# PharmPK Discussion - Dose calculation for IM injections

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• On 24 Nov 2000 at 21:06:52, "skbhavsar" (skbhavsar.aaa.gau.guj.nic.in) sent the message
`Dear members,In a study we calculated the PK parameters of a drug after IV and I'Minjections as follow.After IV administration (5 mg/kg body weight) t1/2beta (1.69 hours),Vd(ss) (2.61 l/kg)After I'M administration (5 mg/kg body weight) t1/2beta (2.63hours),Vd(area) (1.87 l/kg), F(83%) .My question is what dose should we give to maintain a Css(AV) of0.12mcg/ml with a dosing interval of 12 hours by intramuscular route?Kindly give equations (formulas) that are used to calculate suchdosages.comments awaited.ThanksBhavsar S.K.INDIAskbhavsar.-at-.gau.guj.nic.in`
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• On 27 Nov 2000 at 13:12:52, ml11439.-at-.goodnet.com sent the message
`Bhavsar,     One easy way of dose calculation to achieve a steady stateconcentration of .12mg/l is to use the following equation:             Cssave= FSD/Tau*Cl             FSD=  Cssave*Tau*Cl             D=    Cssave*Tau*Cl/FS             D= (.12mg/l)(12hrs)(1.87 l/kg)(.263498 hr-1)/(0.83)(1)             Dose= .85487 mg/kg             F= fraction absorbed= 0.83             S= salt form= 1             Cssave= steady average plasma concentration= 0.12mg/l             Tau= dosage interval in hrs= 12hrs             Beta= .693/T1/2 beta= .263498 hr-1             Cl= clearance= beta*Vd= (.263498 hr-1)(1.87 l/kg)= .49724 l/kg*hr                                          Mike Leibold, PharmD, RPh                                          ML11439.-at-.goodnet.com`
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• On 27 Nov 2000 at 13:24:26, "Melethil, Srikumaran K." (MelethilS.-a-.umkc.edu) sent the message
`Css (ave) = AUC/T or FD/Vd.k T (T = dosing interval).  Hope this helps.Srikumaran Melethil, Ph.D.Professor of Pharmaceutics and  MedicineUniversity of Missouri-KC203 B Katz Hall,  School  of Pharmacy5005 Rockhill RoadKansas City, MO 64110816-235-1794 (voice); 816-235-5190 (fax)`
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• On 27 Nov 2000 at 15:55:27, Nick Holford (n.holford.at.auckland.ac.nz) sent the message
`Mike,I think your answer shows knowledge of PK but not of the usual rulesof precedence for mathematical operators:>               Cssave= FSD/Tau*ClI think you meant:>               Cssave= FSD/Tau/Clalthough it would be more generally true (and simpler?) to write:>               Cssave= Rate/ClWhy make something simple more complicated by introducing "beta" and"vd" which imply a one compartment model and also imply, incorrectly,that CL depends on Vd?>               Beta= .693/T1/2 beta= .263498 hr-1>               Cl= clearance= beta*Vd= (.263498 hr-1)(1.87 l/kg)=>.49724 l/kg*hr--Sender: PharmPK.at.boomer.orgReply-To: Nick Holford MIME-Version: 1.0X-Sybari-Space: 00000000 00000000 00000000From: Nick Holford Date:  Tue, 28 Nov 2000 09:57:59 +1300To: david.-at-.boomer.orgSubject: Re: PharmPK Re: Dose calculation for IM injectionsThe following message was posted to: PharmPKSrikumaran Melethil,I think your answer shows knowledge of PK but not of the usual rules ofprecedence for mathematical operators:>  Css (ave) = AUC/T or FD/Vd.k T (T = dosing interval)I think you meant:>  Css (ave) = AUC/T or FD/Vd/k T (T = dosing interval)although it would be more generally true (and simpler?) to write:>  Css (ave) = Rate/CLWhy make something simple more complicated by introducing "k" and "Vd"which imply a one compartment model and also imply, incorrectly, that CLdepends on Vd?-Sender: PharmPK.-at-.boomer.orgReply-To: Nick Holford MIME-Version: 1.0X-Sybari-Space: 00000000 00000000 00000000From: Nick Holford Date:  Tue, 28 Nov 2000 10:09:56 +1300To: david.at.boomer.orgSubject: [Fwd: PharmPK Re: Dose calculation for IM injections OOPS!]The following message was posted to: PharmPKOOPS!>>  I think you meant:>  > Css (ave) = AUC/T or FD/Vd/k T (T = dosing interval)I should also have inserted a "/":>  > Css (ave) = AUC/T or FD/Vd/k/T (T = dosing interval)--Nick Holford, Divn Pharmacology & Clinical PharmacologyUniversity of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealandemail:n.holford.-at-.auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.htm`
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• On 27 Nov 2000 at 20:40:07, "Melethil, Srikumaran K." (MelethilS.at.umkc.edu) sent the message
`Dear Dr. Holford,I believe what I have written is as simple as what you have written.It is justa matter of your opinion.In many cases, a two-compartment (given IV) drug can be treated as aone-compartment.  So, there is no problem with what I have written.Are you suggesting we get rid of volume terms in PK?Srikumaran Melethil, Ph.D.Professor of Pharmaceutics and  MedicineUniversity of Missouri-KC203 B Katz Hall,  School  of Pharmacy5005 Rockhill RoadKansas City, MO 64110816-235-1794 (voice); 816-235-5190 (fax)`
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• On 27 Nov 2000 at 22:21:14, Nick Holford (n.holford.-at-.auckland.ac.nz) sent the message
`Melethil, Srikumaran K. (by way of David_Bourne)" wrote:>  I believe what I have written is as simple as what you have written.>  It is just a matter of your opinion.You wrote this (I have corrected the mathematical operator errors):Css (ave) = AUC/T or FD/Vd/k/T (T = dosing interval)I wrote this:Css (ave) = Rate/CLI cannot see how your expression involving F,D,Vd,k and T ( 5 terms)is as simple as mine even if I rewrite it as follows ( 4 terms).Css (ave) = FD/T/CLIt is my opinion that 4 terms are simpler than 5 terms.>  In many cases, a two-compartment (given IV) drug can be treated as a>  one-compartment.  So, there is no problem with what I have written.I have no disagreement that under suitable circumstances a onecompartment model is a reasonable approximation to a two compartmentmodel and that both may be reasonable approximations to reality. ButI cannot see what this has to do with the prediction of averagesteady state concentrations. The expressions we have both suggestedare totally independent of any assumption about the number ofcompartments except this number is greater than zero.>  Are you suggesting we get rid of volume terms in PK?My comment was intended to point out that CL is a fundamental** PKparameter describing the relationship between mass transfer rates andconcentration:	Rate = CL * CLook! No Vd! No k! Just CL!I am indeed suggesting that we get rid of volume terms from PK whenwe are applying PK to predict average steady state concentrations.** Roger Jelliffe pretends he has never heard of this although he andI (and many others no doubt) have discussed it on many occasions.--Nick Holford, Divn Pharmacology & Clinical PharmacologyUniversity of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealandemail:n.holford.at.auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.htm`
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