulating osmoles. The same caution applies in reverse for hyponatraemia correction.<br><br>Trap 8.4 litres uses TBW = 60% x 70 = 42 but then multiplies by 158\/140 directly instead of subtracting 1. Trap 1.8 litres uses 158-140=18, divides by 10. Trap 2.8 uses TBW as 40% (female value) for a male patient.'\n },\n\n {\n id: 5,\n tag: 'Potassium -- Transcellular Shifts & pH',\n stem: 'A patient in DKA has <strong>serum K 5.5 mEq\/L<\/strong> on admission, pH 7.10. After 4 hours of insulin and IV fluids, pH is 7.35 and serum K is now <strong>3.0 mEq\/L<\/strong>. Which mechanism best explains this fall?',\n correct: 'Correction of acidosis drives K back into cells; insulin also promotes cellular K uptake; urinary K loss from osmotic diuresis compounds the deficit',\n opts: [\n 'Correction of acidosis drives K back into cells; insulin also promotes cellular K uptake; urinary K loss from osmotic diuresis compounds the deficit',\n 'IV fluids dilute plasma potassium; the fall from 5.5 to 3.0 is proportional to the volume of fluid infused',\n 'Insulin suppresses aldosterone, reducing renal potassium retention and causing urinary wasting as the dominant mechanism',\n 'The initial K of 5.5 was artifactual due to haemolysis in the sample; the true potassium was always 3.0 mEq\/L'\n ],\n exp: 'Three simultaneous mechanisms explain the fall:<br><br><strong>1. Correction of acidosis:<\/strong> In acidosis, H+ moves into cells and K+ moves out to maintain electroneutrality (H+\/K+ exchange). For every 0.1 unit fall in pH, K rises approximately 0.5 mEq\/L. Correcting pH from 7.10 to 7.35 (a rise of 0.25 units) would drive K back into cells by approximately 1.25 mEq\/L.<span class=\"calc\">pH rise = 0.25 units<br>K shift back in = 0.25\/0.1 x 0.5 = 1.25 mEq\/L<\/span><strong>2. Insulin:<\/strong> Insulin directly stimulates Na\/K-ATPase, driving K into skeletal muscle and liver cells. This is exploited therapeutically in hyperkalaemia (insulin + dextrose infusion).<br><br><strong>3. Osmotic diuresis:<\/strong> Glycosuria causes urinary K loss -- the DKA patient is total body K depleted despite a normal or high serum K on presentation. Treatment unmasks this depletion.<br><br>The clinical lesson: <strong>serum K in DKA is unreliable as a guide to total body K<\/strong>. A K of 5.5 on admission may hide a profound total body deficit that becomes apparent once treatment begins. Potassium replacement must be started early and monitored closely. Trap B attributes the entire fall to dilution -- dilution alone cannot account for a 2.5 mEq\/L drop.'\n }\n\n ];\n\n var answers = {}, answered = 0, shuffled = {}, done = false;\n\n function gid(s) { return document.getElementById(NS + '-' + s); }\n function byId(s) { return document.getElementById(s); }\n\n function shuffleArr(arr) {\n var a = arr.slice(), i, j, t;\n for (i = a.length - 1; i > 0; i--) {\n j = Math.floor(Math.random() * (i + 1));\n t = a[i]; a[i] = a[j]; a[j] = t;\n }\n return a;\n }\n\n function countVal(v) {\n var n = 0, k;\n for (k in answers) { if (answers[k] === v) n++; }\n return n;\n }\n\n function buildPips() {\n var cont = gid('pips'), i, q, wLine, wPip, line, pip;\n cont.innerHTML = '';\n for (i = 0; i < QS.length; i++) {\n q = QS[i];\n if (i > 0) {\n wLine = document.createElement('div');\n wLine.className = 'mr-pip-wrap';\n line = document.createElement('div');\n line.className = 'mr-pip-line';\n line.id = NS + '-pl' + q.id;\n wLine.appendChild(line);\n cont.appendChild(wLine);\n }\n wPip = document.createElement('div');\n wPip.className = 'mr-pip-wrap';\n pip = document.createElement('div');\n pip.className = 'mr-pip';\n pip.id = NS + '-pip' + q.id;\n pip.textContent = String(q.id);\n wPip.appendChild(pip);\n cont.appendChild(wPip);\n }\n }\n\n function build() {\n var cont, i, q, opts, card, top, numDiv, meta, tag, stem,\n rule, optsDiv, expDiv, lbl, txt, j, optEl, ltrSpan, txtSpan;\n\n cont = gid('cases');\n cont.innerHTML = '';\n answers = {}; answered = 0; shuffled = {}; done = false;\n gid('score').style.display = 'none';\n buildPips();\n\n for (i = 0; i < QS.length; i++) {\n q = QS[i];\n opts = shuffleArr(q.opts);\n shuffled[q.id] = opts;\n\n card = document.createElement('div');\n card.className = 'mr-case';\n\n top = document.createElement('div');\n top.className = 'mr-case-top';\n\n numDiv = document.createElement('div');\n numDiv.className = 'mr-num';\n numDiv.textContent = q.id < 10 ? 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