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3. Method of inspection
Requirements for the Method of Inspection
 We assume that ka is much larger than kel. That is, ka is at least
five times greater than kel. 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.
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:
 tpeak = 5 * t1/2(absorption)

Ka = (ln 2)/t1/2 (absorption)
Ka = 0.693/t1/2(absorption)

Ka = 0.693/ (tpeak/5)

Ka = 0.693*5 / (tpeak)

Extent of absorption, F value

the fraction of the dose which is absorbed is
termed F

Plotting Cp versus time allow the
calculation of ka and kel, as in the methods
described previously.

From the intercept, one can calculate the term:

The total amount absorbed can be calculated as:
The following data was collected after
administration of an IV and oral dose to a
subject. Calculate Cpo, Vd, and the
bioavailability (F), as well as other kinetic
parameters.
IV data , Dose = 100 mg
Thus the intercept value is 2.50 and the apparent volume of distribution is
Dose/Cp0 = 100/2.5 = 40 L. From the slope kel can be estimated as 0.201 hr1. The AUC (AUC = Dose/V K ) from the IV data is 12.6 mg.hr.L-1.
d el
Oral Dose = 250 mg
Semi-log Plot of Drug Concentration versus Time after an Oral
dose

The time of peak concentration is 1.5 hour, thus the t
absorption might be estimated to be 0.3 hour:
1/2
t1/2 absorption = 1.5/5 = 0.3hr




and the absorption rate constant to be approximately
2.3 hr-1.
Ka = 0.693/t1/2 = 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
F = (24.68 x 100) / (250 x 12.6) = 0.78
Excretion in Urine
Scheme for drug excreted into urine, one
compartment

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 = Vd * Cp + U
Plot Types: a. Cumulative amount
versus time







Rate of appearance of drug in urine = rate of drug
elimination from plasma
dU/dt = Kel Vd Cp
Cp = Cpo e-kel*t
dU/dt = Kel Vd Cpo e-kel*t
Dose = Vd Cpo
dU/dt = Kel Dose e-kel*t
dU = Kel Dose e-kel*t .dt
t=t

Integration of e-kel*t =
e-Kel*t/-Kel
t=o

U = Kel Dose
(e-Kel*t/-Kel) - (1/-Kel)
then
U = DOSE [1 – e -kel * t]
Cumulative amount excreted into urine at time = t
At t = 0; e -kel * t = 1
then U0= DOSE [1 - 1] = 0
At t = infinity ; e -kel * t = 0
then U = DOSE [1 - 0] = DOSE
Plot of Cp versus Time and U versus Time
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 - 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:
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:

Plot of Cumulative Amount
Excreted versus Time
The plot shows U
rapidly increasing at
first then leveling off to
Ua where Ua = DOSE
for this set of data.
Notice that Ua/2 (250
mg) is excreted in about
1½ hours. Otherwise it
is a fairly qualitative
representation of the
data.




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:Intercept = ln (DOSE * kel)
Slope = - kel
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
(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.






Since, DOSE = Amount in body + Amount
eliminated
Thus, DOSE = V * Cp + U = Ua
Ua, total amount excreted
Then Ua - U = V.Cp
Ua - U = U (amount remaining to be extracted
dU/dt = Kel U
a.r.e
a.r.e

dU / Ua.r.e = Kel*dt
Integrating from t = 0 to t = t, and from U = Ua.r.e to
U = Ua, gives:

ln Ua - ln Ua.r.e = Kel * t

OR

ln Ua.r.e = ln Ua - Kel * t
Thus by plotting ln Ua.r.e versus time we should get a
straight line with a slope of - kel. Since the term Ua.r.e
is called the amount remaining to be excreted
(A.R.E.), then if we subtract U from Ua at each time
point we are calculating A.R.E. (Ua.r.e) or (Ua - U).
These results are shown as red circles on the semi- log
graph paper
kel = 0.464 hr - 1
Risk Assessment and
Management
Location of Risk Assessment
In Theory . . . .
Public Health
Health Risk Assessment
Epidemiology
Toxicology
Other Areas
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.
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
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
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
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
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".
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
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
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
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
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
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
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
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.
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
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
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
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
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.
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
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