Pharmacokinetics and pharmacodynamics Peter Dalgaard April/May Introduction to metabolic models

Transcription

1 Pharmacokinetics and pharmacodynamics Peter Dalgaard April/May 2003 Introduction to metabolic models 1 16

2 Ideas 1

3 Ideas Mainly follow Carson, Cobelli, and Finkelstein, Ch.2+5 1

4 Ideas Mainly follow Carson, Cobelli, and Finkelstein, Ch.2+5 Concentrate on biophysics 1

5 Ideas Mainly follow Carson, Cobelli, and Finkelstein, Ch.2+5 Concentrate on biophysics Formulating models rather than solving them 1

6 Sketch of human metabolism 2

7 Inputs: food, air Sketch of human metabolism 2

8 Inputs: food, air Sketch of human metabolism Produce: energy (oxidation), synthesis of tissue 2

9 Sketch of human metabolism Inputs: food, air Produce: energy (oxidation), synthesis of tissue Metabolic sites 2

10 Sketch of human metabolism Inputs: food, air Produce: energy (oxidation), synthesis of tissue Metabolic sites Metabolic processes 2

11 Sketch of human metabolism Inputs: food, air Produce: energy (oxidation), synthesis of tissue Metabolic sites Metabolic processes Regulatory systems 2

12 Metabolic sites 3

13 Metabolic sites Alimentary canal: Extraction of nutrients 3

14 Metabolic sites Alimentary canal: Extraction of nutrients Blood: Nutrient transport + waste removal 3

15 Metabolic sites Alimentary canal: Extraction of nutrients Blood: Nutrient transport + waste removal Lungs: Extract oxygen, excrete CO 2 3

16 Metabolic sites Alimentary canal: Extraction of nutrients Blood: Nutrient transport + waste removal Lungs: Extract oxygen, excrete CO 2 Kidneys, skin: Filtration, excretion 3

17 Metabolic sites Alimentary canal: Extraction of nutrients Blood: Nutrient transport + waste removal Lungs: Extract oxygen, excrete CO 2 Kidneys, skin: Filtration, excretion Liver: Prepare for excretion, breakdown of complex subst. 3

18 Metabolic sites Alimentary canal: Extraction of nutrients Blood: Nutrient transport + waste removal Lungs: Extract oxygen, excrete CO 2 Kidneys, skin: Filtration, excretion Liver: Prepare for excretion, breakdown of complex subst. Bone marrow, pancreas, etc. 3

19 Metabolic concepts 4

20 Metabolic concepts Catabolic processes (break down) 4

21 Metabolic concepts Catabolic processes (break down) Anabolic processes (build up) 4

22 Metabolic concepts Catabolic processes (break down) Anabolic processes (build up) Chemical reactions 4

23 Metabolic concepts Catabolic processes (break down) Anabolic processes (build up) Chemical reactions Enzymes 4

24 Metabolic concepts Catabolic processes (break down) Anabolic processes (build up) Chemical reactions Enzymes Metabolic pathway 4

25 Endocrine systems 5

26 Endocrine systems Glands: Thyroid, testes, etc. 5

27 Endocrine systems Glands: Thyroid, testes, etc. Hormones: 5

28 Endocrine systems Glands: Thyroid, testes, etc. Hormones: Peptides, amino acid complexes 5

29 Endocrine systems Glands: Thyroid, testes, etc. Hormones: Peptides, amino acid complexes Steroids, fat-like 5

30 Endocrine systems Glands: Thyroid, testes, etc. Hormones: Peptides, amino acid complexes Steroids, fat-like H. are generated by glands and regulated by various means: Nervous system, presence of metabolites, external stimuli 5

31 Endocrine systems Glands: Thyroid, testes, etc. Hormones: Peptides, amino acid complexes Steroids, fat-like H. are generated by glands and regulated by various means: Nervous system, presence of metabolites, external stimuli Act on target organs in various ways: Synthesis of enzymes and other substances, affects transport processes (e.g. modify membrane permeability) 5

32 Endocrine systems Glands: Thyroid, testes, etc. Hormones: Peptides, amino acid complexes Steroids, fat-like H. are generated by glands and regulated by various means: Nervous system, presence of metabolites, external stimuli Act on target organs in various ways: Synthesis of enzymes and other substances, affects transport processes (e.g. modify membrane permeability) Transported via blood. 5

33 Compartmental models 6

34 Compartmental models C.: Idealized store of substance 6

35 Compartmental models C.: Idealized store of substance E.g. Blood, extracellular space, liver 6

36 Compartmental models C.: Idealized store of substance E.g. Blood, extracellular space, liver dq i dt = j R i j j R j i 6

37 Compartmental models C.: Idealized store of substance E.g. Blood, extracellular space, liver dq i dt = j R i j j R j i Q i amount in compartment i 6

38 Compartmental models C.: Idealized store of substance E.g. Blood, extracellular space, liver dq i dt = j R i j j R j i Q i amount in compartment i R i j mass transfer to i from j (NB: convention) 6

39 Compartmental models C.: Idealized store of substance E.g. Blood, extracellular space, liver dq i dt = j R i j j R j i Q i amount in compartment i R i j mass transfer to i from j (NB: convention) R i j = R i j (Q j ) 6

40 Chemical reactions 7

41 Chemical reactions Irreversible single-stage reaction A + B products 7

42 Chemical reactions Irreversible single-stage reaction A + B products Law of mass action dc A dt = kc α A Cβ B 7

43 Chemical reactions Irreversible single-stage reaction A + B products Law of mass action dc A dt = kc α A Cβ B C A conc. of A, C B conc of B 7

44 Chemical reactions Irreversible single-stage reaction A + B products Law of mass action dc A dt = kc α A Cβ B C A conc. of A, C B conc of B α, β integers, order with respect to A resp. B 7

45 Chemical reactions Irreversible single-stage reaction A + B products Law of mass action dc A dt = kc α A Cβ B C A conc. of A, C B conc of B α, β integers, order with respect to A resp. B α + β order of reaction 7

46 Single substance case 8

47 First-order reaction Single substance case A products 8

48 First-order reaction Single substance case A products dc A dt = kc A 8

49 First-order reaction Single substance case A products dc A dt Or, assuming constant volume = kc A dq A dt = kq A 8

50 Enzyme-controlled reaction E enzyme, S substrate, X enzyme-substrate complex, P products 9

51 Enzyme-controlled reaction E enzyme, S substrate, X enzyme-substrate complex, P products E + S X E + P 9

52 Enzyme-controlled reaction E enzyme, S substrate, X enzyme-substrate complex, P products E + S X E + P dq E dt dq S dt dq X dt dq P dt = k XE Q E Q S + k EX Q X = k XS Q E Q S + k SX Q X = (k XE + k XS )Q E Q S (k SX + k EX )Q X kpxq X = k PX Q X 9

53 Two compartments Transport across membrane dq 1 dt = dq 2 dt = D A l (C 2 C 1 ) 10

54 Two compartments Transport across membrane dq 1 dt = dq 2 dt Q i quantity in compartment i = D A l (C 2 C 1 ) 10

55 Two compartments Transport across membrane dq 1 dt = dq 2 dt Q i quantity in compartment i C i concentration in compartment i = D A l (C 2 C 1 ) 10

56 Two compartments Transport across membrane dq 1 dt = dq 2 dt Q i quantity in compartment i C i concentration in compartment i D diffusion constant = D A l (C 2 C 1 ) 10

57 Two compartments Transport across membrane dq 1 dt = dq 2 dt Q i quantity in compartment i C i concentration in compartment i D diffusion constant A effective boundary area = D A l (C 2 C 1 ) 10

58 Two compartments Transport across membrane dq 1 dt = dq 2 dt Q i quantity in compartment i C i concentration in compartment i D diffusion constant A effective boundary area = D A l (C 2 C 1 ) l effective separation between compartments 10

59 Compartment washed by fluid Fluid enters free of A, mixed perfectly, then leaves dq A dt = W Q A V 11

60 Compartment washed by fluid Fluid enters free of A, mixed perfectly, then leaves Q A quantity of A dq A dt = W Q A V 11

61 Compartment washed by fluid Fluid enters free of A, mixed perfectly, then leaves Q A quantity of A dq A dt = W Q A V W volume flow of liquid 11

62 Compartment washed by fluid Fluid enters free of A, mixed perfectly, then leaves Q A quantity of A dq A dt = W Q A V W volume flow of liquid V volume of compartment (assumed constant) 11

63 Transport by fluid circulation Two extreme models of blood transport: Totally mixed, or completely non-mixed. (Neither is correct, of course.) 12

64 Transport by fluid circulation Two extreme models of blood transport: Totally mixed, or completely non-mixed. (Neither is correct, of course.) Consider injection at site 1 to time t and appearance at site 2 after delay τ τ = l v 12

65 Transport by fluid circulation Two extreme models of blood transport: Totally mixed, or completely non-mixed. (Neither is correct, of course.) Consider injection at site 1 to time t and appearance at site 2 after delay τ τ = l v l effective distance between site 1 and site 2 12

66 Transport by fluid circulation Two extreme models of blood transport: Totally mixed, or completely non-mixed. (Neither is correct, of course.) Consider injection at site 1 to time t and appearance at site 2 after delay τ τ = l v l effective distance between site 1 and site 2 v effective blood velocity 12

67 Transport by fluid circulation Two extreme models of blood transport: Totally mixed, or completely non-mixed. (Neither is correct, of course.) Consider injection at site 1 to time t and appearance at site 2 after delay τ τ = l v l effective distance between site 1 and site 2 v effective blood velocity Flow into organ at site 2 (δ Dirac unit impulse) R = Dδ(t τ) 12

68 Controlled processes External parameter θ, e.g. temperature for a chemical reaction 13

69 Controlled processes External parameter θ, e.g. temperature for a chemical reaction dq A dt = k(θ)q A 13

70 Controlled processes External parameter θ, e.g. temperature for a chemical reaction dq A dt = k(θ)q A similar role played by fluid flow in washed compartment, or (in a sense) enzyme concentration in enzyme-catalyzed reaction. 13

71 Summary 14

72 Summary Metabolic and endocrine systems are interacting chemical and transport processes 14

73 Summary Metabolic and endocrine systems are interacting chemical and transport processes Even very simple and highly idealized systems like the enzyme example quickly become complex and nonlinear 14

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