{"id":37337,"date":"2026-08-23T10:10:34","date_gmt":"2026-08-23T04:40:34","guid":{"rendered":"https:\/\/atsixty.com\/?p=37337"},"modified":"2026-08-23T10:11:32","modified_gmt":"2026-08-23T04:41:32","slug":"pharmacokinetics-zero-first-the-order-of-elimination","status":"publish","type":"post","link":"https:\/\/atsixty.com\/index.php\/morning-rounds\/pharmacokinetics-zero-first-the-order-of-elimination\/","title":{"rendered":"Pharmacokinetics &#8211; Zero, First &amp; The Order of Elimination"},"content":{"rendered":"\n\n\n<!DOCTYPE html>\n<html lang=\"en\">\n<head>\n<meta charset=\"UTF-8\">\n<meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n<title>Morning Rounds \u00b7 Pharmacokinetics \u00b7 Round 01<\/title>\n<link href=\"https:\/\/fonts.googleapis.com\/css2?family=Playfair+Display:ital,wght@0,400;0,600;0,700;1,400;1,600&#038;family=Source+Serif+4:ital,wght@0,300;0,400;0,600;1,400&#038;display=swap\" rel=\"stylesheet\">\n<style>\n#npk01 *,#npk01 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.mr-stem{font-size:0.9rem}\n  #npk01 .mr-opt-text{font-size:0.86rem}\n}\n<\/style>\n\n<div id=\"npk01\">\n\n  <div class=\"mr-header\">\n    <div class=\"mr-series-tag\">Numerical Series &middot; Pharmacokinetics<\/div>\n    <div class=\"mr-eyebrow\">Morning Rounds &middot; Round 01 of 07<\/div>\n    <div class=\"mr-title\">Zero, First &amp;<br><em>The Order of Elimination<\/em><\/div>\n    <div class=\"mr-subtitle\">Five calculations &middot; Know your kinetics cold before the exam does<\/div>\n    <div class=\"mr-chips\">\n      <span class=\"mr-chip\">5 Questions<\/span>\n      <span class=\"mr-chip\">+4 \/ &minus;1 scoring<\/span>\n      <span class=\"mr-chip\">Options reshuffled<\/span>\n    <\/div>\n  <\/div>\n\n  <div class=\"mr-sentinel\" id=\"npk01-sentinel\"><\/div>\n\n  <div class=\"mr-progress\" id=\"npk01-progress\">\n    <div class=\"mr-prog-inner\">\n      <div class=\"mr-pips\" id=\"npk01-pips\"><\/div>\n    <\/div>\n  <\/div>\n\n  <div class=\"mr-body\">\n    <div id=\"npk01-cases\"><\/div>\n    <div class=\"mr-submit-wrap\">\n      <button class=\"mr-btn\" id=\"npk01-submit\">Submit for Debrief<\/button>\n    <\/div>\n    <div class=\"mr-score\" id=\"npk01-score\">\n      <div class=\"mr-score-in\">\n        <div class=\"mr-score-ey\">Round Complete<\/div>\n        <div class=\"mr-ring\" id=\"npk01-ring\">\n          <div class=\"mr-ring-in\">\n            <span class=\"mr-ring-pct\" id=\"npk01-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=\"npk01-net\"><\/div>\n        <div class=\"mr-verdict\" id=\"npk01-verdict\"><\/div>\n        <div class=\"mr-bands\">\n          <span class=\"mr-band mr-band-c\" id=\"npk01-ct-c\"><\/span>\n          <span class=\"mr-band mr-band-w\" id=\"npk01-ct-w\"><\/span>\n          <span class=\"mr-band mr-band-s\" id=\"npk01-ct-s\"><\/span>\n        <\/div>\n        <button class=\"mr-retry\" id=\"npk01-retry\">&#8635; New Round<\/button>\n      <\/div>\n    <\/div>\n  <\/div>\n\n<\/div>\n\n<script>\n(function () {\n  'use strict';\n\n  var NS    = 'npk01';\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: 'First-Order Kinetics &mdash; Three Half-Lives',\n      stem: 'A drug follows first-order elimination kinetics. What proportion of the drug is eliminated from the body after <strong>three half-lives<\/strong>?',\n      correct: '87.5%',\n      opts: [\n        '87.5%',\n        '75%',\n        '94%',\n        '12.5%'\n      ],\n      exp: 'In first-order kinetics, a <strong>fixed fraction<\/strong> (50%) is eliminated each half-life. Work it out step by step:<br><span class=\"calc\">After t&frac12; 1: 50% eliminated &rarr; 50% remains<br>After t&frac12; 2: 50% of 50% eliminated &rarr; 25% remains<br>After t&frac12; 3: 50% of 25% eliminated &rarr; 12.5% remains<\/span>So <strong>100% &minus; 12.5% = 87.5% eliminated<\/strong>. The trap answer 75% is what you get if you mistakenly add 25% per half-life (zero-order thinking). The residual 12.5% is what <em>remains<\/em>, not what is eliminated &mdash; a classic distractor.'\n    },\n\n    {\n      id: 2,\n      tag: 'Zero-Order Kinetics &mdash; Drug Remaining',\n      stem: '<strong>500 mg<\/strong> of a drug was administered to a patient. <strong>100 mg<\/strong> was cleared in the first hour. Assuming <strong>zero-order kinetics<\/strong>, how much drug remains after <strong>3 hours<\/strong>?',\n      correct: '200 mg',\n      opts: [\n        '200 mg',\n        '400 mg',\n        '300 mg',\n        '100 mg'\n      ],\n      exp: 'Zero-order kinetics: a <strong>constant amount<\/strong> is eliminated per unit time, regardless of concentration. Here, 100 mg\/hour is the fixed rate.<span class=\"calc\">Hour 1: 500 &minus; 100 = 400 mg remaining<br>Hour 2: 400 &minus; 100 = 300 mg remaining<br>Hour 3: 300 &minus; 100 = 200 mg remaining<\/span><strong>200 mg remains after 3 hours.<\/strong> Note: in first-order kinetics, the rate would have <em>slowed<\/em> as concentration fell. Zero-order is the exception &mdash; the enzyme or transporter is <strong>saturated<\/strong>, so rate stays flat. Classic examples: alcohol, phenytoin at high doses, aspirin in overdose.'\n    },\n\n    {\n      id: 3,\n      tag: 'First-Order Kinetics &mdash; Plasma Concentration',\n      stem: 'A drug follows first-order kinetics with a <strong>half-life of 4 hours<\/strong>. The initial plasma concentration is <strong>80 mg\/L<\/strong>. What will the plasma concentration be after <strong>12 hours<\/strong>?',\n      correct: '10 mg\/L',\n      opts: [\n        '10 mg\/L',\n        '20 mg\/L',\n        '5 mg\/L',\n        '40 mg\/L'\n      ],\n      exp: '12 hours = <strong>3 half-lives<\/strong> (12 &divide; 4 = 3). In first-order kinetics, concentration halves with each half-life:<span class=\"calc\">After 4 h (t&frac12; 1): 80 &divide; 2 = 40 mg\/L<br>After 8 h (t&frac12; 2): 40 &divide; 2 = 20 mg\/L<br>After 12 h (t&frac12; 3): 20 &divide; 2 = 10 mg\/L<\/span><strong>Answer: 10 mg\/L.<\/strong> Quick rule: after <em>n<\/em> half-lives, concentration = C<sub>0<\/sub> &times; (1\/2)<sup>n<\/sup>. Here: 80 &times; (1\/2)<sup>3<\/sup> = 80 &times; 1\/8 = <strong>10 mg\/L<\/strong>. The trap 20 mg\/L is after only 2 half-lives; 5 mg\/L would require 4 half-lives (16 hours).'\n    },\n\n    {\n      id: 4,\n      tag: 'First-Order Kinetics &mdash; Half-Life &amp; % Remaining',\n      stem: 'A drug has a <strong>half-life of 6 hours<\/strong> and follows first-order kinetics. What percentage of the drug <strong>remains<\/strong> in the body after <strong>24 hours<\/strong>?',\n      correct: '6.25%',\n      opts: [\n        '6.25%',\n        '12.5%',\n        '25%',\n        '3.125%'\n      ],\n      exp: '24 hours &divide; 6 hours per half-life = <strong>4 half-lives<\/strong>.<span class=\"calc\">After t&frac12; 1 (6 h):  50% remains<br>After t&frac12; 2 (12 h): 25% remains<br>After t&frac12; 3 (18 h): 12.5% remains<br>After t&frac12; 4 (24 h): 6.25% remains<\/span><strong>6.25% remains.<\/strong> Shortcut: (1\/2)<sup>4<\/sup> = 1\/16 = 0.0625 = <strong>6.25%<\/strong>. The trap 12.5% is after only 3 half-lives (18 h); 3.125% would require 5 half-lives (30 h). A useful anchor: after <strong>4&ndash;5 half-lives, &ge;94% is eliminated<\/strong> &mdash; this is the clinical definition of drug washout.'\n    },\n\n    {\n      id: 5,\n      tag: 'Zero-Order Kinetics &mdash; Fixed Elimination Rate',\n      stem: 'A drug following <strong>zero-order kinetics<\/strong> is administered as an infusion at <strong>50 mg\/hour<\/strong>. If the infusion is stopped after <strong>4 hours<\/strong>, how much drug has been <strong>eliminated<\/strong> during that period?',\n      correct: '200 mg',\n      opts: [\n        '200 mg',\n        '150 mg',\n        '100 mg',\n        '250 mg'\n      ],\n      exp: 'In zero-order kinetics, the elimination rate is <strong>constant<\/strong> and independent of concentration. The drug is eliminated at exactly 50 mg\/hour regardless of how much is present.<span class=\"calc\">Eliminated = Rate &times; Time<br>= 50 mg\/hr &times; 4 hr = <strong>200 mg<\/strong><\/span>This is the defining feature of zero-order kinetics: <strong>linear elimination over time<\/strong>, not exponential. Contrast with first-order: if this were first-order, the rate would slow as concentration fell, and the total eliminated in 4 hours would be less than 200 mg. Zero-order saturation kinetics are clinically dangerous &mdash; small dose increases cause disproportionate rises in plasma concentration.'\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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