Exploring how to apply in vitro/in vivo correlations for controlled release dosage forms, Bioavailability of Drug Delivery Systems: Mathematical Modeling clearly elucidates this complex phenomena and provides a guide for the respective mathematical modeling. The book introduces mathematical modeling methods for calculating the profiles of plasma levels obtained with controlled release dosage forms and provides examples and case studies to illustrate the techniques employed. The author has considerable experience in investigating mathematical fundamentals that are related to pharmaco- and toxicokinetics, modified-release drug products, physiologic pharmacokinetics and statistical treatment in clinical situations. The mathematical models he has developed are particularly powerful because they account for such major parameters as the kinetics of drug release controlled by diffusion or by erosion, and the kinetics of absorption into and elimination out of the plasma. They are also able to solve the problem of determining the drug level in plasma as a result of patient non-compliance, incorrect dosage, and incorrect frequency and to determine the best dosage forms necessary for therapy.Using master curves, the book highlights the inter-variability of the patients often expressed by different responses towards a drug. Thus, after evaluating a patient's pharmacokinetic parameters, the dose can be adapted to the patient, with the expectation of decreasing the side effects for each patient. Using dimensionless numbers in repeated doses, either for the time or for the plasma drug concentration, makes the master curves useful for every drug, providing that its pharmacokinetics was linear. These master curves address clear information either to the patients or to the therapists in a didactic and easy way. The patients can see from first look the effects of non-compliance and therapists can see the dramatic effects of inter-variability of patients towards a drug.Drug discovery and dosage forms have become an increasingly time-consuming and expensive process. The development of a single drug can leave behind more than 10 to 15 years of work. Discussing time and cost-effective methods as alternatives to conventional in vivo methods, the book helps you analyze and integrate in vitro/in vivo correlations and apply them to patient care and drug consultation situations.
Author(s): Jean-Maurice Vergnaud, Iosif-Daniel Rosca
Edition: 1
Publisher: CRC Press
Year: 2005
Language: English
Pages: 227
Assessing Bioavailability of Drug Delivery Systems: Mathematical Modeling......Page 2
Table of Contents......Page 9
Preface......Page 4
Authors......Page 7
Acknowledgments......Page 8
SYMBOLS......Page 16
1.1 DRUG (ACTIVE AGENT) AND ITS SUPPLY FORM (DOSAGE FORM)......Page 17
1.2.2 PHARMACOKINETIC STAGE......Page 18
1.3 PHARMACOKINETICS......Page 19
1.6 MEMBRANES......Page 20
1.7 BIOAVAILABILITY......Page 21
1.8 ABSORPTION OF THE DRUG IN THE BLOOD......Page 22
1.10 ELIMINATION OF THE DRUG......Page 23
1.10.3 BIOLOGICAL HALF-LIFE TIME OF THE DRUG......Page 24
1.11 THERAPEUTIC INDEX......Page 25
1.12 DETERMINATION OF THE PHARMACEUTICAL PARAMETERS......Page 26
1.12.2 VOLUME OF DISTRIBUTION (APPARENT VOLUME ) Vp......Page 27
1.12.5 LINEAR OR NONLINEAR PHARMACEUTICS......Page 28
REFERENCES......Page 29
2.1 ADMINISTRATION OF A SINGLE DOSE......Page 30
2.2 REPEATED INTRAVENOUS INJECTION (DIV)......Page 33
2.2.1 CALCULATION OF THE DRUG CONCENTRATION AT PEAKS AND TROUGHS......Page 34
2.2.2 EFFECT OF THE NATURE OF THE DRUG......Page 35
2.2.3 CALCULATION OF THE AREA UNDER THE CURVE......Page 37
2.3.1 GENERAL EXPRESSION OF CIV......Page 39
2.3.2 CHANGE IN THE RATE OF DELIVERY DURING THE COURSE OF INFUSION......Page 42
2.3.3 VALUE OF THE AREA UNDER THE CURVE WITH INFUSION DELIVERY......Page 43
2.4.1 MATHEMATICAL TREATMENT OF THE PROCESS......Page 44
REFERENCES......Page 46
3.1.1 PRINCIPLE OF DRUG TRANSPORT......Page 47
3.1.2 CALCULATION OF THE PROFILES OF DRUG CONCENTRATION......Page 49
3.2.1 EFFECT OF THE RATE CONSTANT OF ABSORPTION ON THE PROCESS......Page 51
3.2.2 EFFECT OF THE RATE CONSTANT OF ELIMINATION ON DRUG TRANSPORT......Page 52
3.2.3 EFFECT OF THE NATURE OF THE DRUG......Page 53
3.3.1 PRINCIPLE FOR REPEATED ORAL DOSES AND PARAMETERS......Page 55
3.3.2 EFFECT OF THE NATURE OF THE DRUG IN MULTIDOSES......Page 58
3.3.3 MASTER CURVES WITH DIMENSIONLESS NUMBER......Page 60
3.4.2 AUC WITH REPEATED DOSES......Page 63
REFERENCES......Page 65
NOMENCLATURE......Page 67
4.1.1.1 Boundary Conditions......Page 68
4.1.1.3 Process of Drug Release......Page 69
4.1.2 KINETICS OF DRUG RELEASE FROM THIN FILMS (THICKNESS 2 L)......Page 70
4.1.2.1 Dimensionless Numbers......Page 72
4.1.2.2 Application to Experiments and Calculation......Page 73
4.1.2.3 Consideration on the Drug–Polymer Couple......Page 76
4.1.3.1 Kinetics of Release from the Sphere......Page 77
4.1.3.2 Calculation for the Parallelepiped of Sides 2a, 2b, 2c......Page 79
4.1.3.4 Calculation for a Cylinder of Radius R and Height 2 H......Page 80
4.1.4 KINETICS OF DRUG RELEASE FROM SPHERICAL DOSAGE FORMS......Page 81
4.1.5 KINETICS OF RELEASE WITH PARALLELEPIPED AND CUBIC FORMS......Page 82
4.1.6 CYLINDRICAL DOSAGE FORMS......Page 85
4.1.7 DETERMINATION OF THE PARAMETERS OF DIFFUSION......Page 86
4.2.2 KINETICS OF RELEASE FOR A SPHERE OF INITIAL RADIUS R0......Page 88
4.2.4 KINETICS OF RELEASE FOR A PARALLELEPIPED OF SIDES 2A, 2B, AND 2C......Page 89
4.2.5 KINETICS OF RELEASE FOR A CUBE OF SIDES 2A......Page 90
4.3.3 PROCESSS WITH DIFFUSION AND SWELLING......Page 91
REFERENCES......Page 93
5.1.1 CONCEPT OF SUSTAINED RELEASE......Page 95
5.1.2 OBJECTIVES OF IN VITRO DISSOLUTION TESTS......Page 96
5.2 IN VITRO–IN VIVO CORRELATIONS FOR IMMEDIATE-RELEASE DRUGS......Page 97
5.3.1 ESTABLISHMENT OF LEVELS FOR IN VITRO–IN VIVO CORRELATIONS......Page 98
5.3.2 REQUIREMENTS FOR ESTABLISHING LEVEL A CORRELATIONS......Page 99
5.3.3 MATHEMATICAL TREATMENT OF IN VITRO–IN VIVO CORRELATIONS......Page 100
REFERENCES......Page 103
6.1 METHODS OF CALCULATION......Page 105
6.1.1 ASSUMPTIONS FOR CALCULATION......Page 106
6.1.3 NUMERICAL TREATMENT......Page 107
6.2.1 ASSESSMENT OF THE AMOUNT OF DRUG IN VARIOUS PLACES......Page 108
6.2.2 EFFECT OF THE SHAPE OF THE DOSAGE FORM......Page 113
6.2.3 EFFECT OF THE NATURE OF THE DRUG......Page 114
6.2.4 EFFECT OF THE POLYMER ON THE SUSTAINED RELEASE......Page 115
6.2.5 EFFECT OF PATIENTS’ INTERVARIABILITY......Page 119
6.3.1 EXAMPLES WITH VARIOUS DRUG–POLYMER COUPLES......Page 121
6.3.2 EFFECT OF THE NATURE OF THE DRUG ON THE PROFILES......Page 124
6.3.3 EFFECT OF THE POLYMER MATRIX ON THE PROFILES......Page 125
6.3.4 EFFECT OF THE PATIENTS’ INTERVARIABILITY......Page 127
6.3.5 EFFECT OF THE DOSE INTERVALS (FREQUENCY)......Page 129
6.4.1 RELATIONSHIPS BETWEEN HALF-LIFE TIMES......Page 133
6.4.2 PLASMA DRUG PROFILE IN TERMS OF CONCENTRATION......Page 135
REFERENCES......Page 136
NOMENCLATURE......Page 138
7.1.1 ASSUMPTIONS FOR CALCULATING THE PLASMA DRUG PROFILE......Page 139
7.2 PLASMA DRUG PROFILE WITH A SINGLE DOSE......Page 140
7.2.1 EFFECT OF THE SHAPE OF THE DOSAGE FORMS......Page 141
7.2.2 EFFECT OF THE TIME OF FULL EROSION......Page 142
7.2.3 EFFECT OF THE NATURE OF THE DRUG......Page 143
7.2.4 PATIENTS’ INTERVARIABILITY......Page 144
7.2.5 COMPARISON OF THE PROCESSES OF DIFFUSION AND EROSION......Page 146
7.3 PLASMA DRUG PROFILE WITH REPEATED MULTIDOSES......Page 148
7.3.1 EFFECT OF THE SHAPE OF THE DOSAGE FORM......Page 149
7.3.2 EFFECT OF THE TIME OF FULL EROSION......Page 150
7.3.3 EFFECT OF THE NATURE OF THE DRUG......Page 151
7.3.4 PATIENTS’ INTERVARIABILITY......Page 152
7.4.1 RELATIONSHIPS BETWEEN THE HALF-LIFE TIMES AND t0.5 T0.5......Page 154
7.4.2 PLASMA DRUG PROFILES IN TERMS OF CONCENTRATION......Page 156
REFERENCES......Page 157
8.1 LIMITED RELIABILITY OF THE PATIENT......Page 160
8.1.4 VARIOUS CASES OF NONCOMPLIANCE......Page 161
8.2.1 PERFECT COMPLIANCE AND OMISSION......Page 162
8.2.2 OMISSION FOLLOWED BY A DOUBLE DOSE......Page 164
8.3.1 RIGHT COMPLIANCE AND OMISSION......Page 168
8.3.2 OMISSION FOLLOWED BY DOUBLE DOSING......Page 170
REFERENCES......Page 172
NOMENCLATURE......Page 173
9.1.1 SHORT BIBLIOGRAPHY......Page 175
9.1.2.1 Assumptions......Page 176
9.1.2.2 Evaluation of the Amount of Drug along the GI Tract and the Plasma......Page 177
9.1.2.3 Transfer of the Drug into the Lung Tissue......Page 178
9.1.2.4 Transfer of Drug in the Bronchial Secretion......Page 179
9.1.5 RESULTS OBTAINED WITH THE LUNG TISSUE......Page 180
9.1.6 RESULTS OBTAINED WITH THE BRONCHIAL SECRETION......Page 182
9.2.1 SHORT BIBLIOGRAPHICAL SURVEY......Page 185
9.2.2.1 Assumptions......Page 187
9.2.2.3 Administration of the Drug through Short Infusions......Page 188
9.2.3 THEORETICAL AND EXPERIMENTAL RESULTS......Page 189
9.3.1 SHORT BIBLIOGRAPHICAL SURVEY......Page 191
9.3.2.2 MATHEMATICAL TREATMENT......Page 193
9.3.3 RESULTS WITH THE DRUG PROFILES IN THE VEGETATION......Page 194
REFERENCES......Page 195
10.1 GENERAL MECHANISMS OF DRUG DELIVERY......Page 199
10.2.1 MAIN CHARACTERISTICS AND PROPERTIES OF THE SKIN......Page 201
10.3.1 ASSUMPTIONS......Page 202
10.3.2 CALCULATION OF THE DRUG TRANSFER INTO THE BLOOD......Page 203
10.3.2.1 Transfer into the Blood Compartment......Page 204
10.4.1.1 Preparation of the Patch [11]......Page 205
10.4.2 RESULTS OBTAINED FROM IN VITRO EXPERIMENTS......Page 206
10.4.4 EVALUATION OF THE PLASMA DRUG LEVEL......Page 208
10.4.5 CONCLUSIONS AND FUTURE PROSPECTS......Page 210
10.5 EFFECT OF THE CHARACTERISTICS OF THE TTS......Page 211
10.5.1 DIFFUSION-CONTROLLED TTS WITH A POLYMER ALONE......Page 212
10.5.1.1 Assumptions......Page 213
10.5.2.1 Assumptions......Page 216
10.5.3 TTS WITH DRUG RELEASE CONTROLLED BY CONVECTION......Page 218
10.6 EFFECT OF THE SKIN PARAMETERS......Page 220
10.6.2 INCREASE IN THE DIFFUSIVITY OF THE DRUG IN THE SKIN......Page 221
REFERENCES......Page 222
Conclusions......Page 225
