Morning Rounds \u00b7 Clinical Numericals \u00b7 Round 02<\/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#ncl02 *,#ncl02 *::before,#ncl02 *::after{box-sizing:border-box;margin:0;padding:0}\n#ncl02{\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#ncl02 .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#ncl02 .mr-band-w{background:var(--wrong-bg);color:var(--wrong)}\n#ncl02 .mr-band-s{background:var(--ob-pale);color:var(--ob)}\n#ncl02 .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#ncl02 .mr-retry:hover{background:var(--ob);color:#E4F4F9}\n@media(max-width:480px){\n #ncl02 .mr-title{font-size:1.4rem}\n #ncl02 .mr-num{font-size:1.7rem}\n #ncl02 .mr-stem{font-size:0.9rem}\n #ncl02 .mr-opt-text{font-size:0.86rem}\n}\n<\/style>\n\n<div id=\"ncl02\">\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 02 of 07<\/div>\n <div class=\"mr-title\">ABG Interpretation<br><em>& Compensation Formulae<\/em><\/div>\n <div class=\"mr-subtitle\">Five questions · Identify the disorder, calculate expected compensation & spot the mixed picture<\/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=\"ncl02-sentinel\"><\/div>\n\n <div class=\"mr-progress\" id=\"ncl02-progress\">\n <div class=\"mr-prog-inner\">\n <div class=\"mr-pips\" id=\"ncl02-pips\"><\/div>\n <\/div>\n <\/div>\n\n <div class=\"mr-body\">\n <div id=\"ncl02-cases\"><\/div>\n <div class=\"mr-submit-wrap\">\n <button class=\"mr-btn\" id=\"ncl02-submit\">Submit for Debrief<\/button>\n <\/div>\n <div class=\"mr-score\" id=\"ncl02-score\">\n <div class=\"mr-score-in\">\n <div class=\"mr-score-ey\">Round Complete<\/div>\n <div class=\"mr-ring\" id=\"ncl02-ring\">\n <div class=\"mr-ring-in\">\n <span class=\"mr-ring-pct\" id=\"ncl02-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=\"ncl02-net\"><\/div>\n <div class=\"mr-verdict\" id=\"ncl02-verdict\"><\/div>\n <div class=\"mr-bands\">\n <span class=\"mr-band mr-band-c\" id=\"ncl02-ct-c\"><\/span>\n <span class=\"mr-band mr-band-w\" id=\"ncl02-ct-w\"><\/span>\n <span class=\"mr-band mr-band-s\" id=\"ncl02-ct-s\"><\/span>\n <\/div>\n <button class=\"mr-retry\" id=\"ncl02-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 = 'ncl02';\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: 'Respiratory Acidosis — Identification & Compensation',\n stem: 'ABG: <strong>pH 7.28, PaCO&sub2; 60 mmHg, HCO&sub3;− 28 mEq\/L<\/strong>. Identify the primary disorder and determine whether compensation is appropriate.',\n correct: 'Acute-on-chronic respiratory acidosis with appropriate renal compensation; HCO3 rise of 4 mEq\/L per 10 mmHg CO2 rise fits chronic pattern',\n opts: [\n 'Acute-on-chronic respiratory acidosis with appropriate renal compensation; HCO3 rise of 4 mEq\/L per 10 mmHg CO2 rise fits chronic pattern',\n 'Primary metabolic alkalosis with respiratory compensation; the elevated HCO3 is the primary driver',\n 'Acute respiratory acidosis with appropriate compensation; HCO3 rise of 1 mEq\/L per 10 mmHg CO2 fits the acute formula',\n 'Mixed respiratory acidosis and metabolic alkalosis; the HCO3 is higher than expected for pure respiratory acidosis'\n ],\n exp: 'Step 1 — identify primary disorder: pH <7.4 = acidosis. PaCO&sub2; = 60 (high) → respiratory acidosis.<br>Step 2 — calculate expected compensation:<span class=\"calc\">Acute: HCO&sub3;− rises 1 mEq\/L per 10 mmHg ↑CO&sub2;<br>CO&sub2; rise = 60−40 = 20 mmHg → acute HCO&sub3; = 24+2 = 26 mEq\/L<br><br>Chronic: HCO&sub3;− rises 3.5 mEq\/L per 10 mmHg ↑CO&sub2;<br>CO&sub2; rise = 20 mmHg → chronic HCO&sub3; = 24+7 = 31 mEq\/L<\/span>Actual HCO&sub3; = 28 mEq\/L — between acute (26) and chronic (31). This pattern = <strong>acute-on-chronic respiratory acidosis<\/strong>: a patient with chronic CO&sub2; retention (COPD) who has acutely decompensated. The kidney has had time to retain some HCO&sub3; but not reach full chronic compensation.<br><br>Trap C says HCO&sub3; rise of 1 fits acute — the acute formula gives 26, but actual is 28, so it is not purely acute. Trap D calls it mixed respiratory acidosis + metabolic alkalosis — the HCO&sub3; of 28 is not high enough to represent an independent metabolic alkalosis; it sits within the compensation range.'\n },\n\n {\n id: 2,\n tag: 'Metabolic Acidosis — Winter\\'s Formula',\n stem: 'ABG: <strong>pH 7.20, PaCO&sub2; 24 mmHg, HCO&sub3;− 9 mEq\/L<\/strong>. Is respiratory compensation appropriate?',\n correct: 'Yes; expected PaCO2 by Winter\\'s formula = 9\u00d71.5+8 = 21.5, range 19.5\u201323.5; measured 24 is within range',\n opts: [\n 'Yes; expected PaCO2 by Winter\\'s formula = 9\\u00d71.5+8 = 21.5, range 19.5\\u201323.5; measured 24 is within range',\n 'No; the PaCO2 of 24 is too high, indicating a superimposed respiratory acidosis',\n 'Yes; expected PaCO2 = HCO3 \\u00d7 1.5 = 13.5 mmHg; the measured 24 indicates over-compensation',\n 'No; respiratory compensation in metabolic acidosis should reduce PaCO2 to equal the HCO3 numerically'\n ],\n exp: \"<strong>Winter's formula<\/strong>: Expected PaCO&sub2; = (HCO&sub3;− × 1.5) + 8 ± 2.<span class=\\\"calc\\\">Expected PaCO&sub2; = (9 × 1.5) + 8 = 13.5 + 8 = <strong>21.5 mmHg<\/strong><br>Acceptable range: 19.5 – 23.5 mmHg<br>Measured PaCO&sub2; = 24 mmHg — borderline but within range<\/span>Compensation is appropriate. The lungs are hyperventilating to blow off CO&sub2; in response to metabolic acidosis. If measured PaCO&sub2; > expected range: <strong>superimposed respiratory acidosis<\/strong> (lungs can't compensate fully). If < expected range: <strong>superimposed respiratory alkalosis<\/strong> (lungs are over-driving).<br><br>This is one of the highest-yield ABG formulae. Metabolic acidosis is the only disorder where a simple formula (×1.5+8) gives expected compensation. The ±2 range acknowledges biological variability. Trap C omits the +8 step — without it, the expected value (13.5) would make 24 appear as a separate respiratory acidosis. Trap D invents a rule that PaCO&sub2; should numerically equal HCO&sub3; — no such rule exists.\"\n },\n\n {\n id: 3,\n tag: 'Metabolic Alkalosis — Respiratory Compensation',\n stem: 'ABG: <strong>pH 7.52, PaCO&sub2; 48 mmHg, HCO&sub3;− 38 mEq\/L<\/strong>. A patient has been vomiting for 3 days. Is the respiratory compensation appropriate?',\n correct: 'Yes; expected PaCO2 rises 0.7 mmHg per 1 mEq\/L rise in HCO3; rise of 14 mEq\/L predicts PaCO2 of 49.8 mmHg; measured 48 is appropriate',\n opts: [\n 'Yes; expected PaCO2 rises 0.7 mmHg per 1 mEq\/L rise in HCO3; rise of 14 mEq\/L predicts PaCO2 of 49.8 mmHg; measured 48 is appropriate',\n 'No; PaCO2 of 48 is too low, indicating a superimposed respiratory alkalosis reducing the pH towards normal',\n 'Yes; in metabolic alkalosis the lung compensates by hyperventilating, reducing PaCO2 below 40 mmHg',\n 'No; the degree of hypoventilation is excessive and indicates a concurrent respiratory acidosis'\n ],\n exp: 'Step 1: pH >7.4 = alkalosis. HCO&sub3; = 38 (high) → primary metabolic alkalosis. Cause = vomiting (loss of HCl → relative HCO&sub3; excess).<br><br>Step 2 — expected respiratory compensation:<span class=\"calc\">Expected ↑PaCO&sub2; = 0.7 × (HCO&sub3;− − 24)<br>= 0.7 × (38 − 24)<br>= 0.7 × 14 = <strong>9.8 mmHg rise<\/strong><br>Expected PaCO&sub2; = 40 + 9.8 = <strong>49.8 mmHg<\/strong><\/span>Measured = 48 mmHg — appropriate compensation. The body <em>hypoventilates<\/em> in metabolic alkalosis to retain CO&sub2; and partially correct the alkalosis. This is counterintuitive — reduced breathing in a conscious patient is limited by hypoxic drive, so PaCO&sub2; rarely rises above 55–60 mmHg even in severe metabolic alkalosis.<br><br>Trap C is the classic misconception — the lung <em>hypoventilates<\/em> (retains CO&sub2;) in metabolic alkalosis, it does <em>not<\/em> hyperventilate. Hyperventilation would worsen the alkalosis. Trap B says PaCO&sub2; of 48 is too low — it is actually close to the expected value of 49.8.'\n },\n\n {\n id: 4,\n tag: 'Respiratory Alkalosis — Anxiety vs Compensation',\n stem: 'ABG: <strong>pH 7.52, PaCO&sub2; 28 mmHg, HCO&sub3;− 22 mEq\/L<\/strong>. The patient is anxious and hyperventilating. Is this acute or chronic respiratory alkalosis, and how can you tell?',\n correct: 'Acute; HCO3 falls 2 mEq\/L per 10 mmHg fall in PaCO2; CO2 drop of 12 mmHg predicts HCO3 of 21.6; measured 22 fits acute pattern',\n opts: [\n 'Acute; HCO3 falls 2 mEq\/L per 10 mmHg fall in PaCO2; CO2 drop of 12 mmHg predicts HCO3 of 21.6; measured 22 fits acute pattern',\n 'Chronic; HCO3 of 22 is below normal, confirming full renal compensation has occurred over days',\n 'Acute; the pH of 7.52 is too high for chronic compensation, which always normalises pH to 7.40',\n 'Chronic; HCO3 falls 5 mEq\/L per 10 mmHg fall in PaCO2; measured 22 fits chronic formula exactly'\n ],\n exp: 'Primary disorder: pH >7.4 = alkalosis. PaCO&sub2; = 28 (low) → respiratory alkalosis (hyperventilation).<br><br>Compensation formulae:<span class=\"calc\">Acute respiratory alkalosis:<br>HCO&sub3;− falls 2 mEq\/L per 10 mmHg ↓CO&sub2;<br>CO&sub2; fall = 40−28 = 12 mmHg → expected HCO&sub3; = 24 − 2.4 = <strong>21.6 mEq\/L<\/strong><br><br>Chronic respiratory alkalosis:<br>HCO&sub3;− falls 5 mEq\/L per 10 mmHg ↓CO&sub2;<br>Expected HCO&sub3; = 24 − 6 = <strong>18 mEq\/L<\/strong><\/span>Measured HCO&sub3; = 22 — matches acute formula (21.6), not chronic (18). Acute respiratory alkalosis: <strong>renal compensation has not yet occurred<\/strong> (kidneys take hours to days). This is consistent with acute anxiety hyperventilation.<br><br>Trap B says HCO&sub3; below normal confirms chronic — wrong; HCO&sub3; is only slightly below 24 and matches the acute pattern. Trap C uses a pH argument — chronic compensation reduces pH towards 7.40 but does not always normalise it fully. Trap D applies the chronic formula (falls 5) and gets 18, but measured is 22 — so it is not chronic.'\n },\n\n {\n id: 5,\n tag: 'Mixed Disorder — Spotting the Second Process',\n stem: 'ABG: <strong>pH 7.38, PaCO&sub2; 60 mmHg, HCO&sub3;− 34 mEq\/L<\/strong>. The patient has severe COPD. Is this simple chronic respiratory acidosis, or is there a mixed disorder?',\n correct: 'Mixed disorder: chronic respiratory acidosis plus metabolic alkalosis; expected HCO3 for CO2 of 60 is 31 mEq\/L but measured is 34, indicating an additional metabolic alkalosis',\n opts: [\n 'Mixed disorder: chronic respiratory acidosis plus metabolic alkalosis; expected HCO3 for CO2 of 60 is 31 mEq\/L but measured is 34, indicating an additional metabolic alkalosis',\n 'Simple chronic respiratory acidosis with full compensation; pH of 7.38 confirms the disorder is fully compensated',\n 'Mixed respiratory acidosis and metabolic acidosis; the near-normal pH masks two opposing processes',\n 'Simple chronic respiratory acidosis; HCO3 of 34 is within the expected compensation range for this degree of CO2 retention'\n ],\n exp: 'Step 1: pH = 7.38 (low-normal), PaCO&sub2; = 60 (high) → primary respiratory acidosis. HCO&sub3; = 34 (high) → compensation.<br><br>Step 2: Is the HCO&sub3; within expected range for chronic respiratory acidosis?<span class=\"calc\">Chronic respiratory acidosis:<br>HCO&sub3;− rises 3.5 mEq\/L per 10 mmHg ↑CO&sub2;<br>CO&sub2; rise = 60−40 = 20 mmHg<br>Expected HCO&sub3; = 24 + (3.5 × 2) = 24 + 7 = <strong>31 mEq\/L<\/strong><\/span>Measured HCO&sub3; = 34 — <strong>3 mEq\/L above expected<\/strong>. This excess HCO&sub3; represents a superimposed <strong>metabolic alkalosis<\/strong>. In COPD patients this commonly arises from loop diuretic use (furosemide → urinary loss of Cl and H&sup+; → contraction alkalosis).<br><br>The near-normal pH (7.38) is the red herring: two processes opposing each other (respiratory acidosis lowering pH, metabolic alkalosis raising it) can produce a deceptively normal-looking pH. Always calculate expected compensation — never assume normal pH means simple disorder. Trap B calls 7.38 \"fully compensated\" — true compensation rarely returns pH to 7.38; moreover the HCO&sub3; is higher than expected. Trap D accepts HCO&sub3; of 34 as within range — it is not; expected is 31.'\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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#ncl02 .mr-opt-text{font-size:0.86rem}\n}\n<\/style>\n\n<div id=\"ncl02\">\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 02 of 07<\/div>\n <div class=\"mr-title\">ABG Interpretation<br><em>& Compensation Formulae<\/em><\/div>\n <div class=\"mr-subtitle\">Five questions · Identify the disorder, calculate expected compensation & spot the mixed picture<\/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=\"ncl02-sentinel\"><\/div>\n\n <div class=\"mr-progress\" id=\"ncl02-progress\">\n <div class=\"mr-prog-inner\">\n <div class=\"mr-pips\" id=\"ncl02-pips\"><\/div>\n <\/div>\n <\/div>\n\n <div class=\"mr-body\">\n <div id=\"ncl02-cases\"><\/div>\n <div class=\"mr-submit-wrap\">\n <button class=\"mr-btn\" id=\"ncl02-submit\">Submit for Debrief<\/button>\n <\/div>\n <div class=\"mr-score\" id=\"ncl02-score\">\n <div class=\"mr-score-in\">\n <div class=\"mr-score-ey\">Round Complete<\/div>\n <div class=\"mr-ring\" id=\"ncl02-ring\">\n <div class=\"mr-ring-in\">\n <span class=\"mr-ring-pct\" id=\"ncl02-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=\"ncl02-net\"><\/div>\n <div class=\"mr-verdict\" id=\"ncl02-verdict\"><\/div>\n <div class=\"mr-bands\">\n <span class=\"mr-band mr-band-c\" id=\"ncl02-ct-c\"><\/span>\n <span class=\"mr-band mr-band-w\" id=\"ncl02-ct-w\"><\/span>\n <span class=\"mr-band mr-band-s\" id=\"ncl02-ct-s\"><\/span>\n <\/div>\n <button class=\"mr-retry\" id=\"ncl02-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 = 'ncl02';\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: 'Respiratory Acidosis — Identification & Compensation',\n stem: 'ABG: <strong>pH 7.28, PaCO&sub2; 60 mmHg, HCO&sub3;− 28 mEq\/L<\/strong>. Identify the primary disorder and determine whether compensation is appropriate.',\n correct: 'Acute-on-chronic respiratory acidosis with appropriate renal compensation; HCO3 rise of 4 mEq\/L per 10 mmHg CO2 rise fits chronic pattern',\n opts: [\n 'Acute-on-chronic respiratory acidosis with appropriate renal compensation; HCO3 rise of 4 mEq\/L per 10 mmHg CO2 rise fits chronic pattern',\n 'Primary metabolic alkalosis with respiratory compensation; the elevated HCO3 is the primary driver',\n 'Acute respiratory acidosis with appropriate compensation; HCO3 rise of 1 mEq\/L per 10 mmHg CO2 fits the acute formula',\n 'Mixed respiratory acidosis and metabolic alkalosis; the HCO3 is higher than expected for pure respiratory acidosis'\n ],\n exp: 'Step 1 — identify primary disorder: pH <7.4 = acidosis. PaCO&sub2; = 60 (high) → respiratory acidosis.<br>Step 2 — calculate expected compensation:<span class=\"calc\">Acute: HCO&sub3;− rises 1 mEq\/L per 10 mmHg ↑CO&sub2;<br>CO&sub2; rise = 60−40 = 20 mmHg → acute HCO&sub3; = 24+2 = 26 mEq\/L<br><br>Chronic: HCO&sub3;− rises 3.5 mEq\/L per 10 mmHg ↑CO&sub2;<br>CO&sub2; rise = 20 mmHg → chronic HCO&sub3; = 24+7 = 31 mEq\/L<\/span>Actual HCO&sub3; = 28 mEq\/L — between acute (26) and chronic (31). This pattern = <strong>acute-on-chronic respiratory acidosis<\/strong>: a patient with chronic CO&sub2; retention (COPD) who has acutely decompensated. The kidney has had time to retain some HCO&sub3; but not reach full chronic compensation.<br><br>Trap C says HCO&sub3; rise of 1 fits acute — the acute formula gives 26, but actual is 28, so it is not purely acute. Trap D calls it mixed respiratory acidosis + metabolic alkalosis — the HCO&sub3; of 28 is not high enough to represent an independent metabolic alkalosis; it sits within the compensation range.'\n },\n\n {\n id: 2,\n tag: 'Metabolic Acidosis — Winter\\'s Formula',\n stem: 'ABG: <strong>pH 7.20, PaCO&sub2; 24 mmHg, HCO&sub3;− 9 mEq\/L<\/strong>. Is respiratory compensation appropriate?',\n correct: 'Yes; expected PaCO2 by Winter\\'s formula = 9\u00d71.5+8 = 21.5, range 19.5\u201323.5; measured 24 is within range',\n opts: [\n 'Yes; expected PaCO2 by Winter\\'s formula = 9\\u00d71.5+8 = 21.5, range 19.5\\u201323.5; measured 24 is within range',\n 'No; the PaCO2 of 24 is too high, indicating a superimposed respiratory acidosis',\n 'Yes; expected PaCO2 = HCO3 \\u00d7 1.5 = 13.5 mmHg; the measured 24 indicates over-compensation',\n 'No; respiratory compensation in metabolic acidosis should reduce PaCO2 to equal the HCO3 numerically'\n ],\n exp: \"<strong>Winter's formula<\/strong>: Expected PaCO&sub2; = (HCO&sub3;− × 1.5) + 8 ± 2.<span class=\\\"calc\\\">Expected PaCO&sub2; = (9 × 1.5) + 8 = 13.5 + 8 = <strong>21.5 mmHg<\/strong><br>Acceptable range: 19.5 – 23.5 mmHg<br>Measured PaCO&sub2; = 24 mmHg — borderline but within range<\/span>Compensation is appropriate. The lungs are hyperventilating to blow off CO&sub2; in response to metabolic acidosis. If measured PaCO&sub2; > expected range: <strong>superimposed respiratory acidosis<\/strong> (lungs can't compensate fully). If < expected range: <strong>superimposed respiratory alkalosis<\/strong> (lungs are over-driving).<br><br>This is one of the highest-yield ABG formulae. Metabolic acidosis is the only disorder where a simple formula (×1.5+8) gives expected compensation. The ±2 range acknowledges biological variability. Trap C omits the +8 step — without it, the expected value (13.5) would make 24 appear as a separate respiratory acidosis. Trap D invents a rule that PaCO&sub2; should numerically equal HCO&sub3; — no such rule exists.\"\n },\n\n {\n id: 3,\n tag: 'Metabolic Alkalosis — Respiratory Compensation',\n stem: 'ABG: <strong>pH 7.52, PaCO&sub2; 48 mmHg, HCO&sub3;− 38 mEq\/L<\/strong>. A patient has been vomiting for 3 days. Is the respiratory compensation appropriate?',\n correct: 'Yes; expected PaCO2 rises 0.7 mmHg per 1 mEq\/L rise in HCO3; rise of 14 mEq\/L predicts PaCO2 of 49.8 mmHg; measured 48 is appropriate',\n opts: [\n 'Yes; expected PaCO2 rises 0.7 mmHg per 1 mEq\/L rise in HCO3; rise of 14 mEq\/L predicts PaCO2 of 49.8 mmHg; measured 48 is appropriate',\n 'No; PaCO2 of 48 is too low, indicating a superimposed respiratory alkalosis reducing the pH towards normal',\n 'Yes; in metabolic alkalosis the lung compensates by hyperventilating, reducing PaCO2 below 40 mmHg',\n 'No; the degree of hypoventilation is excessive and indicates a concurrent respiratory acidosis'\n ],\n exp: 'Step 1: pH >7.4 = alkalosis. HCO&sub3; = 38 (high) → primary metabolic alkalosis. Cause = vomiting (loss of HCl → relative HCO&sub3; excess).<br><br>Step 2 — expected respiratory compensation:<span class=\"calc\">Expected ↑PaCO&sub2; = 0.7 × (HCO&sub3;− − 24)<br>= 0.7 × (38 − 24)<br>= 0.7 × 14 = <strong>9.8 mmHg rise<\/strong><br>Expected PaCO&sub2; = 40 + 9.8 = <strong>49.8 mmHg<\/strong><\/span>Measured = 48 mmHg — appropriate compensation. The body <em>hypoventilates<\/em> in metabolic alkalosis to retain CO&sub2; and partially correct the alkalosis. This is counterintuitive — reduced breathing in a conscious patient is limited by hypoxic drive, so PaCO&sub2; rarely rises above 55–60 mmHg even in severe metabolic alkalosis.<br><br>Trap C is the classic misconception — the lung <em>hypoventilates<\/em> (retains CO&sub2;) in metabolic alkalosis, it does <em>not<\/em> hyperventilate. Hyperventilation would worsen the alkalosis. Trap B says PaCO&sub2; of 48 is too low — it is actually close to the expected value of 49.8.'\n },\n\n {\n id: 4,\n tag: 'Respiratory Alkalosis — Anxiety vs Compensation',\n stem: 'ABG: <strong>pH 7.52, PaCO&sub2; 28 mmHg, HCO&sub3;− 22 mEq\/L<\/strong>. The patient is anxious and hyperventilating. Is this acute or chronic respiratory alkalosis, and how can you tell?',\n correct: 'Acute; HCO3 falls 2 mEq\/L per 10 mmHg fall in PaCO2; CO2 drop of 12 mmHg predicts HCO3 of 21.6; measured 22 fits acute pattern',\n opts: [\n 'Acute; HCO3 falls 2 mEq\/L per 10 mmHg fall in PaCO2; CO2 drop of 12 mmHg predicts HCO3 of 21.6; measured 22 fits acute pattern',\n 'Chronic; HCO3 of 22 is below normal, confirming full renal compensation has occurred over days',\n 'Acute; the pH of 7.52 is too high for chronic compensation, which always normalises pH to 7.40',\n 'Chronic; HCO3 falls 5 mEq\/L per 10 mmHg fall in PaCO2; measured 22 fits chronic formula exactly'\n ],\n exp: 'Primary disorder: pH >7.4 = alkalosis. PaCO&sub2; = 28 (low) → respiratory alkalosis (hyperventilation).<br><br>Compensation formulae:<span class=\"calc\">Acute respiratory alkalosis:<br>HCO&sub3;− falls 2 mEq\/L per 10 mmHg ↓CO&sub2;<br>CO&sub2; fall = 40−28 = 12 mmHg → expected HCO&sub3; = 24 − 2.4 = <strong>21.6 mEq\/L<\/strong><br><br>Chronic respiratory alkalosis:<br>HCO&sub3;− falls 5 mEq\/L per 10 mmHg ↓CO&sub2;<br>Expected HCO&sub3; = 24 − 6 = <strong>18 mEq\/L<\/strong><\/span>Measured HCO&sub3; = 22 — matches acute formula (21.6), not chronic (18). Acute respiratory alkalosis: <strong>renal compensation has not yet occurred<\/strong> (kidneys take hours to days). This is consistent with acute anxiety hyperventilation.<br><br>Trap B says HCO&sub3; below normal confirms chronic — wrong; HCO&sub3; is only slightly below 24 and matches the acute pattern. Trap C uses a pH argument — chronic compensation reduces pH towards 7.40 but does not always normalise it fully. Trap D applies the chronic formula (falls 5) and gets 18, but measured is 22 — so it is not chronic.'\n },\n\n {\n id: 5,\n tag: 'Mixed Disorder — Spotting the Second Process',\n stem: 'ABG: <strong>pH 7.38, PaCO&sub2; 60 mmHg, HCO&sub3;− 34 mEq\/L<\/strong>. The patient has severe COPD. Is this simple chronic respiratory acidosis, or is there a mixed disorder?',\n correct: 'Mixed disorder: chronic respiratory acidosis plus metabolic alkalosis; expected HCO3 for CO2 of 60 is 31 mEq\/L but measured is 34, indicating an additional metabolic alkalosis',\n opts: [\n 'Mixed disorder: chronic respiratory acidosis plus metabolic alkalosis; expected HCO3 for CO2 of 60 is 31 mEq\/L but measured is 34, indicating an additional metabolic alkalosis',\n 'Simple chronic respiratory acidosis with full compensation; pH of 7.38 confirms the disorder is fully compensated',\n 'Mixed respiratory acidosis and metabolic acidosis; the near-normal pH masks two opposing processes',\n 'Simple chronic respiratory acidosis; HCO3 of 34 is within the expected compensation range for this degree of CO2 retention'\n ],\n exp: 'Step 1: pH = 7.38 (low-normal), PaCO&sub2; = 60 (high) → primary respiratory acidosis. HCO&sub3; = 34 (high) → compensation.<br><br>Step 2: Is the HCO&sub3; within expected range for chronic respiratory acidosis?<span class=\"calc\">Chronic respiratory acidosis:<br>HCO&sub3;− rises 3.5 mEq\/L per 10 mmHg ↑CO&sub2;<br>CO&sub2; rise = 60−40 = 20 mmHg<br>Expected HCO&sub3; = 24 + (3.5 × 2) = 24 + 7 = <strong>31 mEq\/L<\/strong><\/span>Measured HCO&sub3; = 34 — <strong>3 mEq\/L above expected<\/strong>. This excess HCO&sub3; represents a superimposed <strong>metabolic alkalosis<\/strong>. In COPD patients this commonly arises from loop diuretic use (furosemide → urinary loss of Cl and H&sup+; → contraction alkalosis).<br><br>The near-normal pH (7.38) is the red herring: two processes opposing each other (respiratory acidosis lowering pH, metabolic alkalosis raising it) can produce a deceptively normal-looking pH. Always calculate expected compensation — never assume normal pH means simple disorder. Trap B calls 7.38 \"fully compensated\" — true compensation rarely returns pH to 7.38; moreover the HCO&sub3; is higher than expected. Trap D accepts HCO&sub3; of 34 as within range — it is not; expected is 31.'\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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