{"id":106,"date":"2019-04-24T12:39:34","date_gmt":"2019-04-24T12:39:34","guid":{"rendered":"https:\/\/sepia2.unil.ch\/pharmacology\/?page_id=106"},"modified":"2020-09-04T03:12:30","modified_gmt":"2020-09-04T03:12:30","slug":"volumeofdistribution","status":"publish","type":"page","link":"https:\/\/sepia2.unil.ch\/pharmacology\/parameters\/volumeofdistribution\/","title":{"rendered":"Volume of Distribution"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\"> &#8220;Fluid volume that would be required to contain the amount of drug  present in the body at the same concentration as in the plasma&#8221;<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Description<\/h3>\n\n\n\n<p>According to its definition the volume of \ndistribution (abbreviated Vd) is not a physical space, but a dilution \nspace, or in other words an apparent volume. Nevertheless, the volume of\n distribution of a drug gives information on its distribution in the \nbody.\n<\/p>\n\n\n\n<p>The Vd is calculated as the ratio of the dose \npresent in the body and its plasma concentration&nbsp; (see below, \n\u201cassessment\u201d), when the distribution of the drug between the tissues and\n the plasma is at equilibrium.\n<\/p>\n\n\n\n<p>Accordingly, a drug that accumulates in tissues as  e.g. fat tissue, will have a relatively low plasma concentration with  regard to the administered dose, and consequently, the calculated Vd  will be high. <\/p>\n\n\n\n<div class=\"wp-block-columns has-2-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p><\/p>\n<\/div>\n<\/div>\n\n\n\n<p>Typical liquid volumes are in % (in L for a man of 70 kg):<\/p>\n\n\n\n<table class=\"wp-block-table\"><tbody><tr><td>total water: &nbsp; <\/td><td>60% (50-80%)&nbsp; &nbsp;<\/td><td>42 L<\/td><\/tr><tr><td>intracellular volume: &nbsp; <\/td><td>40%<\/td><td>28L<\/td><\/tr><tr><td>extracellular volume: &nbsp; <\/td><td>20%<\/td><td>14L<\/td><\/tr><tr><td>plasma volume: &nbsp; <\/td><td>4%<\/td><td>3L<\/td><\/tr><tr><td>blood volume: &nbsp; <\/td><td>8%<\/td><td>5.5L<\/td><\/tr><\/tbody><\/table>\n\n\n\n<p><p class=\"hiddenTitle\">Chart Pharmacokinetics<\/p>\n<div>\n\n    <div id=\"chartContainer\">\n        <canvas id=\"chart\"><\/canvas>\n        <div class=\"\" id=\"divSliderContainer\"><\/div>\n    <\/div>\n\n    <script>\n\n        let chart;\n        let baseDataChartValues = [];\n        let dataChart = [];\n        let dataChartStoredValues = [];\n        let labelsChart = [];\n\n        let dose = 1000;\n        let baseDose = 1000;\n\n        let mDose = 1000;\n        let baseMDose = 1000;\n\n        let tau = 6;\n        let baseTau = 6;\n\n        let vd = 50;\n        let baseVd = 50;\n\n        let cl = 10;\n        let baseCl = 10;\n\n        let f = 0.7;\n        let baseF = 0.7;\n\n        let ka = 1.5;\n        let tH;\n\n        const maxTime = 20;\n\n        function getPlasmaConcentration(h) {\n            let formulaPlasmaConcentration = (dose*f*ka\/(vd*(ka-cl\/vd))*(Math.exp(-cl\/vd*h)));\n\n            return formulaPlasmaConcentration;\n        }\n\n        \/*\n         *\n         * t1\/2 = ln(2) * (volume of distribution \/ clearance)\n         *\n         *\/\n        function getHalfLife() {\n            tH = Math.log(2)*(vd\/cl);\n            return (Math.round(tH * 100) \/ 100);\n        }\n\n        function updateSlider(updateStored = false) {\n            dataChart = [];\n            if(updateStored) dataChartStoredValues = [];\n\n            for(let i = 0; i <= maxTime; i++) {\n                let concentration = getPlasmaConcentration(i);\n                dataChart.push(concentration);\n                if(updateStored) dataChartStoredValues.push(concentration);\n            }\n\n            chart.data.datasets[0].data = dataChart;\n            chart.data.datasets[1].data = dataChartStoredValues;\n\n            $( \"#slider-f\" ).slider( \"option\", \"value\", vd);\n            chart.update();\n        }\n\n        let sliderF = '<div id=\"slider-f\" class=\"sliderRange\">' +\n                            '<span id=\"custom-handle-f\" class=\"ui-slider-handle customHandle\"><\/span>' +\n                            '<span class=\"spanUnit\" id=\"\">Vd<\/span>' +\n                        '<\/div>';\n\n        $('#divSliderContainer').append(sliderF);\n\n\n   \n\n        $(function() {\n\n            let handle = $('#custom-handle-f');\n\n            $( \"#slider-f\" ).slider({\n                orientation: \"vertical\",\n                range: \"true\",\n                min: 7,\n                max: 200,\n                step: 0.1,\n                value: vd,\n                create: function() {\n                    handle.text( $( this ).slider( \"value\" ) );\n                },\n                slide: function( event, ui ) {\n                    vd = ui.value;\n                    handle.text( ui.value );\n                    updateSlider();\n                }\n            });\n        });\n\n        Chart.pluginService.register({\n            beforeInit: function(chart) {\n\n                for(let i = 0; i <= maxTime; i++) {\n                    labelsChart.push(i);\n                    dataChart.push(getPlasmaConcentration(i));\n\n                    dataChartStoredValues = dataChart;\n                    baseDataChartValues = dataChart;\n                }\n\n            }\n        });\n\n        chart = new Chart(document.getElementById(\"chart\"), {\n            type: 'line',\n            data: {\n                labels: labelsChart,\n                datasets: [{\n                    label: \"Plasma Concentration\",\n                    data: dataChart,\n                    borderColor: colorDatasetMain.borderColor,\n                    fillColor: colorDatasetMain.fillColor,\n                    strokeColor: colorDatasetMain.strokeColor,\n                    highlightFill: colorDatasetMain.highlightFill,\n                    highlightStroke: colorDatasetMain.highlightStroke,\n                    borderWidth: \"1\",\n                    pointRadius: 0,\n                    fill: false\n                }, {\n                    label: \"Plasma Concentration\",\n                    data: dataChartStoredValues,\n                    borderColor: colorDatasetStored.borderColor,\n                    fillColor: colorDatasetStored.fillColor,\n                    strokeColor: colorDatasetStored.strokeColor,\n                    highlightFill: colorDatasetStored.highlightFill,\n                    highlightStroke: colorDatasetStored.highlightStroke,\n                    borderWidth: \"1\",\n                    pointRadius: 0,\n                    fill: false\n                }]\n            },\n            options: {\n                scales: {\n                    xAxes: [{\n                        scaleLabel: {\n                            display: true,\n                            labelString: 'H [hour]'\n                        }\n                    }],\n                    yAxes: [{\n                        scaleLabel: {\n                            display: true,\n                            labelString: 'C [mg\/l]'\n                        }\n                    }]\n                },\n                responsive: true,\n                maintainAspectRatio: false\n            }\n        });\n\n    <\/script>\n\n<\/div><\/p>\n\n\n\n<p>Drugs  with a very small Vd (&lt;10 L) are mainly confined to the  intravascular fluid, thus the blood, corresponding to roughly twice the  plasma volume. This may occur for two reason :<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>The molecule is too large to leave this compartment.<\/li><li>The\n molecule binds preferably to plasma proteins (e.g. to albumin) and much\n less to tissue proteins. Competition for plasma protein binding sites \ncan occur between such drugs or with endogenous substances.<\/li><\/ol>\n\n\n\n<p>Some\n drugs cannot enter cells because of their low lipid solubility. These \ndrugs are distributed throughout the body water in the extracellular \ncompartment and have a relatively small Vd (12-20 L).\n<\/p>\n\n\n\n<p>Drugs that accumulate in organs either by active \ntransport or by specific binding to tissue molecules have a high volume \nof distribution, which can exceed several times the anatomical body \nvolume. Therefore, Vd should not be identified too closely with a \nparticular anatomical compartment. Lipid-soluble drugs are stored in \nfat. Bone is a reservoir for drugs such as tetracycline and heavy \nmetals.\n<\/p>\n\n\n\n<p>The figure below shows values of Vd for different drugs (click on the image to visualise an enlarged version):<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><a href=\"https:\/\/sepia2.unil.ch\/pharmacology\/index.php?eID=tx_cms_showpic&amp;file=uploads%2Fpics%2FVd.jpg&amp;md5=6f77b7fe58bb47febbe6705ae94994f63af827c2&amp;parameters[0]=YTo0OntzOjU6IndpZHRoIjtzOjQ6IjgwMG0iO3M6NjoiaGVpZ2h0IjtzOjQ6IjYw&amp;parameters[1]=MG0iO3M6NzoiYm9keVRhZyI7czo0MToiPGJvZHkgc3R5bGU9Im1hcmdpbjowOyBi&amp;parameters[2]=YWNrZ3JvdW5kOiNmZmY7Ij4iO3M6NDoid3JhcCI7czozNzoiPGEgaHJlZj0iamF2&amp;parameters[3]=YXNjcmlwdDpjbG9zZSgpOyI%2BIHwgPC9hPiI7fQ%3D%3D\"><img decoding=\"async\" src=\"https:\/\/sepia2.unil.ch\/pharmacology\/typo3temp\/pics\/bcf2f973dd.jpg\" alt=\"\"\/><\/a><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"161\" height=\"300\" src=\"https:\/\/sepia2.unil.ch\/pharmacology\/wp-content\/uploads\/2020\/09\/45a5cdbccb-161x300.jpg\" alt=\"\" class=\"wp-image-1287\" srcset=\"https:\/\/sepia2.unil.ch\/pharmacology\/wp-content\/uploads\/2020\/09\/45a5cdbccb-161x300.jpg 161w, https:\/\/sepia2.unil.ch\/pharmacology\/wp-content\/uploads\/2020\/09\/45a5cdbccb.jpg 322w\" sizes=\"auto, (max-width: 161px) 100vw, 161px\" \/><\/figure><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Clinical implications<\/h3>\n\n\n\n<p>The volume of distribution is useful in  estimating the dose required to achieve a given plasma concentration as A  = C \u00b7Vd, with A = amount of drug in the body ( \u2248  dose, shortly after  administration) and C = plasma concentration. <\/p>\n\n\n\n<p>Variation of Vd mainly affects the peak plasma \nconcentration of the drug. This is important when peak plasma \nconcentration is essential for the therapeutic effect (e.g. hypnotics). \nDrug dosage must be adapted to the Vd for such drugs. \n<\/p>\n\n\n\n<p>Vd varies with individual height and weight. The \nmost important causes of variation of Vd are accumulation of fat (for \nlipid-soluble drugs) such as for obese patients, or accumulation of \nfluids (for water-soluble drugs) such as ascites, edema or pleural \neffusion. As the proportion of each body compartment varies with age, so\n does the Vd for most drugs.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Assessment<\/h3>\n\n\n\n<div class=\"wp-block-blocks-latex-block-latex\"><script type=\"text\/x-mathjax-config\">   MathJax.Hub.Config({tex2jax: {inlineMath: [['$','$'], ['\\\\(','\\\\)']]}}); <\/script> <p class=\"formula\">$$Vd = {A \\over C}$$<\/p><p class=\"formula\"><\/div>\n\n\n\n<p><strong>A<\/strong> = amount of drug in the body <\/p>\n\n\n\n<p><strong>C<\/strong> = plasma concentration<\/p>\n\n\n\n<p>Most importantly, the Vd is determined in \nconditions under which the drug distribution between the plasma and the \ntissues is at equilibrium.\n<\/p>\n\n\n\n<p>The Vd is commonly determined as shown below, after injection as an iv bolus. As can be appreciated from the description of the <a href=\"\/pharmacology\/distributioneliminationphase\">distribution and elimination&nbsp;phases<\/a>\n (see corresponding figure), the distribution of the drug between the \nplasma and the tissues is at an equilibrium, when the elimination phase \nis reached.<\/p>\n\n\n\n<p>The extrapolated plasma concentration at time 0, \nC(0), is back-extrapolated from the slope of the elimination phase of \nthe semilogarithmic  plasma concentration vs. time  decay curve (see \nfigure in <a href=\"\/pharmacology\/distributioneliminationphase\">Distribution and elimination phases<\/a>\n ). C(0) corresponds to the plasma concentration at time 0, if the \ndistribution of the injected drug had been immediate. The amount of drug\n in the body at time 0 equals the dose administered. Therefore the \nfollowing equation can be applied:\n<\/p>\n\n\n\n<div class=\"wp-block-blocks-latex-block-latex\"><script type=\"text\/x-mathjax-config\">   MathJax.Hub.Config({tex2jax: {inlineMath: [['$','$'], ['\\\\(','\\\\)']]}}); <\/script> <p class=\"formula\">$$Vd = {D \\over C(0)}$$<\/p><p class=\"formula\"><\/div>\n\n\n\n<p><strong>D<\/strong> = dose <\/p>\n\n\n\n<p><strong>C(0)<\/strong> = extrapolated plasma concentration at time 0 <\/p>\n","protected":false},"excerpt":{"rendered":"<p>&#8220;Fluid volume that would be required to contain the amount of drug present in the body at the same concentration as in the plasma&#8221; Description According to its definition the volume of distribution (abbreviated Vd) is not a physical space, but a dilution space, or in other words an apparent volume. Nevertheless, the volume of &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/sepia2.unil.ch\/pharmacology\/parameters\/volumeofdistribution\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Volume of Distribution&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":7,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-106","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sepia2.unil.ch\/pharmacology\/wp-json\/wp\/v2\/pages\/106","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sepia2.unil.ch\/pharmacology\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sepia2.unil.ch\/pharmacology\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sepia2.unil.ch\/pharmacology\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sepia2.unil.ch\/pharmacology\/wp-json\/wp\/v2\/comments?post=106"}],"version-history":[{"count":27,"href":"https:\/\/sepia2.unil.ch\/pharmacology\/wp-json\/wp\/v2\/pages\/106\/revisions"}],"predecessor-version":[{"id":1293,"href":"https:\/\/sepia2.unil.ch\/pharmacology\/wp-json\/wp\/v2\/pages\/106\/revisions\/1293"}],"up":[{"embeddable":true,"href":"https:\/\/sepia2.unil.ch\/pharmacology\/wp-json\/wp\/v2\/pages\/7"}],"wp:attachment":[{"href":"https:\/\/sepia2.unil.ch\/pharmacology\/wp-json\/wp\/v2\/media?parent=106"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}