Using methods of residuals to explain absorption and elimination

How is absorption and elimination explained?

• Absorption - T_1/2 and k.

• Elimination - T_1/2 and k.

• Take a few data points (red crosses) in the absorption phase and find the concentration at each data point (absorbed concentration).

• Extrapolate the linear portion of the elimination slope (red line) from the elimination phase, find the concentration of the drug that has been eliminated (blue line).

• Subtract the absorption values from the elimination values for each timepoint to give new concentration values.

• Plot new values (blue triangles) at each time point and draw a straight line through them (pink line). From these lines can calculate absorption and elimination.

What is the lag phase?

• Interval between the Y-axis and the intersection. 

• Time difference between the time of drug administration and the time point of intersection.

• period of time before absorption starts. 

• The elimination and absorption lines will cross at a time point which will not always be at 0 hrs on the Y-intercept.

• Drug absorption begins here (intersection can give the time and concentration when this happens.

What is the calculation of absorption and elimination half life?

Separate graph into two parts:

• Absorption - T_1/2 and k.

• Elimination - T_1/2 and k.

• From the elimination line - T_1/2 =T₂ - T₁.

• From Absorption line - T_1/2 =T₂ - T₁.

What is the equation for a single oral does at any given time?

• C - Plasma concentration.

•  F - Bioavailability.

• S - Salt factor.

• D - Drug dose.

• K_a - Absorption rate constant.

• K - Elimination rate constant. 

• V - Volume of distribution.

• t - Time.

  

How does t_max reach maximum plasma concentration?

Dependent on the two rate constants for absorption and elimination phases.

What is the rate of absorption and elimination?

• Conform the elimination rate constant of a drug by comparing the IV profile with the oral profile.

• IV dose - No absorption, all drugs reach circulation and eliminate at the natural rate (k).

• Oral dose - Absorption occurs (K_a), some drug reaches the circulation and is eliminated at the natural rate (k).

• Comparison- Elimination slope for IVand oral does are parallel.

When does flip flop occur?

when rate of absorption is slower than the rate of elimination:

• Most drugs - K_a> K.

• k depends on processes of clearance (liver and kidneys).

• In some slow releasing drugs K_a = K.

• Flip flop kinetics - K_a < K.

What drugs exhibit flip flop characteristics?

• Not all drugs exhibit flip flop Kinect’s K_a < K.

• If the rate of absorption is slowed down enough, past a limit, the flip flop can occur.

• Need to monitor these drugs.

• Especially true for controlled sustained release drugs with short half life (antipsychotics steroid hormones).

• Need to maintain plasma drug level to a threshold in patients (increase adherence and consistency).

What is steady state?

• For chronic long-term  conditions can administer drugs on a regular basis (unlike a single oral dose or IV-bolus).

• Regular intake of drugs = accumulation in the body.

• Reaching steady state.

• This steady state needs to be within the therapeutic window.

What is constant IV-infusion?

Constant IV-infusion at steady state:

• Rate of change of the amount of drug in the body at any given time =dD/dt.

Changing IV-infusion rates:

• It takes 4.5-5 half lives to reach steady state and to be eliminated. 

• Increase concentration at steady state = Increase infusion rate.

• Clearance rate remains the same. 

Equation - Can determine the concentration of the drug at any given time during the infusion.

• During infusion - C₁ = R₀/CL (1-e^-kt1).

• End of infusion - C₂ = R₀/CL (1-e^-kt1)(e^-kt2).

What is repeated IV bolus and time to steady state?

If give same dose (50 mg/L) at same interval the at each half life:

• C₀ - 50 mg/L (first dose at 50mg).

• First half life - 25 mg/L.

• Second dose - 50mg.

• Total concentration. - 25 + 50 = 75 mg/L.

• Second half life - 37.5mg/L.

• Third dose - 50 mg/L.

• Total concentration - 37.5 +50 = 87.5mg/L.

• Third half-life - 43.75mg/L.

• Until reaching steady state C_Max.

What is the equation for steady state?

• At steady state, rate in = rate out.

• Steady state concentration depends upon the balance between the infusion rate (input) and the clearance (output).

• Steady state concentration is independent of Volume of distribution.

• Time to reach steady state is dependent upon half-life (4.5 to 5) and not infusion rate.

What are loading doses?

• If needed, give a loading dose for immediate effect and then keep that maintenance dose.

• can combine IV bolus and IV infusion. 

• Concentration at any given time (C_t) - IV bolus + IV infusion.

What is drug accumulation?

• If drugs are given over a longer period of time for chronic conditions they accumulate in the body.

• Drug accumulation depends on - The ratio of half life to dosing interval.

• When the dosing interval (T) is less than half life, drug levels are higher and there is less fluctuation between C_Max C_MIN.

What is clearance?

• Volume of plasma cleared of drug per unit time (L/h).

• Depends on the volume of distribution (V) and rate of elimination (k).

• Often quoted per Kg of body weight (L/h/Kg).

• Determines the maintenance dose that is required to obtain.

• Concentration at steady state (Css).