3. Method of inspection3. Method of inspection

Requirements for the Method of InspectionRequirements for the Method of Inspection We assume that kWe assume that kaa is much larger than k is much larger than kelel. That is, k. That is, kaa is at least is at least

five times greater than kfive times greater than kelel. This is the same requirement as for . This is the same requirement as for the Method of Residuals the Method of Residuals

Assume that absorption is complete (i.e. greater than 95 % Assume that absorption is complete (i.e. greater than 95 % complete) at the time of the peak concentration. complete) at the time of the peak concentration.

The MethodThe Method The first step is to estimate the time of the peak drug The first step is to estimate the time of the peak drug

concentration by inspection. If we assume that the concentration by inspection. If we assume that the time of peak is approximately five times the time of peak is approximately five times the absorption half-life:absorption half-life:

ttpeakpeak = 5 * t = 5 * t1/2(absorption)1/2(absorption)

KKaa = (ln 2)/t = (ln 2)/t1/2 (absorption)1/2 (absorption)

KKaa = 0.693/t = 0.693/t1/2(absorption)1/2(absorption)

KKaa = 0.693/ (t = 0.693/ (tpeakpeak/5)/5)

KKaa = 0.693*5 / (t = 0.693*5 / (tpeakpeak))

Extent of absorption, Extent of absorption, FF value value

the fraction of the dose which is absorbed is the fraction of the dose which is absorbed is termed F termed F

Plotting CPlotting Cpp versus time allow the versus time allow the

calculation of kcalculation of kaa and k and kelel, as in the methods , as in the methods

described previously.described previously.

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:

The following data was collected after The following data was collected after administration of an IV and oral dose to a administration of an IV and oral dose to a subject. Calculate Csubject. Calculate Cpp

oo, V, Vdd, and the , and the

bioavailability (F), as well as other kinetic bioavailability (F), as well as other kinetic parameters.parameters.

IV data , Dose = 100 mgIV data , Dose = 100 mg

Thus the intercept value is 2.50 and the apparent volume of distribution is Thus the intercept value is 2.50 and the apparent volume of distribution is Dose/CDose/Cp0p0 = 100/2.5 = 40 L. From the slope k = 100/2.5 = 40 L. From the slope kelel can be estimated as 0.201 hr can be estimated as 0.201 hr--

11. The AUC (AUC = Dose/V. The AUC (AUC = Dose/VddKKelel) from the IV data is 12.6 mg.hr.L) from the IV data is 12.6 mg.hr.L-1-1 . .

Oral Dose = 250 mgOral Dose = 250 mg

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

dosedose

The time of peak concentration is 1.5 hour, thus the tThe time of peak concentration is 1.5 hour, thus the t 1/21/2 absorption might be estimated to be 0.3 hour:absorption might be estimated to be 0.3 hour:

and the absorption rate constant to be approximately and the absorption rate constant to be approximately 2.3 hr2.3 hr-1-1. .

KKaa = 0.693/t = 0.693/t1/21/2 = 0.693/0.3 = 2.31 = 0.693/0.3 = 2.31 The AUC from the oral data is 24.91 mg.hr.LThe AUC from the oral data is 24.91 mg.hr.L-1-1 and and

thus the bioavailability might be estimated as 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

t1/2 absorption = 1.5/5 = 0.3hr

Excretion in UrineExcretion in Urine

Scheme for drug excreted into urine, one Scheme for drug excreted into urine, one compartmentcompartment

The rate of elimination from plasma is the The rate of elimination from plasma is the same as the rate of appearance of drug into same as the rate of appearance of drug into urine urine

Dose = Amount in body + Amount excreted in urine = Vd * Cp + U

Plot Types: a. Cumulative amount Plot Types: a. Cumulative amount versus timeversus time

Rate of appearance of drug in urine = rate of drug Rate of appearance of drug in urine = rate of drug elimination from plasmaelimination from plasma

dU/dt = KdU/dt = Kelel V Vdd C Cpp

CCpp = C = Cppoo e e-kel*t-kel*t

dU/dt = KdU/dt = Kelel V Vd d CCppoo e e-kel*t-kel*t

Dose = VDose = Vd d CCppoo

dU/dt = KdU/dt = Kelel Dose e Dose e-kel*t-kel*t

dU = KdU = Kelel Dose e Dose e-kel*t -kel*t .dt.dt

Integration of eIntegration of e-kel*t -kel*t = = e-Kel*t/-Kel

t = t

t = o

U = KU = Kelel Dose Dose

thenthenU = DOSE [1 – e U = DOSE [1 – e -kel * t-kel * t] ]

Cumulative amount excreted into urine at time = t Cumulative amount excreted into urine at time = t At t = 0; e At t = 0; e -kel * t-kel * t = 1 = 1 then Uthen U00= DOSE [1 - 1] = 0 = DOSE [1 - 1] = 0 At t = infinity ; e At t = infinity ; e -kel * t-kel * t = 0 = 0 then U = DOSE [1 - 0] = DOSEthen U = DOSE [1 - 0] = DOSE

(e-Kel*t/-Kel) - (1/-Kel)

Plot of Cp versus Time and U versus Time

b. Rate of excretionb. 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 - kel.

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

Example:Example: Ampicillin almost 100% (actually closer to Ampicillin almost 100% (actually closer to

90%) excreted unchanged into urine.90%) excreted unchanged into urine. After giving an IV dose of 500 mg, urine is After giving an IV dose of 500 mg, urine is

collected and assayed for drug content. Data collected and assayed for drug content. Data collected is time interval versus amount (mg) collected is time interval versus amount (mg) excreted during the time interval. The excreted during the time interval. The cumulative amount excreted is readily cumulative amount excreted is readily calculated. The following table summarizes calculated. The following table summarizes the results:the results:

Plot of Cumulative Amount Excreted versus Time

The plot shows U The plot shows U rapidly increasing at rapidly increasing at first then leveling off to first then leveling off to UU where U where U = DOSE = DOSE for this set of data. for this set of data. Notice that UNotice that U/2 (250 /2 (250 mg) is excreted in about mg) is excreted in about 1½ hours. Otherwise it 1½ hours. Otherwise it is a fairly qualitative is a fairly qualitative representation of the representation of the data. data.

We can then calculate the rate of excretion We can then calculate the rate of excretion during each time interval. Then the time point during each time interval. Then the time point is the midpoint time. If we plot U/t versus t is the midpoint time. If we plot U/t versus t midpoint on semi-log graph paper we have the midpoint on semi-log graph paper we have the blue squares on the graph paper. As you can blue squares on the graph paper. As you can see this gives a straight line plot. see this gives a straight line plot.

From the equation before we have:- From the equation before we have:- Intercept = ln (DOSE * kIntercept = ln (DOSE * kelel) ) Slope = - kSlope = - kelel

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

kel = 0.440 hr - 1 (t1/2 = 1.58 hr) Consequently with this plot we can estimate kel and t1/2.

C. Amount remaining to be excreted C. Amount remaining to be excreted (A.R.E.)(A.R.E.)

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

Since, DOSE = Amount in body + Amount Since, DOSE = Amount in body + Amount eliminated eliminated

Thus, DOSE = V * Cp + U = UThus, DOSE = V * Cp + U = U UU, total amount excreted , total amount excreted Then UThen U - U = V.Cp - U = V.Cp UU - U = U - U = Ua.r.ea.r.e (amount remaining to be extracted (amount remaining to be extracted dU/dt = KdU/dt = Kel el UUa.r.ea.r.e

dU / UdU / Ua.r.ea.r.e = K = Kelel*dt*dt

Integrating from t = 0 to t = Integrating from t = 0 to t = tt, and from U = U, and from U = Ua.r.ea.r.e to to

U = UU = U, gives:, gives:

ln Uln U - ln U - ln Ua.r.ea.r.e = K = Kelel * t * t

OROR

ln Uln Ua.r.ea.r.e = ln U = ln U - K - Kelel * t * t

Thus by plotting ln Thus by plotting ln UUa.r.ea.r.e versus time we should get a versus time we should get a straight line with a slope of - kstraight line with a slope of - kelel. Since the term . Since the term UUa.r.ea.r.e is is called the amount remaining to be excreted (A.R.E.), called the amount remaining to be excreted (A.R.E.), then if we subtract U from Uthen if we subtract U from U at each time point we at each time point we are calculating A.R.E. (are calculating A.R.E. (UUa.r.ea.r.e) or (U) or (U - U). - U).

These results are shown as red circles on the semi- log These results are shown as red circles on the semi- log graph papergraph paper

kkelel = 0.464 hr = 0.464 hr - 1- 1

Risk Assessment and Risk Assessment and ManagementManagement

Location of Risk AssessmentLocation of Risk Assessment

Public Health

Health Risk Assessment

Epidemiology Toxicology

Other Areas

In Theory . . . .

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

IUPAC DefinitionsIUPAC Definitions

HAZARD vs. RISKHAZARD vs. RISK

hazard:hazard: inherent property of an agent capable of inherent property of an agent capable of having adverse effects on something. having adverse effects on something.

riskrisk: the probability of adverse effects caused : the probability of adverse effects caused under specified circumstances by an agentunder specified circumstances by an agent

DOSE vs. CONCENTRATIONDOSE vs. CONCENTRATION

dosedose: total amount of a substance administered : total amount of a substance administered to, taken, or absorbed by an organism to, taken, or absorbed by an organism

concentrationconcentration: quantity of a material or : quantity of a material or substance contained in unit quantity of a given substance contained in unit quantity of a given medium or system medium or system

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

exposureexposure: Concentration, amount, or intensity of : Concentration, amount, or intensity of a particular agent that reaches a target system. a particular agent that reaches a target system.

dose-response relationshipdose-response relationship: link between the : link between the amount of an agent absorbed by a population amount of an agent absorbed by a population and the change developed in that population in and the change developed in that population in reaction to itreaction to it

Response versus effectResponse versus effect

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

SAFETY AND UNCERTAINTYSAFETY AND UNCERTAINTY

safetysafety: practical certainty that adverse effects : practical certainty that adverse effects will not be caused by an agent under defined will not be caused by an agent under defined circumstancescircumstancesNote: It is a reciprocal of risk.Note: It is a reciprocal of risk.

safety factorsafety factor: factor by which an observed or : factor by which an observed or estimated toxic concentration or dose is estimated toxic concentration or dose is divided to arrive at a criterion or standard that divided to arrive at a criterion or standard that is considered safeis considered safe

ACCEPTABLE DAILY INTAKE (ADI)ACCEPTABLE DAILY INTAKE (ADI)

acceptable daily intakeacceptable daily intake: maximum amount of a : maximum amount of a substance to which a subject may be exposed substance to which a subject may be exposed daily over the subject’s lifetime without daily over the subject’s lifetime without appreciable health risk appreciable health risk

tolerable intaketolerable intake: estimate of the amount of a : estimate of the amount of a substance that can be ingested or absorbed substance that can be ingested or absorbed over a specified period of time without over a specified period of time without appreciable health riskappreciable health risk

hazard assessmenthazard assessment: process designed to determine : process designed to determine factors contributing to the possible adverse effects of factors contributing to the possible adverse effects of a substance to which a human population or an a substance to which a human population or an environmental compartment could be exposed. The environmental compartment could be exposed. The process includes three steps: process includes three steps: hazard identification, hazard identification, hazard characterization, and hazard evaluationhazard characterization, and hazard evaluation ..

Note: Factors may include mechanisms of toxicity, Note: Factors may include mechanisms of toxicity, dose-effect and dose-response relationships, dose-effect and dose-response relationships, variations in target susceptibility, etc variations in target susceptibility, etc

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

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

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

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

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

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

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

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

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

Risk managementRisk management

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

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

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