藥物非房室模型分析

1、藥物非房室模型分析GENERAL 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 cholesterol2Examples of

2、 Statistical Moment UsageIn statistics In physicsM0NweightM1(mean)Center of massM2(variance)Moment of inertiaM3(skewness)M4(kurtosis)3In statistics, the mean is a measure of a sample mean and is actually an estimate of the true population mean. In pharmacokinetics, we can calculate the moment of the

3、 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 sample moments and are estimates of the true curves.4Assu

4、me a theoretical relationship of C(t) as a function of time. The non-normalized moments, Sr , about the origin are calculated as:5Non-normalized moments Kinetic parameter AUCArea under the curve AUMC Area under the moment curve6From: Rowland M, Tozer TN. Clinical Pharmacokinetics Concepts and Applic

5、ations, 3rd edition, Williams and Wilkins, 1995, p. 487.7Normalized moments Kinetic parameterFirst moment: MRTMean residence time8AREA DETERMINATIONA. Integration of Specific FunctionMust elucidate the specific functionInfluenced by the quality of the fit9B. Numerical IntegrationLinear trapezoidalLo

6、g trapezoidal10B. Numerical IntegrationLinear trapezoidal11B. Numerical IntegrationLinear trapezoidalAdvantages: Simple (can calculate by hand)Disadvantages:Assumes straight line btwn data pointsIf curve is steep, error may be largeUnder or over estimate depends on whether curve is ascending of desc

7、ending1213B. Numerical IntegrationLinear trapezoidalLog trapezoidal14B. Numerical IntegrationLinear trapezoidalLog trapezoidalAdvantages:Hand calculatorVery accurate for mono-exponentialVery accurate in late time points where interval btwn points is substantially increasedDisadvantages:Limited appli

8、cationMay produce large errors on an ascending curve, near the peak, or steeply declining polyexponential curve15B. Numerical IntegrationLinear trapezoidalLog trapezoidalExtrapolation to infinityAssumes log-linear decline1617Time (hr) C (mg/L) 5 0.70 AUC DeterminationArea (mg-hr/L)-1.830.900 AUMC De

9、termination C x t(mg/L)(hr) 0 Area(mg-hr2/L) - 1819CLEARANCE CONCEPTSORGANQCaQCveliminationIf Cv Ca, then it is a clearing organ20Rate In = QCaRate Out = QCvRate of elimination = QCa QCv= Q(Ca Cv)21Extraction Ratio:Ratio of the rate of xenobiotic elimination and the rate at which xenobiotic enters t

10、he organ.22Clearance:The volume of blood from which all of the drug would appear to be removed per unit time.23Relationship between CL & QSince CL = QE, if E1: CL QPerfusion rate-limited clearance24Total ClearanceTotal (systemic) Clearance:25Total ClearanceTotal (systemic) Clearance:26Additivity of

11、clearanceRate of elimination = Rate of Renal Excretion + Rate of Hepatic MetabolismDividing removal rate by incoming concentration:Total Clearance = Renal Clearance + Hepatic ClearanceCLT = CLR + CLH27Exception: sig. pulmonary eliminationFrom: Rowland M, Tozer TN. Clinical Pharmacokinetics Concepts

12、and Applications, 3rd edition, Williams and Wilkins, 1995, p. 12.28100 mg drug administered to a volunteer resultedin 10 mg excreted in urine unchanged:29Application of Clearance ConceptsPrediction of the effect of pathophysiological changesA new antibiotic has just been introduced onto the market.

13、Currently, there are no studies examining the effect of renal disease on the pharmacokinetics of this compound. Is dosage 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 t

14、he following data was included (mean):30Application of Clearance ConceptsPrediction of the effect of pathophysiological changesCLT = 1.2 L/hr Div = 500 mgAmount in urine unchanged = 63 mg31Mechanisms of altered eliminationVerapamil has been shown to elevate serum digoxin concentrations in patients r

15、eceiving both drugs concurrently. A study by Pedersen et al (Clin Pharmacol Ther 30:311-316, 1981.) examined this interaction with the following results.: TreatmentDigoxinDig + verapamilCLTCLRCLNR32STEADY-STATE VOLUME OF DISTRIBUTIONCfCbpCfCbtVPVT33CfCbpCfCbtVPVTCP = Cf + Cbp CT = Cf + Cbt 34At stea

16、dy-state:Substitute:35Simplifying:36Using blood concentrations:37Calculation via moment analysis:Assumptions:Linear dispositionAdministered and eliminated via sampling siteInstantaneous input38If administration via a short term infusion:K0 = infusion rate T = infusion duration39MEAN RESIDENCE/TRANSI

17、T TIMEAdministration of a small dose may represent a large number of molecules:Dose = 1 mg MW = 300 daltons# of molecules = (10-3 g/300) x (6.023 x 1023) 2 x 1018 molecules40Instantaneous administration of the entire dose will result in xenobiotic molecules spending various amounts of time in the bo

18、dy. Evaluation of the time various molecules spend in the body (residence time) 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. 41A conceptual understanding can be gained from the followin

19、g example: Assume a child received 20 dimes for his birthday and immediately 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 re

20、moves 4 dimes, on day 21 he removes 6 dimes and on day 30 he removes 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.4243MRT can be determined for any given numbe