药物非房室模型分析PPT学习教案

1、会计学1药物非房室模型分析药物非房室模型分析2GENERAL PRINCIPLES OF STATISTICAL MOMENTSMOMENT: A mathematical description of a discrete distribution.STATISTICAL MOMENTS:Utilized in chemical engineering to describe flow dataFirst applied to biological systems by Perl and Samuel in 1969 to describe the kinetics of cholester

2、ol第1页/共49页3Examples of Statistical Moment UsageIn statistics In physicsM0NweightM1NXXi(mean)Center of massM2NXXi22(variance)Moment of inertiaM32/3231NXXi(skewness)M42242NXXi(kurtosis)第2页/共49页4In statistics, the mean is a measure of a sample mean and is actually an estimate of the true population mea

3、n. In pharmacokinetics, we can calculate the moment of the theoretical probability density function (i.e., the solution of a differential equation describing the plasma concentration time data), or we can calculate moments from measured plasma concentration-time data. These curves are referred to as

4、 sample moments and are estimates of the true curves.第3页/共49页5Assume a theoretical relationship of C(t) as a function of time. The non-normalized moments, Sr , about the origin are calculated as:0),.2 , 1 , 0( )(mrdttCtSrr第4页/共49页6Non-normalized moments Kinetic parameter00)( dttCS AUCArea under the

5、curve01)( dtttCS AUMC Area under the moment curve第5页/共49页7From: Rowland M, Tozer TN. Clinical Pharmacokinetics Concepts and Applications, 3rd edition, Williams and Wilkins, 1995, p. 487.第6页/共49页8Normalized moments Kinetic parameterFirst moment:AUCAUMCdttCdtttCSS0001)()( MRTMean residence time第7页/共49

6、页9AREA DETERMINATIONA. Integration of Specific FunctionMust elucidate the specific functionInfluenced by the quality of the fit2211 :example CCAUCCAUCii2222112 :example CCAUMCCAUMCii第8页/共49页10B. Numerical Integration1.Linear trapezoidal2.Log trapezoidal第9页/共49页11B. Numerical Integration1.Linear trap

7、ezoidalCCtt1212ConcentrationTime)(21122121CCttAreatt)( .)()(11212332211221210nnnntttCCttCCttCCArean第10页/共49页12B. Numerical Integration1.Linear trapezoidalAdvantages: Simple (can calculate by hand)Disadvantages:Assumes straight line btwn data pointsIf curve is steep, error may be largeUnder or over e

8、stimate depends on whether curve is ascending of descending第11页/共49页13第12页/共49页14B. Numerical Integration1.Linear trapezoidal2.Log trapezoidal211221lnln)(21CCttCCAreatt第13页/共49页15B. Numerical Integration1.Linear trapezoidal2.Log trapezoidal211221lnln)(21CCttCCAreattAdvantages:Hand calculatorVery acc

9、urate for mono-exponentialVery accurate in late time points where interval btwn points is substantially increasedDisadvantages:Limited applicationMay produce large errors on an ascending curve, near the peak, or steeply declining polyexponential curve第14页/共49页16B. Numerical Integration1.Linear trape

10、zoidal2.Log trapezoidal3.Extrapolation to infinitynntzntCCdtAUCAssumes log-linear declineznnzntCtCAUMCn2第15页/共49页17zntCAUCAUCn00znnzntCtCAUMCAUMCn200第16页/共49页18Time (hr) C (mg/L) 0 2.55 1 2.00 3 1.13 5 0.70 7 0.43 10 0.20 18 0.025AUC DeterminationArea (mg-hr/L)-2.2753.131.831.130.9450.900 Total 10.2

11、1AUMC Determination C x t(mg/L)(hr) 0 2.00 3.39 3.50 3.01 2.00 0.45 Area(mg-hr2/L) - 1.00 5.39 6.89 6.51 7.52 9.80 37.11LhrmgAUMCLhrmgAUCtt/ 11.37/ 21.10 2001818第17页/共49页19LhrmgAUChrLmgLhrmgAUCCAUCAUCzt/ 31.10 26. 0/ 025. 0/ 21.10 010180018LhrmgAUMChrLmghrLhrmgLhrmgAUMCCCtAUMCAUMCzzt/ 21.39 26. 0/ 0

12、25. 0 26. 0/ 45. 0/ 11.37202112021818180018第18页/共49页20CLEARANCE CONCEPTSORGANQCaQCveliminationIf Cv Ca, then it is a clearing organ第19页/共49页21Rate In = QCaRate Out = QCvRate of elimination = QCa QCv= Q(Ca Cv)第20页/共49页22Extraction Ratio:Ratio of the rate of xenobiotic elimination and the rate at whic

13、h xenobiotic enters the organ.avaavaCCCQCCCQEE)(Entry of RatenEliminatio of Rate第21页/共49页23avaCCCQQECL)(Clearance:The volume of blood from which all of the drug would appear to be removed per unit time.第22页/共49页24Relationship between CL & QSince CL = QE, if E1: CL QPerfusion rate-limited clearance第2

14、3页/共49页25Total ClearanceTotal (systemic) Clearance:bloodin ion concentratraten EliminatioCdtdXCLT第24页/共49页26Total ClearanceTotal (systemic) Clearance:bloodin ion concentratraten EliminatioCdtdXCLT00000 Therefore and (Div) eliminatedamt total where,0 from gIntegratinAUCDCLAUCCdtdtdtdXCdtdtdtdXCLivTT第

15、25页/共49页27Additivity of clearanceRate of elimination = Rate of Renal Excretion + Rate of Hepatic MetabolismDividing removal rate by incoming concentration:aaaCCCMetabolism Hepatic of RateExcretion Renal of RatenEliminatio of RateTotal Clearance = Renal Clearance + Hepatic ClearanceCLT = CLR + CLH第26

16、页/共49页28Exception: sig. pulmonary eliminationFrom: Rowland M, Tozer TN. Clinical Pharmacokinetics Concepts and Applications, 3rd edition, Williams and Wilkins, 1995, p. 12.第27页/共49页29RTRivuRfCLCLDXf ,100 mg drug administered to a volunteer resultedin 10 mg excreted in urine unchanged:RivRTRivuRfAUCD

17、fCLCLmgmgDXf1 . 0 100 10第28页/共49页30Application of Clearance ConceptsPrediction of the effect of pathophysiological changesA new antibiotic has just been introduced onto the market. Currently, there are no studies examining the effect of renal disease on the pharmacokinetics of this compound. Is dosa

18、ge adjustment necessary for this drug when used in pts with renal failure? How can we gain some insight into this question? A study in normal volunteers was recently published and the following data was included (mean):第29页/共49页31Application of Clearance ConceptsPrediction of the effect of pathophys

19、iological changesCLT = 1.2 L/hr Div = 500 mgAmount in urine unchanged = 63 mghrLhrLfCLCLmgmgDXfRTRivuR/ 15. 0126. 0/ 2 . 1 126. 0 500 63第30页/共49页32Mechanisms of altered eliminationVerapamil has been shown to elevate serum digoxin concentrations in patients receiving both drugs concurrently. A study

20、by Pedersen et al (Clin Pharmacol Ther 30:311-316, 1981.) examined this interaction with the following results.: TreatmentDigoxinDig + verapamilCLT3.282.17CLR2.181.73CLNR1.100.44第31页/共49页33STEADY-STATE VOLUME OF DISTRIBUTIONCfCbpCfCbtVPVT第32页/共49页34CfCbpCfCbtVPVTTfutPfupCCfCCf CP = Cf + Cbp CT = Cf

21、+ Cbt 第33页/共49页35At steady-state:TPssTssPSSTTssPPssSSPssSSSSVCCVVorVCVCACAV Substitute:upfPssutfTssfCCfCC and 第34页/共49页36TutfupfPSSVfCfCVVSimplifying:TutupPSSVffVV第35页/共49页37TutubBSSVffVVUsing blood concentrations:第36页/共49页38Calculation via moment analysis:2AUCAUMCDVivSSAssumptions:Linear dispositio

22、nAdministered and eliminated via sampling siteInstantaneous input第37页/共49页39If administration via a short term infusion:AUCTKAUCAUMCTKVSS2)(2020K0 = infusion rate T = infusion duration第38页/共49页40MEAN RESIDENCE/TRANSIT TIMEAdministration of a small dose may represent a large number of molecules:Dose

23、= 1 mg MW = 300 daltons# of molecules = (10-3 g/300) x (6.023 x 1023) 2 x 1018 molecules第39页/共49页41Instantaneous administration of the entire dose will result in xenobiotic molecules spending various amounts of time in the body. Evaluation of the time various molecules spend in the body (residence t

24、ime) can be characterized in the same manner as any statistical distribution. Mean residence time: The average time the molecules of a given dose spend in the body. 第40页/共49页42A conceptual understanding can be gained from the following example: Assume a child received 20 dimes for his birthday and i

25、mmediately places them in his piggy bank. Over the next month, he periodically removes 1 or more dimes from the piggy bank to purchase candy. Specifically, 3 days after placing the coins in his bank he removes 5 dimes, on day 10 he removes 4 dimes, on day 21 he removes 6 dimes and on day 30 he remov

26、es 5 dimes. At the 30th day after placing the coins in his bank, all of the coins have been removed. Hence, the elimination of the deposited dimes is complete. The MRT of the dimes in the piggy bank is simply the sum of the times that coins spend in the bank divided by the number of dimes placed in the bank.第41页/共49页432030303030302121212121211010101033333 MRT20)530()621()410()53(MRTdaysMRT 55.16第42页/共49页44MRT can be determined for any given number of drug molecules (Ai) that spend a given amount of time (ti) i