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Pharmacokinetics of Adderall

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Pharmacokinetics of Adderall ESP Project Pharmacokinetics of Adderall Vivian Chow & Thukarasha Sivapatharajah Differential Equations, Section 00001 Professor Ivan T. Ivanov May 15 2015 Table of Contents Introduction 2 Theory behind Pharmacology 2 Adderall 4 Pharmacokinetics 6 Situation 1: Blood-Gut Pharmacokinetic Model Using Adderall 7 Situation 2: Contrasting Behaviours of Adderall IR and Adderall XR 11 Situation 3: Adderall’s Effect on a Rhesus Monkey 14 Situation 4: Administering Drugs every 4, 8 & 16 hours 16 Conclusion 19 Works Cited 20 Appendix A 21 Appendix B 23 1 Introduction Most drugs fall into the categories of stimulants, depressants, opiates and hallucinogens, where the drugs can be addictive, induce dependency and have different effects on the human body. Some examples of drugs are Tylenol and Aspirin, as well as Marijuana and Tobacco. In addition, pharmacologists help expand the medical field by studying drugs through examining the interactions between chemical substances and living organisms before making drugs available to the population. Hence, this project will model the pharmacokinetics of a drug by studying its dissipation and removal rates in the body. Theory behind Pharmacology Pharmacology is the science that deals with drugs, their properties, actions and effects in the body. It involves the sciences of pharmaceutics for the preparation of the drugs, therapeutics for using drugs to treat diseases and toxicosis for the various side-effects (Magoma). Pharmacology can be divided into five processes: 1. The pharmaceutical process of drugs – chemical synthesis, formulation and distribution of drugs. 2. The pharmacokinetic process – the time course of drug concentration in the body via absorption, distribution, biotransformation and excretion of the drug. 3. The pharmacodynamics process – the mechanism of drug action – interaction of drugs with the body. 4. The therapeutic process – the clinical response arising from the pharmacodynamics process. 5. The toxicological process – various effects of drugs. 2 Figure 1: Relationships between the five pharmacological processes *This project will examine mainly the pharmacokinetics of Adderall Extended (XR)* 3 Adderall History: Shire Pharmaceuticals Group created the Adderall drug in 1996 and has continued to produce this drug until 2007. After 2007, Teva Pharmaceuticals started to produce this drug. Presently, two types of Adderall exist: Adderall XR (extended released) and Adderall IR (immediate release). Originally, the instant released tablet version had been the only type available. In 2002, Adderall XR began to be manufactured. Adderall XR provides an extended release by distributing only half the drug immediately within the system whilst releasing the other half after about four to six hours using the controlled release bead technology. Usage: This drug is currently prescribed to patients with ADHD (Attention Deficit Hyperactivity Disorder) or narcolepsy (disorder with the nerves that affects the users control over sleep and staying awake). Starting from around 2009, more students, mostly college students started to use the drug without being prescribed during the mid-semester and final weeks in order to keep themselves awake whilst cramming for exams. Since Adderall is a stimulant, the student will take it in order to reduce tiredness and increase focus during the examination period. Similarly to Ritalin, the FDA (Food & Drug Administration (US)) has labelled this Schedule II drug due to its high risk of abuse, which in consequence can lead to severe physical and psychological effects. Composition: This drug is the remake of the former drug known as Obetrol, a discontinued dieting drug. With slight modification of Obetrol, Adderall was created. Adderall is composed of two amphetamine stereoisomers salt: 75% dextero-amphetamine (d) and 25% levo- amphetamine (l). The half-life for dextero-amphetamine is ten hours whilst its other isomer is thirteen hours. Its given molecular formula is C9H13N. Within this drug, there is one benzene aromatic (arene) ring linked to an amine group on the side. 4 Figure 2: Molecular Structure Effects: For children, some side-effects may include vomiting, nausea, fever and insomnia. For adolescents, some side-effects include weight loss, nervousness, lack of appetite and insomnia. For adults, some side-effects can include headaches, diarrhea, anxiety attacks, insomnia, dizziness and dry mouth. Dosage: The Adderall IR tablets are instructed to be taken up to three tablets daily with a time gap of four to six hours after the intake of each tablet. But, the total daily intake dose should be 40mg or more if required. These tablets are available in different doses: 5mg, 7.5mg, 10mg, 15mg, 20mg and 30mg. The Adderall XR is available in capsules of 5mg, 10mg, 15mg, 20mg, 25mg and 30mg. But, the total daily recommended dose is 30mg and is slightly lower than daily recommended dose of Adderall IR. Figure 3: Dosages of Adderall XR (left) and Adderall IR (right) available 5 Pharmacokinetics Bioavailability physiology: “The proportion of a drug or other substance which enters the circulation when introduced into the body and so is able to have an active effect" (Oxford English Dictionary). Within Adderall XR, the active compound is known as amphetamine. The amount of amphetamine available within the system is dependent on the pH of the gut and the intestines. Amphetamine has a pKa of about nine to ten and considered a weak base. If the pH within the system between the gut and intestines is above seven, more of the drug will be absorbed. On the contrary, if the gastrointestinal pH is below seven, the drug will not be easily absorbed resulting in lower bioavailability of amphetamine. About less than forty percent of the amphetamine is transported with the proteins found with the blood around the bloodstream. The half-life as stated previously of dextroamphetamine ranges from nine to eleven hours whilst that of levoamphetamine ranges from eleven to fourteen hours. But, the half-life can vary according to the user’s diet which can in turn affect the pH of their urine. The instant-release (Adderall IR) reaches its peak concentration of amphetamine within the plasma at about three hours. Whereas, the extend-release drug after ingestion delays its peak concentration until about seven hours. Amphetamine is excreted through the kidney, but the amount that will be excreted is dependent on the urine pH. An increase in urine basicity will result in a decrease of excretion and vice-versa. 6 Situation 1: Blood-Gut Pharmacokinetic Model Using Adderall The pharmacokinetic model using Adderall will illustrate how the drug is consumed and transferred between the gut and blood. This is examined through a math model of Adderall with two compartments. What follows are a brief description of the each parameters and the procedures in solving this situation. To solve this situation, variation of parameters is used. Although, variation of parameters is the simplest method to solve for the equations that model the concentration in the blood and gut, diagonalization (D=T-1MT) can be used to solve for the nonhomogeneous system since , where T is the combination of the eigenvectors of M and z is the driving function. Let Compartment 1 be Gut and Compartment 2 be Blood, then: c1 = concentration in the gut as a function of time c2 = concentration in the blood as a function of time k12 = rate of transfer from blood to gut k21 = rate of transfer from gut to blood K = rate constant at which the drug is removed from the blood ti = initial time (hours) tf = final time (hours) V1 = volume of blood in gut (litres) V2 = volume of blood in body (litres) Some values are assumed to be zero, for instance, ti, c1(0) and c2(0), while k12 is 0.05 and k21 is 2.95. This project will analyze the effects of Adderall XR in humans, so V1 is assumed to be 1L, V2 is 5L and K is (ln2)/8=0.086643397. 7 The rates of the drug circulating in the system are represented by the following equations: 1. 3. 2. 4. Equation 1 represents what occurs to the drug in compartment 1 (gut), while equation 2 represents what occurs to the drug in compartment 2 (blood). In both equations, the ‘x’ variable represents the quantity of the drug. Equations 1 and 2 are modified into Equations 3 and 4 repetitively using the relation where x is the amount of Adderall, V is the volume of blood in the compartments and C is the concentration of Adderall in the compartments. Since the drug is circulating in the system, a positive equation indicates the drug flowing into the system while a negative equation indicates the drug flowing out the system. To find the equations that model the pharmacokinetics of Adderall, meaning to find the equations that represent the change in concentration over a period of time in the gut and the blood, combine equations 3 and 4 because that way a matrix is formed, which can be solved using variation of parameters to get the functions based on the formula where M= . Since there is one driving function that represents each dosage, use variation of parameters , where z is the driving function and C is the constants derived from the general solution to solve for the equations that demonstrate the concentrations over a period of time in the gut and blood. 8 Step 1: Eigenvalues of M: (-2.95-λ)(-ln(2)/8+0.05-λ)-(0.25)(0.59) λ1 = -3.0015 & λ2 = -0.0852 Step 2: Eigenvectors of M: Step 3: Step 4: Step 5: Step 6: Step 7: Step 8: Particular solution + General solution Step 9: Using the initial conditions (t=0 & y=0), the constants can be solved C1 = 0.5011 and C2 = -0.2220 Step 10: Plug-in the constants and extract the equations -3.0015t + -0.0852t -t y1 (t) = -0.49081e 0.01929e + 0.51010e -3.0015t + -0.0852t - -t y2 (t) = 0.10108e 0.22114e 0.32222e 9 These functions represent the modeling of one dosage with respect to time and the results are graphed below.
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