WORKSHOP ON MODELLING IN PAEDIATRIC MEDICINES tuoslogo_cmy... & 14-15 APRIL 2008; EMEA, London Day 2: Part 3 Day 2: Part 3 PBPK- Mechanistic Models-Allometry PBPK- Mechanistic Models-Allometry Tuesday 15 April 2008 Tuesday 15 April 2008 Using the Knowledge of Biology in the Prediction Using the Knowledge of Biology in the Prediction of Clearance as the Main Determinant of Drug of Clearance as the Main Determinant of Drug Exposure in Paediatric Populations Exposure in Paediatric Populations Amin Rostami Professor of Systems Pharmacology, University of Sheffield, UK a.rostami@sheffield.ac.uk)
What Has Changed? tuoslogo_cmy... & 1984 Preface 1984 Preface At any point in history of health care, our knowledge was considered to be quite extensive; however, in perspective, the knowledge of yesterday seems to have been very limited , just as today’s knowledge can be expected to seem one day as such. Fundamental in applying basic scientific and mathematical concepts to patient care is an appreciation of the physiologic constraints placed on these concepts and appreciation of how disease and/or physiologic changes can further affect these constraints.
A Key Factor: Clarity & Validity of Assumptions tuoslogo_cmy... &
tuoslogo_cmy... Well-Stirred Liver Model & Q H .fu B .CLu int CL H = Q H + fu B .CLu int Q H F H = Q H + fu B .CLu int fu B .CLu int E H = Q H + fu B .CLu int Cu liver /C total (blood) Cu liver /C total (blood) >fu B if drug is substrate for influx transporters Cu liver /C total (blood) <fu B if drug is substrate for efflux transporters
Parallel Tube Liver Model tuoslogo_cmy... & fu B .CLu int Q H CL H = Q H . (1 – e ) fu B .CLu int Q H F H = e fu B .CLu int Q H E H = 1 - e Dispersion Model ⎡ ⎤ ⎢ 4 a ⎥ CL = Q 1 − ⎢ ⎥ ⎡ ⎤ ⎡ ⎤ H H ( ) ( ) a − 1 a + 1 − ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ 2 ⎣ ⎦ 2 ⎣ ⎦ ( ) 2 Dn ( ) 2 Dn ⎣ ⎦ 1 1 + a e − − a e CLu × fu int B Rn = a = 1 + 4 RnDn ; ( e . g . Dn = 0 . 17 ) Q H
tuoslogo_cmy... Scaling Factors in Human IVIVE Scaling Factors in Human IVIVE & In vitro CLu int per CLu int g Liver Scaling Scaling In vitro CLu int per Factor 1 Factor 2 system Liver µL.min -1 HLM MPPGL X mg mic protein µL.min -1 Liver HHEP X X HPGL 10 6 cells Weight µL.min -1 pmol P450 isoform rCYP X MPPGL X pmol P450 isoform mg mic protein
Non-CYP Related Variation: MPPGL and Donor Age tuoslogo_cmy... & 150 MPPGL (mg.g -1 ) 100 50 43 mg.g -1 0 60 0 20 40 60 80 32 mg.g -1 Age (years) MPPGL (mg.g -1 ) 40 20 0 1 25 45 65 Barter et al. 2007 Curr Drug Met Age (years) Barter et al. 2008 Submitted
tuoslogo_cmy... Development of CYP: Abundance & 100 CYP1A2 % EXPRESSION of 80 CYP2A6 CYP2B6 60 ADULT CYP2C9 40 CYP2D6 CYP2E1 20 CYP3A4/5 0 Fetal 1-12 Month Fraction of adult value CYP2C9 CYP2C9 1.4 1.4 1.2 1.2 CYP1A2 CYP1A2 1.2 1.2 1 1 1 1 0.8 0.8 0.8 0.8 0.6 0.6 0.6 0.6 0.4 0.4 0.4 0.4 0.2 0.2 0.2 0.2 0 0 0 0 0 0 2 2 4 4 6 6 8 8 10 10 12 12 0 0 0.5 0.5 1 1 Age (y) Age (y) Some enzymes negligible at Birth but some are not; thus any modelling should consider baseline activity at birth.
tuoslogo_cmy... Rate per pmol of “Each Enzyme” & The abundance of each CYP isoform per mg of microsomal protein � The relative activity of the isoform(s) responsible for metabolism � The microsomal protein per gram of liver � Liver Volume = 0.722.BSA 1.176 (L/m 2 ) The size of liver � ⎡ ⎤ ⎛ Vmax (rCYP ) CYP abundance ⎞ n n = ∑ ∑ × ⎜ ⎟ j i j CL [ L / h ] MPPGL Liver Weight ⎢ ⎥ × × ⎜ ⎟ h K (rCYP ) ⎢ ⎥ ⎝ ⎠ ⎣ ⎦ j 1 i 1 m j i = = Adults Proctor et al. Xenobiotica 2004 Paediatrics 2.4% 12.5% 34.4% 4.8% 2.6% 5.8% 17.3% 14.6% 3.4%0.3% 1.9%
tuoslogo_cmy... Liver Blood Flow & fu B & 4.5 Proportion of cardiac output 4 22% and 7% for portal vein and arterial liver blood Cardiac Index supply, respectively) 3.5 (L/min/m 2 ) 3 Cardiac output based on BSA and age 2.5 (2.5, 4, 3 and 2.4 L/min/m 2 for 1, 10, 20 and 80 2 years of age, respectively) 0 20 40 60 80 100 Age (years) C B /C p = (C RBC :C P )*HC + (1- HC) fu B = fu Min (C B /C p ) = 1- Hematocrit C B /C p Max (C B /C p ) = ∞ HC & Age: - Children See Commentary by: Yang et al. (2007) Drug Metabolism Disposition, 35(3): 501-502
tuoslogo_cmy... Intestinal Drug Metabolism (CYP3A) & Adult CYP3A = 70,000 pmol/intestine Expression and activity of Intestinal CYP3A with age Relative Gut surface area 25 25 25 CYP3A4 (pm ol/m g p ro t CYP3A4 (pm ol/m g p ro t CYP3A4 (pm ol/m g p ro t (20) (20) (20) (Duodenum/ Jejunum) 20 20 20 (25) (25) (25) (6) (6) (6) (17) (17) (17) 15 15 15 (6) (6) (6) 1.8 10 10 10 intestine relative to adult 1.6 Surface area of small 5 5 5 (11) (11) (11) 1.4 0 0 0 1.2 V Fetus Fetus Fetus Neonate Neonate Neonate >3mn-2yr >3mn-2yr >3mn-2yr >2yr-5yr >2yr-5yr >2yr-5yr >5yr-12yr >5yr-12yr >5yr-12yr >12yr >12yr >12yr 1 Age Age Age CLu 0.8 max + + int = 0.6 0.12 0.12 0.12 Km 6OHT (n m o l/m g pr o te in / 6OHT (n m o l/m g pr o te in / 6OHT (n m o l/m g pr o te in / 0.4 (20) (20) (20) 0.1 0.1 0.1 (25) (25) (25) 0.2 (6) (6) (6) (17 (17 (17 0.08 0.08 0.08 0 0.06 0.06 0.06 0 5 10 15 20 25 30 35 (6) (6) (6) 0.04 0.04 0.04 Age 0.02 0.02 0.02 ND ND ND 0 0 0 Fetus Fetus Fetus Neonate Neonate Neonate >3mn-2yr >3mn-2yr >3mn-2yr >2yr-5yr >2yr-5yr >2yr-5yr >5yr-12yr >5yr-12yr >5yr-12yr >12yr >12yr >12yr Age Age Age fu CLu × gut int gut E Gut Metabolism / − = g Permeability Model Q fu CLu + × gut gut int gut − Drug specific parameter related to permeability
tuoslogo_cmy... Age Related Protein Binding & Serum Albumin & Age Serum AAG & Age 0.887 Age 0.38 × AAG D Alb = 1.1287Ln(t) + 33.746 = g/L 8.89 0.38 Age 0.38 + D 1.4 60 1.2 50 1 Albumin (g/L) 40 AAG (g/L) 0.8 30 0.6 20 0.4 10 0.2 0 0 0.1 1 10 100 1000 10000 100000 0.1 1 10 100 1000 10000 100000 Age (days) Age (days) 1 fu In the absence of = neonate fu ⎡ [ P ] ⎤ ( ) 1 − changes in dynamics neonate adult ⎢ ⎥ 1 + × [ P ] fu of binding: ⎣ ⎦ adult adult
tuoslogo_cmy... Drug Dependent Influence of Plasma Proteins on CL & 125.0% HC 112.5% 0 % of Adult Value 1 100.0% C RBC :C P 2 87.5% 50 75.0% 0.1 10 Age (month)
tuoslogo_cmy... “Drug Dependent” Influence of Haematocrit on CL & 500% 450% 400% AAG 350% 0.99 % of Adult Value 300% 0.5 fu in 250% Adults 0.1 200% 0.01 150% 100% 50% 0% 0.1 1 10 100
Non-Monotonic Drug Dependent CL/kg with Age tuoslogo_cmy... & 4.5 4.5 Omeprazole (Oral) 1.5 1.5 Cisapride (Oral) 4 4 CL (L.kg.h) 3.5 3.5 3 3 1 1 2.5 2.5 2 2 1.5 1.5 0.5 0.5 1 1 0.5 0.5 0 0 0 0 0 0 20 20 40 40 60 60 80 80 100 100 0 0 20 20 40 40 60 60 80 80 100 100 0.4 0.4 0.016 0.016 Phenytoin (Oral) S-Warfarin (Oral) 0.35 0.35 0.014 0.014 0.3 0.3 0.012 0.012 0.25 0.25 0.01 0.01 0.2 0.2 0.008 0.008 0.15 0.15 0.006 0.006 0.1 0.1 0.004 0.004 0.05 0.05 0.002 0.002 0 0 0 0 0 0 20 20 40 40 60 60 80 80 100 100 0 0 20 20 40 40 60 60 80 80 100 100 Weight (kg)
Organ Blood Flows & Tissue Composition tuoslogo_cmy... & • Known changes in blood flow & tissue composition with age 70 60 e.g. Brain BBF as % CO 50 40 30 20 10 0 0 5 10 15 Age (y) Questions? 100 - CL vs CLu 90 % Water - PK in plasma vs PK in Organs 80 - True PD vs Apparent PD 0 0 5 10 15 20 Age (y)
tuoslogo_cmy... Knowledge of System Could Describe Observed Data & Clin Pharmacol Ther 2007 CYP2D6 activity was detectable and concordant with genotype by 2 weeks of age, showed no relationship with gestational age, and did not change with post natal age up to 1 year. However: we know that: Thus, the development of renal function from birth may change in parallel with the development of the enzyme such that the drug/metabolite ratio may be relatively constant !!!!
Bottom-Up Approach Meets Top-Down Analysis (1): tuoslogo_cmy... & Clin Pharmacol Ther 2008 1 1 (A) (B) CYP3A4 activity (DX/3HM CYP2D6 activity (DM/DX ratio) relative to adult ratio relative to adult 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 0 0 4 8 12 0 4 8 12 Age (Months) Age (Months) Figure 1. Changes in CYP2D6 (a) and CYP3A4 (b) activity relative to adult values. The data of Blake et al , corrected for the development of renal function, are indicated by the diamonds. The simulated change in in the activity of each enzyme (solid line) was derived from in vitro data on hepatic enzyme expression and increase in liver weight with age.
Pop-PK and Covariate Effects tuoslogo_cmy... & Sometimes obvious (what to look for and also to see the effect): Example
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