Bio-pharmaceutics and Pharmacokinetics
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Derive the equation to determine the plasma drug concentration at steady state level after multiple injection
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Calculating c max^α,c (mⅈ
1) To calculate the maximum (cmaxα), minimum (Cminα), and average (cavα) drug concentrations for an intravenous multiple dose regimen, divide the amount of drug in the body by the volume it is dissolved in.
2) cmaxα is the highest drug concentration and indicates drug safety and accumulation. Cminα is the lowest concentration and determines drug activity. cavα is important for the desired therapeutic effect.
3) cavα is not the average of cmaxα and Cminα, but is instead calculated using the area under the curve, dosing interval, and drug clearance and volume of distribution.
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A loading dose is an initial higher dose of a drug given at the beginning of treatment to more rapidly reach steady state plasma concentrations. Drugs with long half-lives benefit from a loading dose to quickly achieve therapeutic drug levels. The loading dose should approximate the amount of drug in the body at steady state. The main importance of a loading dose is to attain the average plasma concentration at steady state as quickly as possible to provide quick therapeutic effects in some cases.
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1) The document discusses the determination of the time to reach maximum drug concentration (tmax) after oral administration of a drug.
2) It presents equations that model the absorption and elimination rates of drugs in the body over time and how these rates impact the drug concentration in plasma.
3) It derives an equation that shows tmax is independent of dose and depends only on the absorption and elimination rate constants (ka and k). The tmax occurs when the rates of drug absorption and elimination are equal, making the rate of concentration change equal zero.
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The document defines maintenance dose as the dose of a drug administered to replace the amount eliminated from the body during the dosing interval, in order to maintain a steady state drug level in the body. It derives the maintenance dose equation as Q = k_e D_B, where Q is the maintenance dose, k_e is the elimination rate constant, and D_B is the total amount of drug in the body at the effective drug concentration level. Alternatively, the maintenance dose can be calculated as Q = Cl_T(EDC), where Cl_T is the total clearance and EDC is the effective drug concentration.
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Congestive heart failure
Congestive heart failure occurs when the heart fails to pump enough blood to meet the body's needs. It results from the heart's inability to contract sufficiently. Diagnosis involves tests like chest X-rays, ECGs, blood tests, and cardiac catheterization. Treatment includes diuretics to reduce preload, nitrates to reduce afterload, ACE inhibitors to reduce both, and cardiotonics like digoxin to increase contractility and cardiac output. The goal of treatment is to increase stroke volume and cardiac output in order to correct symptoms and heart enlargement caused by heart failure.
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Autacoids are endogenous compounds that act as local hormones near their site of synthesis. They have short half-lives and include substances like histamine, serotonin, prostaglandins, and kinins. Autacoids are involved in processes like inflammation, allergic reactions, neurotransmission, and gastric acid secretion. Histamine promotes smooth muscle contraction and gastric acid secretion by interacting with H1 and H2 receptors. Serotonin is derived from tryptophan and is found in the GI tract, blood platelets, and CNS, where it contributes to feelings of well-being. H1 receptor antagonists are used to treat allergic reactions while H2 receptor antagonists reduce gastric acid secretion and treat ulcers.
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Hypertension, or high blood pressure, refers to blood pressure above 140/90 mmHg. It puts stress on blood vessels and vital organs like the heart, brain, and kidneys over time if not controlled. The document discusses what causes hypertension, risk factors, potential health effects, diagnosis through blood pressure monitoring, treatment through lifestyle modifications and medications, and treatment goals of lowering blood pressure to reduce risks of heart disease, stroke, and other complications. Treatment involves lifestyle changes like losing weight, reducing salt, exercising, and quitting smoking, as well as medications like diuretics, beta-blockers, calcium channel blockers, ACE inhibitors, and ARBs.
Calculating c max^α,c (mⅈ
1) To calculate the maximum (cmaxα), minimum (Cminα), and average (cavα) drug concentrations for an intravenous multiple dose regimen, divide the amount of drug in the body by the volume it is dissolved in.
2) cmaxα is the highest drug concentration and indicates drug safety and accumulation. Cminα is the lowest concentration and determines drug activity. cavα is important for the desired therapeutic effect.
3) cavα is not the average of cmaxα and Cminα, but is instead calculated using the area under the curve, dosing interval, and drug clearance and volume of distribution.
Loading dose plus iv infusion
A loading dose is an initial higher dose of a drug given at the beginning of treatment to more rapidly reach steady state plasma concentrations. Drugs with long half-lives benefit from a loading dose to quickly achieve therapeutic drug levels. The loading dose should approximate the amount of drug in the body at steady state. The main importance of a loading dose is to attain the average plasma concentration at steady state as quickly as possible to provide quick therapeutic effects in some cases.
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2) It presents equations that model the absorption and elimination rates of drugs in the body over time and how these rates impact the drug concentration in plasma.
3) It derives an equation that shows tmax is independent of dose and depends only on the absorption and elimination rate constants (ka and k). The tmax occurs when the rates of drug absorption and elimination are equal, making the rate of concentration change equal zero.
Bio pharmaceutics
The document defines maintenance dose as the dose of a drug administered to replace the amount eliminated from the body during the dosing interval, in order to maintain a steady state drug level in the body. It derives the maintenance dose equation as Q = k_e D_B, where Q is the maintenance dose, k_e is the elimination rate constant, and D_B is the total amount of drug in the body at the effective drug concentration level. Alternatively, the maintenance dose can be calculated as Q = Cl_T(EDC), where Cl_T is the total clearance and EDC is the effective drug concentration.
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7. Discuss the placement and polarity of the leads of electrocardiograph
8. Describe the normal electrocardiograms recorded from the limb leads and explain the physiological basis of the different records that are obtained
9. Define mean electrical vector (axis) of the heart and give the normal range
10. Define the mean QRS vector
11. Describe the axes of leads (hexagonal reference system)
12. Comprehend the vectorial analysis of the normal ECG
13. Determine the mean electrical axis of the ventricular QRS and appreciate the mean axis deviation
14. Explain the concepts of current of injury, J point, and their significance
Study Resources:
1. Chapter 11, Guyton and Hall Textbook of Medical Physiology, 14th edition
2. Chapter 9, Human Physiology - From Cells to Systems, Lauralee Sherwood, 9th edition
3. Chapter 29, Ganong’s Review of Medical Physiology, 26th edition
4. Electrocardiogram, StatPearls - https://www.ncbi.nlm.nih.gov/books/NBK549803/
5. ECG in Medical Practice by ABM Abdullah, 4th edition
6. Chapter 3, Cardiology Explained, https://www.ncbi.nlm.nih.gov/books/NBK2214/
7. ECG Basics, http://www.nataliescasebook.com/tag/e-c-g-basics
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Bio-pharmaceutics and Pharmacokinetics
- 1. DERIVE THE EQUATION TO DETERMINE THE PLASMA DRUG CONCENTRATION AT STEADY STATE LEVEL AFTER MULTIPLE INJECTION. PREPARED BY: MD. AMZAD HOSSAIN
- 2. 𝐶 𝑚𝑎𝑥 α 𝐶 𝑎𝑣 α Plasma level 𝐶 𝑚𝑖𝑛 α 1 8 12 16 Time Concentration of drug in the body after 1st dose , 2nd dose ……. nth dose can be determined by the following ways: Drug concentration immediately after 1st dose— 𝐶 𝑜. 1= 𝐷𝑜 𝑉
- 3. At the end of the 1st dose 𝐶τ. 1 = 𝐷𝑜 𝑉 𝑒−𝑘τ where , τ = dosing interval, 𝐷𝑜= dose. let, 𝑒 𝑘τ = R so, 𝐶τ. 1 = 𝐷𝑜 𝑉 R --------------- ( 1 ) Immediately after 2nd IV dose, the plasma concentration is --- 𝐶 𝑜. 2 = 𝐷𝑜 𝑉 𝑅 + 𝐷𝑜 𝑉 And at the end of the 2nd dose ---- 𝐶 𝑇. 2 = ( 𝐷𝑜 𝑉 𝑅 + 𝐷𝑜 𝑉 ) R = 𝐷𝑜 𝑉 𝑅2 + 𝐷𝑜 𝑉 𝑅 Immediately, after the 3rd dose the plasma concentration is--- 𝐶 𝑜. 3 = 𝐷𝑜 𝑉 𝑅2 + 𝐷𝑜 𝑉 R + 𝐷𝑜 𝑉 And at the end of the 3rd dose--- 𝐶 𝑜. 3 = ( 𝐷𝑜 𝑉 𝑅2 + 𝐷𝑜 𝑉 R + 𝐷𝑜 𝑉 ) R = 𝐷𝑜 𝑉 𝑅3 + 𝐷𝑜 𝑉 𝑅2 + 𝐷𝑜 𝑉 R ------------- ( 2 )
- 4. From the above equation (1), (2) and (3) we can see that there is a require among the equation indicating drug concentrations after 1st, 2nd and 3rd dose at dosing interval τ. So, immediately after 𝑛 𝑡ℎ dose drug concentration is determined by the following equation : 𝐶 𝑜. n = 𝐷𝑜 𝑉 𝑅 𝑛−1 + 𝐷𝑜 𝑉 𝑅 𝑛−2 + 𝐷𝑜 𝑉 𝑅 𝑛−3 + ------------ + 𝐷𝑜 𝑉 …………………(4) And at the end of the 𝑛 𝑡ℎ dose: 𝐶τ. n = 𝐷𝑜 𝑉 𝑅 𝑛 + 𝐷𝑜 𝑉 𝑅 𝑛−1 + 𝐷𝑜 𝑉 𝑅 𝑛−2 + ------------ + 𝐷𝑜 𝑉 R = 𝐷𝑜 𝑉 [𝑅 𝑛 + 𝑅 𝑛−1 + 𝑅 𝑛−2 + ------------ + R] ……………………… (5) After simplifying the equation (4) and (5) we get… 𝐶 𝑜. n = 𝐷𝑜 𝑉 ( 1−𝑅 𝑛 1−𝑅 ) ……………… (6) and, 𝐶τ. n = 𝐷𝑜 𝑉 ( 1−𝑅 𝑛 1−𝑅 ) R ………….. (7) = 𝐷𝑜 𝑉 ( 1−𝑒−𝑛𝑘τ 1−𝑒−𝑘τ ) 𝑒−𝑘τ ……… (8)
- 5. From equation (6), since the plasma concentration at any time “t” during the dosing interval is equal to the plasma concentration at the start of the 𝑛 𝑡ℎ dose multiplied by 𝑒−𝑘𝑡 ؞ 𝐶𝑡. n = 𝐷𝑜 𝑉 ( 1−𝑒−𝑛𝑘τ 1−𝑒−𝑘τ ) 𝑒−𝑘𝑡 ؞ 𝐶 𝑃 = 𝐷𝑜 𝑉 ( 1−𝑒−𝑛𝑘τ 1−𝑒−𝑘τ ) 𝑒−𝑘𝑡 ………… (9) From this equation, the plasma drug concentration at any time “t” can be calculated after the administration of 𝑛 𝑡ℎ dose. At steady state, n=α , so, 𝑒−𝑛𝑘τ ≡ 0 𝐶𝑠𝑠 or 𝐶 𝑃 α = 𝐷𝑜 𝑉 ( 1 1−𝑒−𝑘τ ) 𝑒−𝑘𝑡 ………… (10) Where 𝐶 𝑃 α is the steady state drug concentration at time “t” after the dose. THE END