Biopharmaceutics Lab Manual (2)

                                   Index

Sr no	Experiment	signature
1	Mathematical Fundamentals in Pharmacokinetics
2	Elimination of Clearance by Model Independent Method
3	Calculation of Infusion Rate, Time to reach 99% of Steady State Concentration and Loading Dose for IV Infusion
4	Calculation of “K” from Urinary Excretion By Rate Method and Sigma Minus Method
5	Calculation of Various Pharmacokinetic Parameter after IV Bolus Injection
6	Calculation of Various Pharmacokinetic Parameters after IV Infusion
7	Determine the Absolute Bioavailability of IV Injection
8	Determine the Relative Bioavailability of Oral Tablets and Oral Solution
9	Dose Adjustment in Renal Impairment and Hepatic Impairment Patient
10	Dose Adjustment in Renal Impairment and Hepatic Impairment Patient

Practical # 1

Mathematical Fundamentals in Pharmacokinetics

 

Exponents and Logarithms

Exponential functions:

Exponential functions have the form:

f (x) = b ^x

Where b is the base and x is the exponent (or power).

Logarithmic Functions:

A logarithm is simply an exponent that is written in a special way.

The logarithmic function is defined as:

f (x) = log _b x

The base of the logarithm is b.

Examples:

1)      e^x = 0.44

 

 

 

2)      e^-2X-1 = 75

 

 

 

 

 

3)      log x = 0.95

 

 

4)      ln x = 1.22

 

 

5)       e-4k = 25/50

 

 

 

 

 

 

6)      Cp = Cp_o e^-kt               where Cp_o=35   k=0.15    t1/2=2 hrs.

 

 

 

 

Graphs:

1-            Examples:

     Q) Plot the following data on semi-log graph and standard rectangular coordinate graph:

Time	Drug(mg)
10	96
20	89
40	73
60	57
90	34
120	10
130	2.5

Curve fitting:

Curve Fitting: It is the fitting a curve to the points on a graph sows that there is some sort of relation between the variables ‘x’ and ‘y’. For e.g. dose of drug vs. pharmacological effects.

Least Square Method: The least square method is a useful procedure for obtaining the line of best fit through a set of data points.

Reasons for Using Least Square Method: It is used for obtaining a straight line from which different pharmacokinetic parameters can be calculated more accurately. Ø It minimizing the deviation between experimental and theoretical line, so we obtain a straight line on simple rectilinear graph instead of curved one

Regression Line: The straight line that characterizes the relationship between two variables is called regression line.

Equation for Regression Line: The general equation of regression line is:

y = mx+b

m = slope

b = y-intercept

Equation for (m) and (b):

m =

 

b =

Graph Method:

m= slope = Y₂-Y₁ / X₂-X₁

b= y-intercept on graph.

Determination of Slope:

Slope: is a measure of the steepness of a line, or a section of a line, connecting two points. 

Slope of straight line on rectangular coordinate graph:

Zero order reaction:    slope = y₂-y₁/x₂-x₁     &    k = slope

Slope of straight line on Semi-log graph:

First order reaction:      slope =log y₂-log y₁/x₂-x₁      &   k = 2.3 (slope)

Rate and Order of Reaction:

Rate: it is the velocity with which a reaction occurs.

Order: it is the way through which a reaction occurs.

 

Examples:

Q) A pharmacist dissolved exactly 10g of a drug into 100 mL of water. The solution is kept at room temperature and samples removed periodically and assayed for drug.

Following date is obtained:

 

 

 

Dug (mg/mL)	Time	Log Drug conc.
100	0	2
50	4	1.6
25	8	1.3
12.5	12	1.09
6.25	16	0.79
3.13	20	0.49
1.56	24	0.17

 

 

 “Since the log values are plotted on quadrant graph, thus it’s a First order process”

t_1/2 graphically:

 

 

t_1/2 through formula:              

t_1/2 = 0.693/k

 

 

 

 

 

 

 

 

 

 

 

Q)  A pharmacist dissolved few mgs of antibiotic into exactly 100 mL of distilled water and placed the solution if refrigerator (5C). at various time intervals, the pharmacist removed a 10 mL liquid from the solution and measured the amount of drug contained in each liquid. Following data is obtained:

 

Time	Antibiotic (μg/mL)
0.5	84.5
1	81.2
2	74.5
4	61
6	48
8	35
12	8.7

 

 

a-      Is the decomposition of this antibiotic a first order or zero order process?

 

b-      What is the rate of decomposition of this antibiotic?

 

 

 

 

 

 

 

c-      How many mgs of antibiotic were in the original solution prepared by the pharmacist?

 

 

 

 

 

d-     Give the equation for the first line that best fit the experimental data.

y=mx+b

Practical # 2

Determination of Clearance by Model Independent Method.

Introduction:

Clearance: Clearance is a measure of drug elimination from the body without identifying the mechanism or process.

Volume of distribution: The volume of fluid in which the drug appears to be distributed. (V_D)

Physiological model: This model depends upon the blood flow in body and drug is determined by extraction ratio.

Model

dependant: This model is also compartmental model and body is considered to have single or two compartments in which the drug is distributed.

Model independent: This type of model is used to perform non compartmental analysis

Cl = D_o/(AUC)_o^∞

Q-1)  A single IV dose of an antibiotic was given to a 50-kg woman at a dose level of 20 mg/kg. Urine and blood samples were removed periodically and assayed for parent drug. The following data were obtained:

Time (hr)	Cp (ug/ml)
0.25	4.2
0.5	3.5
1.0	2.5
2.0	1.25
4.0	0.31
6.0	0.08

 

 

 

 

 

 

 

 

 

 

Slope:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Rate constant:

 

 

 

 

 

Area under curve (AUC):

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  Clearance:

 

 

 

 

 

 

 

 

Practical # 3

Calculate infusion rate, time to reach 99% of steady state concentration and loading dose for IV infusion.

Introduction:

Steady state drug concentration: At steady state rate of drug leaving the body is equal to rate of drug entering the body so at steady state the rate of change in plasma drug concentration is zero. Represented by C_ss

dCp/dt=0

Infusion rate: The rate at which the drug is infused directly into the systemic circulation is known as infusion rate, which is denoted by R.

Loading dose: It is initial bolus dose of a drug that is used to obtain desired concentration as early as possible. Loading dose is represented by symbol D_L.

Desired steady state or targeted drug concentration: The plasma drug concentration prior to reach the theoretical steady state is considered the steady state plasma drug concentration; this concentration is the targeted or desired steady state drug concentration.

Time to reach 99% of C_ss

C_ss=R/V_dk

For C_ssto be 99%:

99% (R/V_dk)

Conc. Of drug at any time during infusion:

C_p=R/V_dk (1-e^-kt)

 

We want:

C_p=99%C_ss

Putting values

 

 

 

 

 

 

 

 

 

 

Clearance of IV infusion:                                                     

C_ss=R/v_dk

 (Cl=V_dk)

C_ss=R/Cl

Cl=R/ C_ss

Q1) An antibiotic has a volume of distribution of 10 L and a k of 0.2 h^-1. A steady-state plasma concentration of 10 μg/mL is desired.

a.       Calculate the rate of infusion?

 

 

 

 

 

 

 

 

 

 

b.      Calculate time required to reach 99% C_ss?

 

 

 

 

 

 

 

c.       Calculate clearance?

 

 

 

 

 

 

 

 

Q2) A patient was given an antibiotic (t_1/2=6hr) by constant IV infusion at a rate of 2mg/hr at the end of 2days the serum concentration was 10mg/L. calculate total body clearance for this antibiotic?

 

 

 

 

 

 

Q3) A physician wants to administer an anesthetic agent at a rate of 2 mg/h by IV infusion. The elimination rate constant is 0.1 h-1 and the volume of distribution is 10 L.

a.       What loading dose would be recommended if the doctor wants drug level to reach 2μg/ml immediately?

 

 

 

 

b.      Calculate C_ss?

 

 

 

 

 

 

 

Practical # 4

Calculate “K” from Urinary Excretion Data By Using Rate Method and Sigma Minus Method.

Introduction: If a drug is eliminated unchanged through urinary route then its appearance In urine will be a reflection of drug disappearance from plasma. So, the urine data can be used to calculate the pharmacokinetic parameters. In such case the collection of samples of urine after administration of drug is an alternative approach to obtain pharmacokinetics information. In this situation the excretion rate of drug is assume to be first order. Rate of drug excretion in urine can be given as:

dDu/dt= Ke.Db^o. e^-kt

There are two methods to determine urinary excretion rate constant

·         Rate method

·         Sigma-minus-method

1)      Rate method:

In this method the urinary excretion rate is plotted against time on semi-log graph paper. The slope of the curve is –k/2.3 (as it is first order) and y-intercept= ke.Db^o

As drug’s urinary excretion rate can not be determined experimentally for any given instant therefore the average rate of urinary drug excretion Du/t is plotted against T*(where T* is mid points of collection period and t is the time interval for collection of urine sample).

 

Ke.Db^o   

                                                                  Slope = -k/2.3

                       Du/t

 

 

                                                  Time T*

 

Q: A single IV dose of an anti-biotic was given to a 50kg woman at a dose of 20mg/kg. Urine samples are removed periodically and assayed for parent drug. The following data was obtained

Data:

Sr. #	Time (hrs)	Du (mg)	Du/t	T*	slope
1	0.25	160
2	0.50	140
3	1	200
4	2	250
5	4	188
6	6	46

 

Slope = log y₂ – log y₁/x₂ – x₁

 

 

 

 

 

 

 

 

 

Average slope:

 

 

Find “k”:

 

 

Half life t1/2 =  0.693/K

 

 

2) Sigma-Minus  Method:

An alternative method for the calculation of elimination rate constant K from urinary excretion data is “sigma-minus” method or amount of drug remaining to be excreted method.

In this method the amount of drug remaining to be excreted (Du^α-Du) is plotted against time on semi-log graph. The slope of the curve is –K/2.3 and y-intercept is maximum amount to be excreted i.e Du^α.          

Data:

Sr #	Time	Du (mg)	Cumulative   Du	Duα-Du
1	0.25	160
2	0.50	140
3	1	200
4	2	250
5	4	188
6	6	46

 

Slope = log y₂ – log y₁/x₂ – x₁

 

 

 

 

 

 

 

 

 

 

 

 

 

Find ‘K’?

 

 

Find ‘ t _1/2 ’?

 

 

 

y-intercept:

Comparison of Rate and Sigma-minus Method:

Rate Method	Sigma-minus Method
·         Rate method does not require complete knowledge of Du* so the loss of one urine sample does not invalidate the study	·         Sigma-minus method requires an accurate method of Du* which requires the collection of urine until a urinary excretion complete
·         Fluctuation in the rate of drug elimination and experimental error including incomplete bladder emptying for a collection and period can affect the linearity in rate method	·         In this case sigma-minus method is less effected
·         Rate method is applicable to zero-order drug elimination process	·         It is not applicable to zero-order processes
·         Renal excretion rate constant can be calculated from rate method           Ke.Db	·         Renal excretion rate constant Ke cannot be calculated from sigma-minus method         Duα Duα -Du

       Du/t

 

 

                           t*                                                                                      t

Practical # 5

Calculation of various pharmacokinetic parameter after IV bolus injection.

Introduction:

Clearance: Clearance is a measure of drug elimination from the body without identifying the mechanism or process.

Volume of distribution: The volume of fluid in which the drug appears to be distributed. (V_D)

Procedure:

1-      Select cycle according to data.

2-      Plot concentration on y-axis and time on x-axis.

3-      Mark conc. For respected time on graph.

4-      Draw straight line in such a way that it covers maximum points on graph paper.

5-      Y-intercept is C^o

Estimation of half life by graphical method; To estimate half life on graph select conc. (C₁) on straight line, now draw straight line towards the plotted line so that it intercepts plotted line. From intercepted line draw a perpendicular straight line on x-axis which gives t₁ from y-axis draw a line from point which is half of C₁ , which is C₂ and then draw a straight line on selective points towards the plotted line from intercepted line draw perpendicular line on x-axis which gives t₂

Calculate half life by measuring difference of t₁-t₂

Data A

Q) Plasma data obtained after IV bolus dose of 184mg of and antibiotic is as followed:

 

Time (hr)	Cp (g/ml)
1	137
6	120
12	103
24	76
48	42
72	23
96	12

 

Prepare semi-log graph and estimate t_1/2 of drug from this plot?

 

1-      Slope?

 

 

 

 

2-      Find k?

 

 

 

 

 

 

 

3-      Estimate total AUC?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 3-Calculate V_D? (Model dependant)

 

 

 

 

 

 

 

 4-Calculate total clearance?

 

 

 

 

 

 

Data B

Q) Data given in table below are the plasma concentrations of cocaine after IV  administration of 330mg of cocaine HCl to a subject:

Time (hr)	Conc. (ug/ml)
0.16	170
0.5	122
1	74
1.5	45
2	28
2.5	17
3	10

 

Prepare semi log graph and estimate t_1/2from plot?

 

1)      Slope?

 

 

 

 

 

 

 

 

 

2)      Find k?

 

 

      3) Calculate total AUC?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4 -Calculate V_D?

 

 

 

 

 

 

4- Calculate Total Clearance?

 

 

 

 

 

 

 

 

 

 

 

 

 

Practical # 6

Calculation of Various Pharmacokinetic Parameters after IV Infusion.

Estimate the volume of distribution, area under the curve, elimination rate constant, half-life and clearance from the data in following table obtained on infusing a drug at the rate of 50 mg/hr for 7.5 h in a dose of 375mg.

 

x(time) (hrs.)	y(Cp)(µg/ml)
0	0
2	3.4
4	5.4
6	6.5
7.5	7
9	4.6
12	2
15	0.9

 

 

a. Prepare a semi logarithmic plot and estimate the half-life of drug

b. Calculate AUC

c. Calculate volume of distribution

d. Calculate elimination half-life from formula

e. Calculate total clearance

 

Introduction:

Clearance: Clearance is a measure of drug elimination from the body without identifying the mechanism or process. Calculate clearance by using following equation.

Cl= kV_D

Volume of distribution: The volume of fluid in which the drug appears to be distributed (V_D). Calculate volume of distribution by using following equation

V_D = Dose/C_P

Elimination half-life: Calculate volume of distribution by using following equation

t_1/2 =

IV Infusion: Intravenous therapy is the infusion of liquid substances directly into a vein. Intravenous (IV) means "within vein". Intravenous infusions are commonly referred to as drips. The intravenous route is the fastest way to deliver fluids and medications throughout the body.

Procedure;

1-      As the data is first order so we will plot the graph on semi log graph paper. Select cycle according to data.

2-      Plot concentration on y-axis and time on x-axis.

3-      Mark conc. For respected time on graph.

4-      Draw straight line in such a way that it covers maximum points on graph paper.

5-      Y-intercept is C^o

6-      Determine slope of the line and calculate elimination rate constant by using this formula:

 

 

Estimation of half-life by graphical method:To estimate half-life on graph select conc. (C₁) on straight line, now draw straight line towards the plotted line so that it intercepts plotted line. From intercepted line draw a perpendicular straight line on x-axis which gives t₁ from y-axis draw a line from point which is half of C₁ , which is C₂ and then draw a straight line on selective points towards the plotted line from intercepted line draw perpendicular line on x-axis which gives t₂

Calculate half-life by measuring difference of t₁-t₂

Estimation of Elimination half-life from formula: Calculate elimination half-life by using following equation

t_1/2=

Calculations:

1-Estimate total AUC?

=

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

= ∑+

 

 

 

 

2-Calculate slope?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3- Find k?

K=Slope*2.3

 

 

 

4- Calculate elimination half-life ?

t_1/2=

 

 

 

 

5-Calculate Volume of Distribution (V_D) (Modeldependant)?

V_D=Dose/C_P

 

 

 

 

 

 

6- Calculate total clearance?

Cl=KV_D

 

 

 

Practical # 7

TO STUDY AND DETERMINE THE ABSOLUTE BIOAVAILABILTY OF IV INJECTION AND ORAL SOLUTION

 

BIOAVAILABILITY: It is defined as the rate and extent to which the drug is available systemically in an unchanged form at the site of action.

It is further divided into two types

Ø  Relative Bioavailability

The availability of the drug in formulation is compared to the availability of drug in standard dosage formulation

Ø  Absolute Bioavailability

It is the systemic availability of drug after extra vascular administration (oral, rectal, transdermal, subcutaneous) compared to IV dosing.

It is generally measured by comparing the respective AUC after extra vascular and IV administration.

Measurement of Absolute bioavailability:

Absolute bioavailability

                                           F=   [AUC]oral/Dose oral

                                                    [AUC]iv/Dose iv

It may be expressed as a fraction or as percentage by multiplying F with 100.

For drugs administered in iv bolus injection F=1 as the drug is completely absorbed while for for drugs administered by other routes F may not exceed 100% or F>1

DATA:

The dose for Iv injection is 2mg/kg while for oral solution is 10mg/kg

Sr.No   1 2 3 4 5 6 7 8

Time   0.5 1.0 1.5 2 2.0 4.0 6.0 8.0

Cp  (IV)   5.94 5.30 4.72 4.21 3.34 2.66 1.68 1.06

Cp (oral solution)   23.4 26.6 25.2 22.8 18.2 14.6 9.14 5.77

 

Calculation for Oral:

1)      Calculate of Slope:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Calculation of ‘K’:

 

 

 

 

 

Calculation of AUC:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Calculation for IV:

Calculation of Slope:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Calculation of ‘K’:

 

 

 

 

 

 

Calculation of AUC:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Calculation of Absolute Bioavailability:

 

 

 

 

 

 

Practical # 8

TO STUDY AND DETERMINE THE RELATIVE  BIOAVAILABILTY OF ORAL TABLETS AND ORAL SOLUTION

 

BIOAVAILABILITY: It is defined as the rate and extent to which the drug is available systemically in an unchanged form at the site of action.

It is further divided into two types

Ø  Relative Bioavailability

The availability of the drug in formulation is compared to the availability of drug in standard dosage formulation

Ø  Absolute Bioavailability

It is the systemic availability of drug after extravascular administration(oral, rectal, transdermal, subcutaneous) compared to IV dosing.

Measurement of Relative Bioavailability:  [AUC] test/Dose test

                                                                    [AUC] standard/Dose standard

DATA:

The dose for test and standard is 10mg/kg

Sr.No   1 2 3 4 5 6 7 8

Time   0.5 1.0 1.5 2 2.0 4.0 6.0 8.0

Cp  (oral tablets)   13.2 18.0 19.0 18.3 15.4 12.5 7.92 5.00

Cp (oral solution)   23.4 26.6 25.2 22.8 18.2 14.5 9.14 5.77

 

Calculation for Oral Tablets:

Calculation of Slope:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Calculation of ‘K’:

 

 

 

 

 

 

 

Calculate AUC:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Calculation for Oral Solution:

Calculation of Slope:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Calculation of ‘K’:

 

 

 

 

 

Calculation of AUC:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Calculation of Relative Bioavailability:

 

 

 

 

 

 

 

Practical # 9

DOSE ADJUSTMENT IN RENAL AND HEPATICALLY IMPAIRED PATIENTS.

Introduction:

RENAL IMPAIRMENT: Acute disease or trauma to the kidney can cause uremia, in which glomerular filteration is impaired or reduced leading to accumulation of excessive fluid and blood nitrogenous products in body.

GENERAL APPROACHES FOR DOSE ADJUSTMENT IN RENAL DISEASE;

1.      The required therapeutic plasma drug concentration in uremic patients is similar to that required in normal renal function patients.

2.      Uremic patients are maintained on the same Cav^∞ after multiple oral doses or multiple IV bolus injection.

3.      For IV infusion same Css is maintained.

DOSE ADJUSTMENT BASED ON DRUG CLEARANCE:

   This method based on drug clearance tries to maintain desired Cav^∞ after multiple oral doses or multiple IV bolus injection.

The calculation for Cav^∞ :

F= fraction of drug

Cl_T= total body clearance

t= dosing interval

      ∴ F=1 for IV

 To maintain desire Cav^∞, ureamic dose or dose interval must be changed to t^u

N= Normal Condition

U=uremic condition

By rearranging equation,

If dosage interval is kept constant then,

 For IV infusion the same desired Css is maintain both or Patient with normal renal function and for patients with renal impairment. Therefore the rate of infusion R, must be changed

DOSE ADJUSTMENT BASED ON CHANGES IN ELIMINATION RATE CONSTANT:

     The overall elimination rate constant for many drugs is reduced in uremic patients .By reducing the normal dose of the drug and keeping the frequency of the dosing constant or by decreasing the frequency of dosing and keeping dose constant.

     Assuming the V_D is same in both normal and uremic patients and t is constant, then the uremic dose D_o^u  is a function  of the normal dose,

DOSE CALCULATION ON BASIS PF ELIMINATION RATE CONSTANT:

1.      The renal elimination rate constant decrease proportionally as renal function decreases.

2.      The non renal routes of elimination remain unchanged.

3.      Changes in the renal clearance of the drug are reflected by changes in the creatinine clearance.

The overall route of elimination rate constant is the sum total of all routes of elimination in the body, including the renal rate and non renal rate constant.

 +

Non renal elimination rate constant.

 Renal elimination rate constant.

 Renal clearance is product of V_D and k_R.

By rearranging,

  

Assuming that the apparent V_D and non renal route of elimination do not change in ureamia then,

 And

By substitution:

               

A change in renal clearance Cl_R^U due to renal impairment will be reflected in the change in overall elimination rate constant.

NUMERICAL:

 The maintenance dose of gentamycin is 80mg every 6hrs for a patient with normal renal function. Calculate the maintenance dose for uremic patient with Cl_crof 20mL/min .assume a normal Cl_cr is of 100mL/min.

SOLUTION:

 

                

 

 

 

 

 

 

 

Practical # 10

DOSE ADJUSTMENT IN RENAL AND HEPATICALLY IMPAIRED PATIENTS.

Introduction:

RENAL IMPAIRMENT: Acute disease or trauma to the kidney can cause uremia, in which glomerular filteration is impaired or reduced leading to accumulation of excessive fluid and blood nitrogenous products in body.

GENERAL APPROACHES FOR DOSE ADJUSTMENT IN RENAL DISEASE;

4.      The required therapeutic plasma drug concentration in uremic patients is similar to that required in normal renal function patients.

5.      Uremic patients are maintained on the same Cav^∞ after multiple oral doses or multiple IV bolus injection.

6.      For IV infusion same Css is maintained.

DOSE ADJUSTMENT BASED ON DRUG CLEARANCE:

   This method based on drug clearance tries to maintain desired Cav^∞ after multiple oral doses or multiple IV bolus injection.

The calculation for Cav^∞ :

F= fraction of drug

Cl_T= total body clearance

t= dosing interval

      ∴ F=1 for IV

 To maintain desire Cav^∞, ureamic dose or dose interval must be changed to t^u

N= Normal Condition

U=uremic condition

By rearranging equation,

If dosage interval is kept constant then,

 For IV infusion the same desired Css is maintain both or Patient with normal renal function and for patients with renal impairment. Therefore the rate of infusion R, must be changed

DOSE ADJUSTMENT BASED ON CHANGES IN ELIMINATION RATE CONSTANT:

     The overall elimination rate constant for many drugs is reduced in uremic patients .By reducing the normal dose of the drug and keeping the frequency of the dosing constant or by decreasing the frequency of dosing and keeping dose constant.

     Assuming the V_D is same in both normal and uremic patients and t is constant, then the uremic dose D_o^u  is a function  of the normal dose,

DOSE CALCULATION ON BASIS PF ELIMINATION RATE CONSTANT:

4.      The renal elimination rate constant decrease proportionally as renal function decreases.

5.      The non renal routes of elimination remain unchanged.

6.      Changes in the renal clearance of the drug are reflected by changes in the creatinine clearance.

The overall route of elimination rate constant is the sum total of all routes of elimination in the body, including the renal rate and non renal rate constant.

 +

Non renal elimination rate constant.

 Renal elimination rate constant.

 Renal clearance is product of V_D and k_R.

By rearranging,

  

Assuming that the apparent V_D and non renal route of elimination do not change in ureamia then,

 And

By substitution:

               

A change in renal clearance Cl_R^U due to renal impairment will be reflected in the change in overall elimination rate constant.

Numerical: Lincomycin is given at 500mg every 6hrs to a 75kg normal patient. What dose would be use :

a)      In complete renal shutdown ,creatinine clearance = 0

b)      When creatinine clearance = 10ml/min