1. 3. Method of inspection Requirements for the Method of Inspection We assume that k a is much larger than k el. That is, k a is at least five times greater than k el. This is the same requirement as for the Method of Residuals We assume that k a is much larger than k el. That is, k a is at least five times greater than k el. This is the same requirement as for the Method of Residuals Assume that absorption is complete (i.e. greater than 95 % complete) at the time of the peak concentration. Assume that absorption is complete (i.e. greater than 95 % complete) at the time of the peak concentration.

2. The Method The first step is to estimate the time of the peak drug concentration by inspection. If we assume that the time of peak is approximately five times the absorption half-life: The first step is to estimate the time of the peak drug concentration by inspection. If we assume that the time of peak is approximately five times the absorption half-life: t peak = 5 * t 1/2(absorption) t peak = 5 * t 1/2(absorption)

3. K a = (ln 2)/t 1/2 (absorption) K a = (ln 2)/t 1/2 (absorption) K a = 0.693/t 1/2(absorption) K a = 0.693/t 1/2(absorption) K a = 0.693/ (t peak /5) K a = 0.693/ (t peak /5) K a = 0.693*5 / (t peak ) K a = 0.693*5 / (t peak )

5. Extent of absorption, F value the fraction of the dose which is absorbed is termed F the fraction of the dose which is absorbed is termed F Plotting C p versus time allow the calculation of k a and k el, as in the methods described previously. Plotting C p versus time allow the calculation of k a and k el, as in the methods described previously.

6. From the intercept, one can calculate the term: From the intercept, one can calculate the term: The total amount absorbed can be calculated as: The total amount absorbed can be calculated as:

8. The following data was collected after administration of an IV and oral dose to a subject. Calculate C p o, V d, and the bioavailability (F), as well as other kinetic parameters.

9. IV data, Dose = 100 mg

10. Thus the intercept value is 2.50 and the apparent volume of distribution is Dose/C p0 = 100/2.5 = 40 L. From the slope k el can be estimated as 0.201 hr - 1. The AUC (AUC = Dose/V d K el ) from the IV data is 12.6 mg.hr.L -1.

11. Oral Dose = 250 mg

13. Semi-log Plot of Drug Concentration versus Time after an Oral dose

14. The time of peak concentration is 1.5 hour, thus the t 1/2 absorption might be estimated to be 0.3 hour: The time of peak concentration is 1.5 hour, thus the t 1/2 absorption might be estimated to be 0.3 hour: and the absorption rate constant to be approximately 2.3 hr -1. and the absorption rate constant to be approximately 2.3 hr -1. K a = 0.693/t 1/2 = 0.693/0.3 = 2.31 K a = 0.693/t 1/2 = 0.693/0.3 = 2.31 The AUC from the oral data is 24.91 mg.hr.L -1 and thus the bioavailability might be estimated as The AUC from the oral data is 24.91 mg.hr.L -1 and thus the bioavailability might be estimated as F = (24.68 x 100) / (250 x 12.6) = 0.78 F = (24.68 x 100) / (250 x 12.6) = 0.78 t 1/2 absorption = 1.5/5 = 0.3hr

15. Excretion in Urine Scheme for drug excreted into urine, one compartment

16. The rate of elimination from plasma is the same as the rate of appearance of drug into urine The rate of elimination from plasma is the same as the rate of appearance of drug into urine Dose = Amount in body + Amount excreted in urine = V d * Cp + U

17. Plot Types: a. Cumulative amount versus time Rate of appearance of drug in urine = rate of drug elimination from plasma Rate of appearance of drug in urine = rate of drug elimination from plasma dU/dt = K el V d C p dU/dt = K el V d C p C p = C p o e -kel*t C p = C p o e -kel*t dU/dt = K el V d C p o e -kel*t dU/dt = K el V d C p o e -kel*t Dose = V d C p o Dose = V d C p o dU/dt = K el Dose e -kel*t dU/dt = K el Dose e -kel*t dU = K el Dose e -kel*t.dt dU = K el Dose e -kel*t.dt Integration of e -kel*t = Integration of e -kel*t = e -Kel*t /-Kel t = t t = o

18. U = K el Dose U = K el Dose then U = DOSE [1 – e -kel * t ] Cumulative amount excreted into urine at time = t At t = 0; e -kel * t = 1 then U 0 = DOSE [1 - 1] = 0 At t = infinity ; e -kel * t = 0 then U = DOSE [1 - 0] = DOSE (e -Kel*t /-Kel)- (1/-Kel)

19. Plot of C p versus Time and U versus Time

20. b. Rate of excretion Taking the logarithms of both sides gives:- Thus by plotting ln (dU/dt) versus time should result in a straight line with a slope of - k el.

21. The amount excreted is the product of the volume of urine voided and concentration of drug in the urine sample. Again, this is a rate measurement. Since we estimate dU/dt as U/t, an average rate of excretion over the collection interval, the t value used with this plot is the time at the midpoint of the collection interval

22. Example: Example: Ampicillin almost 100% (actually closer to 90%) excreted unchanged into urine. Ampicillin almost 100% (actually closer to 90%) excreted unchanged into urine. After giving an IV dose of 500 mg, urine is collected and assayed for drug content. Data collected is time interval versus amount (mg) excreted during the time interval. The cumulative amount excreted is readily calculated. The following table summarizes the results: After giving an IV dose of 500 mg, urine is collected and assayed for drug content. Data collected is time interval versus amount (mg) excreted during the time interval. The cumulative amount excreted is readily calculated. The following table summarizes the results:

24. Plot of Cumulative Amount Excreted versus Time The plot shows U rapidly increasing at first then leveling off to U  where U  = DOSE for this set of data. Notice that U  /2 (250 mg) is excreted in about 1 ½ hours. Otherwise it is a fairly qualitative representation of the data. The plot shows U rapidly increasing at first then leveling off to U  where U  = DOSE for this set of data. Notice that U  /2 (250 mg) is excreted in about 1 ½ hours. Otherwise it is a fairly qualitative representation of the data.

25. We can then calculate the rate of excretion during each time interval. Then the time point is the midpoint time. If we plot U/t versus t midpoint on semi-log graph paper we have the blue squares on the graph paper. As you can see this gives a straight line plot. We can then calculate the rate of excretion during each time interval. Then the time point is the midpoint time. If we plot U/t versus t midpoint on semi-log graph paper we have the blue squares on the graph paper. As you can see this gives a straight line plot. From the equation before we have:- From the equation before we have:- Intercept = ln (DOSE * k el ) Intercept = ln (DOSE * k el ) Slope = - k el Slope = - k el

26. Plot of Rate of Excretion and A.R.E. versus Time

27. k el = 0.440 hr - 1 (t 1/2 = 1.58 hr) Consequently with this plot we can estimate k el and t 1/2.

28. C. Amount remaining to be excreted (A.R.E.) There is a third method of plotting the data which is commonly used. That is the amount remaining to be excreted (A.R.E.) plot. The equation describing this plot can be derived from the differential equation. There is a third method of plotting the data which is commonly used. That is the amount remaining to be excreted (A.R.E.) plot. The equation describing this plot can be derived from the differential equation.

29. Since, DOSE = Amount in body + Amount eliminated Since, DOSE = Amount in body + Amount eliminated Thus, DOSE = V * Cp + U = U  Thus, DOSE = V * Cp + U = U  U , total amount excreted U , total amount excreted Then U  - U = V.Cp Then U  - U = V.Cp U  - U = U a.r.e (amount remaining to be extracted U  - U = U a.r.e (amount remaining to be extracted dU/dt = K el U a.r.e dU/dt = K el U a.r.e

30. dU / U a.r.e = K el *dt Integrating from t = 0 to t = t, and from U = U a.r.e to U = U , gives: dU / U a.r.e = K el *dt Integrating from t = 0 to t = t, and from U = U a.r.e to U = U , gives: ln U  - ln U a.r.e = K el * t ln U  - ln U a.r.e = K el * t OR OR ln U a.r.e = ln U  - K el * t ln U a.r.e = ln U  - K el * t

31. Thus by plotting ln U a.r.e versus time we should get a straight line with a slope of - k el. Since the term U a.r.e is called the amount remaining to be excreted (A.R.E.), then if we subtract U from U  at each time point we are calculating A.R.E. ( U a.r.e ) or (U  - U). These results are shown as red circles on the semi- log graph paper k el = 0.464 hr - 1

32. Risk Assessment and Management

34. Location of Risk Assessment

35. Health risk assessment, or herein risk assessment (RA) for short, is the process by which the potential adverse health effects of human exposure to etiologic agents are characterized and assessed. Etiologic agents are agents that may modify the frequency or distribution of adverse health effects (also more commonly referred to as diseases) in a human community.

36. IUPAC Definitions HAZARD vs. RISK hazard: inherent property of an agent capable of having adverse effects on something. risk: the probability of adverse effects caused under specified circumstances by an agent

37. DOSE vs. CONCENTRATION dose: total amount of a substance administered to, taken, or absorbed by an organism concentration: quantity of a material or substance contained in unit quantity of a given medium or system

38. adverse effect: change in morphology, physiology, growth, development, or life span of an organism, which results in an impairment of functional capacity, an impairment of the capacity to compensate for additional stress, or an increase in susceptibility to other environmental influences

39. exposure: Concentration, amount, or intensity of a particular agent that reaches a target system. dose-response relationship: link between the amount of an agent absorbed by a population and the change developed in that population in reaction to it

40. Response versus effect The response may be expressed as the proportion of a population exposed to an agent that shows a specific reaction (dose – response relationship). It may also be used to signify the magnitude of an effect (severity) in one organism (or part of an organism); in that case, it is more specifically called "dose-effect relationship".

41. SAFETY AND UNCERTAINTY safety: practical certainty that adverse effects will not be caused by an agent under defined circumstances Note: It is a reciprocal of risk. safety factor: factor by which an observed or estimated toxic concentration or dose is divided to arrive at a criterion or standard that is considered safe

42. ACCEPTABLE DAILY INTAKE (ADI) acceptable daily intake: maximum amount of a substance to which a subject may be exposed daily over the subject ’ s lifetime without appreciable health risk tolerable intake: estimate of the amount of a substance that can be ingested or absorbed over a specified period of time without appreciable health risk

43. hazard assessment: process designed to determine factors contributing to the possible adverse effects of a substance to which a human population or an environmental compartment could be exposed. The process includes three steps: hazard identification, hazard characterization, and hazard evaluation. Note: Factors may include mechanisms of toxicity, dose-effect and dose-response relationships, variations in target susceptibility, etc

44. hazard identification: the first stage in hazard assessment, consisting of the determination of substances of concern, the adverse effects they may have inherently on target systems under certain conditions of exposure, taking into account toxicity data

45. hazard characterization: the second step in the process of hazard assessment, consisting in the qualitative and, wherever possible, quantitative description of the nature of the hazard associated with a biological, chemical, or physical agent, based on one or more elements, such as mechanisms of action involved, biological extrapolation, dose-response and dose-effect relationships, and their respective attendant uncertainties

46. hazard evaluation: the third step in the process of hazard assessment aiming at the determination of the qualitative and quantitative relationship between exposure to a hazard under certain conditions, including attendant uncertainties and the resultant adverse effect

47. risk assessment: process intended to calculate or estimate the risk for a given target system following exposure to a particular substance, taking into account the inherent characteristics of a substance of concern as well as the characteristics of the specific target system. The process includes four steps: hazard identification, dose-response assessment, exposure assessment, and risk characterization. It is also the first step in risk analysis

48. hazard identification: the first stage in risk assessment, consisting of the determination of particular hazards a given target system may be exposed to, including attendant toxicity data Note: Definition may vary depending on the context. Thus, here: the first stage in hazard assessment, consisting of the determination of substances of concern and the adverse effects they may inherently have on target systems under certain conditions of exposure, taking into account toxicity data.

49. dose-response assessment: the second of four steps in risk assessment, consisting of the analysis of the relationship between the total amount of an agent absorbed by a group of organisms and the changes developed in the group in reaction to the agent, and inferences derived from such an analysis with respect to the entire population

50. exposure assessment: a step in the process of risk assessment, consisting of a quantitative and qualitative analysis of the presence of an agent (including its derivatives) that may be present in a given environment and the inference of the possible consequences it may have for a given population of particular concern

51. risk characterization: integration of evidence, reasoning, and conclusions collected in hazard identification, dose-response assessment, and exposure assessment and the estimation of the probability, including attendant uncertainties, of occurrence of an adverse effect if an agent is administered, taken, or absorbed by a particular organism or population. It is the last step of risk assessment. Or: qualitative and/or quantitative estimation, including attendant uncertainties, of the severity and probability of occurrence of known and potential adverse effects of a substance in a given population

52. acceptable risk: type of risk such that the benefits derived by an organism, a population, or an ecological system outweigh the adverse effects that might affect them as a result of being administered or exposed to a particular agent

53. Risk management risk evaluation: establishment of a qualitative or quantitative relationship between risks and benefits, involving the complex process of determining the significance of the identified hazards and estimated risks to those organisms or people concerned with or affected by them. It is the first step in risk management. Note: It is synonymous with risk-benefit evaluation.

54. risk monitoring: process of following up the decisions and actions within risk management in order to ascertain that risk containment or reduction with respect to a particular hazard is assured

55. risk analysis: process for controlling situations where populations or ecological systems could be exposed to a hazard. It usually comprises three steps, namely risk assessment, risk management, and risk communication