hi today let us discuss the calculations on one compartment model what is one compartment model for example we have given the drug and this drug is going to be entering into the blood and from the blood drug can enter into the liver through the entró hepatic circulation so here the drug is going to be metabolized by the first pass effect again after the metabolism what are the drug that is unchanged and not metabolized within the labor that again reaches into the systemic circulation and what are the drug that is present in the system in circulation can be distributed into the various organs like the heart otherwise it can be reaching into the lungs or it can enter into the CNS based on the nature of the track so after the first pass metabolism the track is going to be distributed based on its Lippo Felicity and volume of distribution and finally the drug can also be entering into the kidney where it is going to be excreted within the urine so this is the fate of the drug that is going to be entering into the body if the distribution of the drug into the various organs is instantaneous then we can consider kindest of the drug as one compartment model that means that drug distribution into the various organs is very rapid and all the organs they present a single compartment then we can consider the kind X as one compartment model so today in this video we will see what are the kind is involved with the one compartment model and how we can solve you have the problems in the one compartment model if you liked this video please subscribe to our channel and post your comments in the comment box so compartment modeling is in hypothetical condition where we are thinking that that Wragge is going to be distribute into the different compartments according to the type of compartment model for example in one compartment model all the organs are collectively considered as single compartment so distribution of the drugs from the one organ to the other argonne is instantaneous and third one the drug is eliminated from the central compartment particularly in the one compartment model we have only one compartment and from that the drug is going to be eliminated so by taking these assumptions now we will see what are the Funko kind involved with the one compartment model X naught is the amount of the drug that is we are going to initially admit it into the body and now this drug is going to be entering into the single compartment where the amount of the drug can be indicated by XC and again the drug can be eliminated out of the body from the same compartment so this is a simple design of one compartment model and here we can also have an interface where the drug can be entered into the system exert elation through a barrier this barrier is nothing but the absorption phase the presence of absorption phase depends on the route of administration of the track if the drug is given by IV Road absorption phase is not present but if it is given by the extravascular Road we can observe the absorption phase so now if you see the kindest of compartment model we can discuss this kind X in three categories based on the route of administration like IV bolus administration or IV infusion or finally extravascular administration so in this video we will see mainly the IV route of administration where the drug can be given by as a bolus administration that is a single administration or by infusion that means continuous administration so let us go with the first one one compartment model IV bolus administration now the drug X naught is going to be admitted into the body where X is the amount of the drug that reads into the single compartment and then the drug is going to be eliminated since the drug is given by IV bolus administration that means the drug is given at a single dose which directly enters into the single compartment so there is no kinda Keys involved during the administration but the drug is going to be eliminated from the single compartment where the elimination of the drug depends on the elimination rate constant K now the elimination follows first-order kinetics so based on that the rate of elimination is minus DX by DT is equal to K into X so in a simple way one compartment model IV bolus administration follows first-order kinetics because there is no absorption here the kind X of the drug only depends on the elimination which follows the first-order kinetics now the equation for this one compartment model IV bolus can also be written as X is equal X naught into e to the power of minus K into T when we integrate the equation we will get this equation X is equal to X naught into e to the power of minus K into T what is X here X is the amount of the drug in the body at time T but actually we will measure the drug levels within the plasma as a concentration so this equation can also be converted into concentration terms where C is equal to C naught into e to the power of minus K into T C is the concentration of the drug in the body at time T how this is possible because we have 1 of parameter volume of distribution which is going to relate the amount of the drug in the body with the conservation of the drug in the body so we know this equation X is equal to VD into C where V is the volume of distribution so X is always directly proportional to concentration so amount of the drug in the plasma is directly proportional to the concentration of the drug in the plasma so based on that we can write C is equal to C naught into e to the power of minus K into T so this equation is sufficient to define the kind excel for drag in the one compartment model IV bolus administration so let us go with one working example and let us see how we can solve the problem working example one 500 mg of a drug is given by IV bolus administration and has shown the following funko kinetics calculate the concentration of the drug in the plasma after 4 hours so what are the equation given is C is equal to 20 into e to the power of minus 0.57 into T now what is this equation so just by seeing this equation we can see that this drug is going to follow the first order kinetics because it is just like the equation C is equal to C naught into e to the power of minus K into T so based on that we can draw what is C naught so from this equation we can call C naught is equal to 20 but what are the units we are always measuring the drug concentration in the plasma as microgram per ml so the what are the units are microgram per ml so C naught is equal to 20 microgram per ml and what is K k is equal to 0.57 and again what are the units because we are going to the time interval within the body in terms of ours so K will be 0.57 R inverse so this is the data that is given and we have to calculate the plasma concentration after 4 hours so let us go with the solution the solution to the working example 1 so whatever the data given is C naught is equal to 20 microgram per ml and K is equal to 0.57 R inverse so we have to calculate the C 4 that is what are the concentration of the drug in the plasma after 4 hours so which equation we had to use so this drug follows the first-order kinetics so C is equal to C naught into e to power of minus K into T but this is not convenient if we convert into the logarithmic form then T is equal to 2.303 by ke into log of C naught by C so by using this equation we can calculate what is a concentration of the drug in the plasma after 4 hours so here T is equal to the time interval that is for ours and K is equal to 0.57 and C naught is equal to 20 microgram per ml so by substituting all the values for is equal to 2 point 3 0 3 by 0.5 7 into log of 20 by C where 20 is the C naught and C is the water the concentration of the drug in the plasma after 4 hours which we have to calculate so now by solving this 2.303 by 0.5 7 will give 4.04 and which is then multiplied by log 20 by C otherwise log 20 by c is equal to 1 because 4 by 4.04 is approximately equal to 1 so log 20 by c is equal to 1 and if you take the antilog atom 20 by c is equal to 10 to the power of 1 otherwise 10 and then c is equal to 20 by 10 that is equal to 2 so concentration of the drug in the plasma after 4 hours is that - but what are the units since we have taken the units as microgram per ml so here again the same units will be applied so the conservation of the drug in the plasma after 4 hours are the 2 microgram per M let's go with an example from the above drug calculate half-life volume of distribution and what will be the time for the next dose if minimum plasma concentration is to be above the one microgram per ml that means we had to take that dad of the drug off in the previous question and we had to calculate the half-life volume of distribution and what is the next dosing interval so here first of all let us calculate the half-life we know the half-life T half is equal to 0.693 by ke so already we know the K value K is given as point 5 sine R inverse so we can directly substitute in this equation so T half is equal to 0.693 by 0.5 seven which gives the one point two two R so the given drug is having half-life of one point two two R similarly second one is a volume of distribution how we can calculate the volume of distribution how do we have seen one of the equation the X is equal to VD into C so this equation we can use to calculate the volume of distribution otherwise in a volume of distribution is equal to X naught by C naught so we know the X naught X naught is the amount of the drug initial we have administered into the body that is a 500 MZ and C naught C naught is the 20 microgram per ml and here you can observe that the units are not similar the X naught is in the mg but C naught is in the microgram so we can convert this microgram into the mg we know that 1 MZ is equal to thousand micrograms then we can simultaneously convert the ml into the later because you know again the 1 liter is equal mm mm so this 20 microgram per ml is nothing but the 20 mg per liter now the units are similar and we can apply this equation so volume of distribution VD is equal to 500 by 20 which is nothing but 25 liters so the track is hanging the 25 liters of volume of distribution now let us go with the calculation of the next dose that should be given to achieve a desired plasma concentration so here the initial concentration of the drug is 20 microgram per ml and what are the desired concentration is the one microgram per ml so that means the drug level should be always above the one microgram per ml now if we calculate what is the time required for this drug to reduce its consideration from the 20 microgram per ml to one microgram per ml we can easily assess what is the time required for the next dose so here we have to calculate what is the time for this reduction of the concentration from twenty to one microgram per ml so which equation we have to use again we can use the same equation T is equal to two point three zero three by K into log of C naught by C and here we have to calculate that T value so applying in this equation T is equal to two point three zero three by here K is already given as point five seven so by 0.5 seven into log of twenty by one twenty is the initial concentration and one is the final concentration 2.303 by 0.5 seven will gives the four point zero four already we have calculated and log 20 is nothing but of one point three zero one so now this is four point zero four into one point three zero one and finally if we calculate where you'll get five point two six hours that means this drug requires five point two six hours to reduce its plasma concentration from 20 microgram per ml to the one microgram per ml so if we want to maintain the minimum concentration of one microgram per ml we have to give the next dose of the drug less than five point two six hours in this way we can easily assess what is the dosing interval we have to maintain for a drug when it is given by IV bolus administration now let us go the working example three so here we have given the dose of the drug as XL and we are going to administer the drug into the body and where we are going to give the drug continuously by IV infusion and we require the steady-state concentration CSS as 0.1 microgram per ml and then the drug is going to be eliminated from the single compartment where the volume of distribution is 20 liters and half-life is a rental loss so with the data given here calculate the following the value of the queue and value of the Excel again by just seeing this diagram we can easily say that this is one compartment model because the track is given by IV infusion it will have some Q value that is indicates the infusion rate or rate of infusion the drug is given at a particular rate of infusion so that the steady-state concentration is going to be maintained and what is Excel Excel is the loading dose in order to achieve the steady-state concentration immediately we are giving a loading dose so with this data we had to calculate what is the rate of infusion and what is the loading dose of the track so this is an example of a drug following the one compartment model IV infusion solution to the working example 3 which equation we had to follow so here the change of the drug in the single compartment depends on two factors here we are going to administer the drug continuously that means it depends on the rate of infusion similarly the drug is going to be eliminated out of the body which depends on the rate of elimination so DX by DT is equal to Q minus K into X where Q indicates the rate of infusion which is a zero order because we are always giving the infusion at a constant rate it follows the zero order and minus K into XK into X indicates the elimination which follows the first order so simply the rate of change of the drug in the plasma DX by DT is equal to the rate of input minus rate of output that means Q minus K into X on integrating the equation becomes C is equal to CSS into 1 minus e to the power of minus K into T so what is the CSS CSS is the steady state concentration which can be given as CSS is equal to Q by CL that is Q is the rate of infusion and CL is the clearance so steady state concentration is equal to rate of infusion by clearance now let us calculate the rate of infusion so here CSS is equal to Q by clearance where Q is the rate of infusion then what is the q q is equal to CSS into clearance but here in the data we have not given with the clearance value then we can expand this equation so Q is equal to CSS into clearance can be written as K into VD but again the K is again not given half-life is given now we can further expand this equation this is equal to CSS in to 0.693 by T half because K is equal to 0.693 by T half so you can write like this in to VD now we have the video as 20 liters and CSS as point one microgram per ml but again the volume of distribution is given in the laters but the CS is given in terms of milliliters so we have to convert into the similar units so this point one microgram per ml can also be written as 0.1 mg per liter and then T half is given as trailers so by substituting these values in the equation so Q will be point one into 0.6 nine three by 12 into 20 so by solving this we will get point 1 1 6 mg / R so the rate of infusion should be point 1 1 6 mg per our next let us calculate the loading dose how we can get the loading dose the loading dose can be given as X L is equal to VD into CSS so now V DS given as 20 liters and CSS is given as point 1 microgram per ml again we have to convert the units which is equal to 0.1 mg per liter and we can directly substitute in this equation so X L is equal to 20 into 0.1 so which gives to mg as the loading dose so we have to entered we have to give it loading dose of 2 mg in order to achieve the steady state conservation of point 1 microgram per ml immediately in this way in one compartment model the rate equation depends on the route of administration we can give the dragged by a the IV route or extravascular route within the IV road we can give the drug as a single administration like a bolus administration otherwise we can give as a continuous administration such as IV in future in case of IV single highly Boras administration the kind X of the drug just follows the first-order kinetics because the change of the drug in the plasma depends on the only elimination similarly in case of IV infusion the rate equation can be written as rate of input minus rate of output which is nothing but Q minus K into X otherwise by integrating we can call the C is equal to CSS into 1 minus e to the power of minus K into T and sometimes we can also give the loading dose such that we can achieve the steady state concentration immediately so that's about these one compartment model IV root administration and hope you have enjoyed this video and please don't forget to subscribe to our Channel and post your comments in the comment box thank you for watching 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