Population Pharmacokinetics in Support of Analgesics and Anaesthetics Studies in

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1 Pyry Välitalo Population Pharmacokinetics in Support of Analgesics and Anaesthetics Studies in Special Populations Publications of the University of Eastern Finland Dissertations in Health Sciences

18 η ɛ

20 α 1

21 α 2

24 HO O 7.4 O O F OH OH O Flurbiprofen Ketoprofen Ibuprofen

29 0.5 % 0.2 % 0.1 % fu 0.05 % 0.02 % 0.01 % Mortensen et al 1979 Diana et al 1989 Borga and Borga Naproxen plasma conc (mg/l)

30 CH 3 CH 3 CH 3 CH 3 Oxycodone CH 3 CH 3 Thebaine Morphine μ κ δ κ μ κ μ 7.4 α β

31 μ

32 ± ± ± ± ± ±

33 age LBM

34 CL = (LBM 54.58) (age 44.81) R N N N H Dexmedetomidine N N G-dex-1 N R G-dex-2 HO RO N N N 3-hydroxymethyl dexmedetomidine RO N N H-1 metabolite N 3-hydroxymethyl dexmedetomidine O-glururonide N HO N N O N H HO H-3 metabolite Dexmedetomidine carboxylic acid

36 CO C p ( CO = CO base ) C3 p C 3 p ( ) 0.37 C3.15 p CO = CO base C 3.15 p CL = Q H f UB CL INT Q H + f UB CL INT C B /C P (0.3 CO)(0.0602/0.704) 1.8 L/h = (0.3 CO)+(0.0602/0.704) 1.8 L/h ( ) CO 1.24 CL = 57 L/h CO base C p

37 P(H E) = P(E H) P(H) P(E) H E P(H) H P(H E) H E P(E H) E H P(E)

38 θ Θ θ θ Θ ω Ω η ω 2 σ Σ ɛ ɛ ɛ

40 CL/V c Q/V c Q/V p CL/k 10 V c k 12 /k 21 V c k 10 V c k 12 = V p k 21 CL H = Q H CL u,int f u,b Q H + CL u,int f u,b CL H Q H CL u,int f u,b Q H CL u,int f u,b CL H = Q H CL u,int f u,b Q H + CL u,int f u,b Q H CL u,int f u,b Q H CL u,int f u,b Q H CL u,int f u,b CL H = Q H CL u,int f u,b Q H + CL u,int f u,b Q H CL u,int f u,b CL u,int f u,b Q H

42 A p Q/V c Q/V p A c CL/V c V c V p Q CL da c dt da p dt = A c V c (CL + Q)+ A p V p Q = A p V p Q + A c V c Q A c A p C p t C p (t) =A c (t)/v c

43 P i = θ P e η i θ P P i η i A B C Density Density Density η value Clearance (L/h) Baseline RASS P i = e(η i+θ P ) 1 + e (η i+θ P ) 9 5 P i

44 ω CV = e ω2 1 ω ω Coefficient of variation (%) ω exp(ω 2 ) ω ω ω log(y) =log(ipred)+ɛ Y = IPRED e ɛ

45 P i = θ 1 + θ 2 (COV i COV) ( ) θ2 COVi P i = θ 1 COV P i = θ 1 e θ 2 (COV i COV) P i θ 1 θ 2 COV i COV COV i θ 2 COV i = 1 P i = θ 1 (1 + θ 2 COV i )

46 η η η η η ɛ

47 P i P i = θ P e η i ( ) θcov COVi P i = θ P e η i COV θ cov θ cov θ cov

48 θ cov Σ n i=1 (x i x) n Σi=1 n (x i x) n 1 x n n

49 AIC = 2k 2log(L) OFV = 2log(L) AIC = 2k + OFV CL =(V max )/(C p + K m ) V max K m BIC =k log(n) 2log(L) =k log(n)+ofv FIM(q, Θ) 1 COV( ˆΘ) ˆΘ Θ

51 s

52 PRED = θ 1 WT θ 2

53 ( ) WT 0.75 PMA CL = CL pop Hill 70 PMA Hill + PMA50 Hill CL CL pop PMA Hill PMA 50

54 ( ( ) ) FBHILL 1 + FB MAX / 1 + PNA TB 50 F Birth = 1 + FB MAX F Birth FB MAX PNA TB 50 FB HILL F Birth k k = k 0 k max WT Hill k50 Hill + WT Hill ( ) WT k CL = θ CL WT std k 0 k k max k Hill k 50 k WT std θ CL k k = k coe f f WT k exp ( ) WT k CL = θ CL 70 k coe f f k exp k

55 A B C D Weight (kg) Clearance maturation Clearance (L/h/kg) Clearance (L/h/kg) Age (y) Age (y) Age (y) Weight (kg) E F G H k Clearance (L/h/kg) k Clearance (L/h/kg) Weight (kg) Weight (kg) Weight (kg) Weight (kg) MPE (predicted observed) MPE = n

56 PMA 50 Hill ( ) WT 0.75 CL = CL pop (1 βrf e PNA log(2)/tr f ) 70 PNA βrf Tr f

57 LV LV = BSA BSA a WT 2/3 LV =0.722 a WT (2/3)1.176 =b WT a b = a

62 1 1 ss 1

64 1

65 K centraltocsf = QCSF f u UPTK/V CSF K CSFtocentral = QCSF/V CSF K centraltocsf K CSFtocentral f u V CSF V central PARM = θ TV e η θ TV η ω 2

66 PARM = θ TV (1 + CA θ 2 ) ( ) WT θexponent CL = θ CL 70 θ CL θ exponent η ɛ η ɛ η shrinkage = 1 SD(EBEs) ω ɛ shrinkage = 1 SD(IWRES)

67 a b n of patients n of samples Age (years) Age (years) 1 1

68 A B Flurbiprofen conc. (mg/l) Flurbiprofen conc. (mg/l) Time (h) Time (h) C D Flurbiprofen conc. (mcg/l) Flurbiprofen conc. (mcg/l) Time (h) Time (h) 1 1 1

69 0.75 c p,shallow p,shallow p,deep p,deep ω CL ω fu ω Vd ω K12 σ plasma σ CSF 1 1 1

70 A B Plasma conc (mg/l) CSF conc (mg/l) Time (h) Time (h) η CL η V η fu η KA

71 1 1

72 a Numeral Predictive Check results b Observed/Expected Upper PI Limit Lower PI Limit Observed/Expected Upper PI Limit Lower PI Limit Prediction Interval Prediction Interval c d Observed/Expected Upper PI Limit Lower PI Limit Observed/Expected Upper PI Limit Lower PI Limit Prediction Interval Prediction Interval

73 8 =IV dosing =oral dosing 6 Flurbiprofen conc (mg/l) Time after dosing (h)

79 K centraltocsf = QCFS f u UPTK/V CSF K CSFtocentral = QCFS/V CSF K centraltocsf K CSFtocentral

82 ωcl ω Vd ωcl ω Vd ωka ωfu σ p,post abs σ p,abs σcsf

83 A Naproxen conc (mg/l) Time (h) Naproxen conc (mg/l) B Naproxen conc (mg/l) C Time (h) Time (h)

84 A B Plasma conc (mg/l) CSF conc (mg/l) Time (h) Time (h)

96 2

98 a b Concentration (ng/ml) Concentration (ng/ml) Time after dose (h) Time after dose (h) c d Concentration (ng/ml) Concentration (ng/ml) Time after dose (h) Time after dose (h)

99 A B Observations Observations Individual predictions Population predictions

100 A B Conc (ng/ml) Conc (ng/ml) Time (h) Time (h) C D Conc (ng/ml) Conc (ng/ml) Time (h) Time (h)

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106 P i = θ pop e η P i θ pop η ω 2

107 ( ) θexp COVi P i = θ pop e η COV std COV i COV std θ exp C ss R inf CL R inf = C ss CL

108

109 A B Frequency conc (ng/ml) Infusion rate (μg/kg/h) Time (days)

110 A B Frequency Frequency Number of observations per patient Duration of treatment (days) θ exp θ exp θ exp

111 A B Observations Observations Population predictions Individual predictions

112 CL = 36.6 WT 70 ( CL = 40.3 AST 41 ( CL = 39.8 ( BIL Vd = 91 ALB 23 ( ) 0.76 ) ) ) 0.091

113 A B Concentration (ng/ml) Concentration (ng/ml) Dexmedetomidine infusion rate (μg/kg/h) Dexmedetomidine infusion rate (μg/kg/h) C Clearance (L/h) Dexmedetomidine infusion rate (μg/kg/h)

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117 ( ) WT 0.75 PMA CL = CL pop Hill 70 PMA Hill + PMA50 Hill

118 N(patients) N(samples) Frequency Frequency Age (years) Age (years) Oxycodone conc (ng/ml) Age: 0 6 months Age: 6 months to 7 years Time (h)

119 θ i = θ pop e η θ i θ pop η η ω 2

120 2 20 = 40 = θ orig θ sim precision = n (θ sim θ sim ) 2 n 1 i=1 θ orig bias = θ sim θ orig θ orig

121 ( ) WT 0.75 PMA CL = 48L/h PMA PMA 50 Hill

122 A B Observations Observations Individual predictions Population predictions A B C p (ng ml) C p (ng ml) Time (h) Time (h)

123 ω ω ω ω ω σ σ σ

124 C p (ng ml) 50.0 Pre term neonates (n=20) months (n=42) months (n=5) 6 12 months (n=5) Time (h) Time (h) CL pop PMA 50 ω CL ω Vc

125 A B Maturation Body weight (kg) Current model CYP2D6 CYP3A Age (months after birth) Age (months after birth) C D Clearance (L/h/kg) Current model Ince et al Anderson & Larsson 2011 Clearance (L/h/kg) Current model Ince et al Anderson & Larsson Body weight (kg) Age (months after birth)

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156 C b = P 1 C u + P P C u C u C b C u P 1 P 2 P 3 P 1 P 3 C b = N P C u + NS C u K d + C u N P K d NS NS C b [Alb] = N 1 K 1 C u + N 2 K 2 C u 1 + K 1 C u 1 + K 2 C u [Alb] N 1 N 2 K 1 K 2 C b [Alb] = N 1 C u + N 2 C u K 1 + C u K 2 + C u [Alb] N 1 N 2 K 1 K 2

157 A B fu 0.5 % Szpunar et al Knadler et al Deschamps Labat et al Borga and Borga % 0.1 % 0.05 % 0.02 % 0.01 % Flurbiprofen plasma conc (mg/l) ratio [total CSF]/[unbound CSF] 25 Szpunar et al Knadler et al Deschamps Labat et al Borga and Borga Flurbiprofen plasma conc (mg/l)

158 C b [Alb] = N 1 K 1 C u + N 2 K 2 C u 1 + K 1 C u 1 + K 2 C u [Alb] N 1 N 2 K 1 K 2 N 1 N 2 K 1 = K 2 = N 1 N 2 K 1 = K 2 = C b [Alb] = N 1 C u + N 2 C u K 1 + C u K 2 + C u [Alb] N 1 N 2 K 1 K 2

159 A B fu 0.5 % 0.2 % 0.1 % 0.05 % 0.02 % 0.01 % Mortensen et al 1979 Diana et al 1989 Borga and Borga 1997 ratio [total CSF]/[unbound CSF] Mortensen et al 1979 Diana et al 1989 Borga and Borga Naproxen plasma conc (mg/l) Naproxen plasma conc (mg/l)

160 Pyry Välitalo Population Pharmacokinetics in Support of Analgesics and Anasesthetics Studies in Special Populations Pharmacokinetic differences between individuals can often explain variability in drug response. Pharmacokinetic differences are often observed between healthy adults and special populations. Therefore, in this thesis project, the pharmacokinetics of flurbiprofen, naproxen and oxycodone were quantified in children, oxycodone pharmacokinetics were quantified in the elderly, and dexmedetomidine pharmacokinetics were quantified in critically ill patients. Publications of the University of Eastern Finland Dissertations in Health Sciences isbn

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