5003PhaSci: Pharmacokinetics of Lithium – coursework

5003PhaSci: Pharmacokinetics of Lithium – coursework

A simulation of lithium dosing in a specific patient and dose adjustment in response to monitoring

Background

The following exercise simulates the clinical objective of safe and effective treatment using a drug of narrow therapeutic window (dose interval between therapeutic and toxic effects). First the pharmacokinetic parameters (V, K, Cl) for the drug in a specific patient are determined by a bolus dose; thereby enabling the calculation of a regimen of dosing by i.v. bolus injection followed by an infusion. Second, the infusion rate is reviewed – adjusted, or maintained – in response to monitoring plasma levels achieved. This approach is used to successfully maintain the patient within a narrow therapeutic window.

Salts of lithium are classified as mood stabilizers; are used primarily for bipolar disorder; and are included on the WHO’s list of essential medicines. However, lithium along with other drugs has a narrow therapeutic window. Therefore, plasma levels are required to be monitored and dosing adjusted to maintain efficacy, while avoiding adverse symptoms (nausea, vomiting, seizure, coma) preceding death… from overdose.

When determining the concentration of lithium in a solution such as plasma, the Beer–Lambert law applies. One instrument to take practical advantage of this is the Atomic Absorption Spectrophotometer (AAS). The basic principle is that the absorption of light of a specific wavelength by lithium atoms when vaporised is proportional to its concentration.

Aim(s) of exercise:

  • To consider the accurate, calibrated use of quantitative analytical equipment (AAS and others) for the determination of absorption of light by free atoms in the gaseous state.
  • Apply the use of calibration graphs to determine sample concentrations.
  • Practice the use of semi-log graphs to linearize data and determine relevant pharmacokinetic parameters (C0 and t ½) from slope and intercept.
  • Practice the analysis of data, reporting of results (completed tables, and graphs) and basic pharmacokinetic calculations underlying therapeutic dosing by bolus and infusion (LD, Rinf).
  • Simulate “therapeutic drug monitoring” (TDM) of a sample of patient plasma taken after dosing: Consider the consequences for dose adjustment were your rate of infusion (Rinf) to achieve an ineffective, effective or toxic dose in the plasma of your patient.
  • Reflect on the importance of combining accuracy and dose monitoring for the safe use of medicines, especially those having narrow therapeutic range.

Data analysis

Tables and graphs to prepare from the data given below

• First, plot the calibration curve (Fig 1) of absorption (Y) versus concentration (X) from the standards (Table 2). Graphs can be hand-drawn or by excel. Include labels, axes, fig number & title.

• Use this calibration line (Fig 1) to read off the lithium concentrations in the 4 patient samples and enter these in Table 3.

• Next, draw a semi-log graph of lithium concentration versus time (Fig 2).  The 4 samples were taken at the following times:  1, 16, 36 and 72 hours.

• Fit a straight line through the points; derive the concentration at time=0 (C0) & the half-life (t ½).

• Using reference equations (Table 4), determine your estimate of volume of distribution (V), elimination rate constant (K) and clearance (Cl) for lithium in your patient.

Design of dosage regimen / TDM

• Use reference equations (Table 4) and the pharmacokinetic parameters of your patient (V, K, Cl) to calculate an appropriate bolus i.v. loading dose (LD) followed by a constant i.v. infusion (Rinf).

• The therapeutic target concentration is between 0.7 and 1.1 mMole/L.

• Therefore, let TD and Css = 0.9 mMole/L. Assume F = 1.

Were therapeutic drug monitoring performed you would find what concentrations would arise immediately after the loading dose and once the infusion had reached equilibrium.  Consider what would be the consequence and appropriate course of action were the dose too low, too high. What other advice is appropriate when managing a drug of narrow therapeutic index, such as Li ?

Assessment for this exercise

• 23 marks are allocated:

1) Accuracy of pharmacokinetic estimates (V, K, CL, Loading Dose, Rinf) (10 marks)

2) Two graphs (10 marks)

3) Answers to 3 questions (3)

Submission

• Complete this document and submit as a Word (.doc or .docx) or PDF file.

• Upload to Canvas using the submission link provided.

Pages to complete for coursework submission

Were you to have prepared a graduated series of known concentrations (“standards”) of Li with which to calibrate the Atomic Absorption Spectrophotometer (AAS) you would be provided with a 10 mMole/Litre stock of lithium and blank plasma as diluent. The lithium standard would be added first and the blank plasma second.  This would ensure good mixing, which is key to reliable determinations of concentration; and might be one cause of error if not done competently.

• 1. Complete the Table 1 which would have been used to create Lithium “standards” and calibrate the Atomic Absorption Spectrophotometer.

TABLE 1 Tube no.Volume of 10mMole/L standard  (ml)Volume of blank plasma  (ml)Resultant concentration (mMole/L)
1 2 3 4 “Blank”0.2 0.5 1.0 2.0 09.8 9.5 9.0 8.0 10.0? ? ? ? 0

• 2. Use the concentrations calculated in Table 1 and corresponding absorbance values in Table 2 to construct a calibration plot (Fig 1). Expect a curvilinear function, passing through the origin. Use either excel or linear paper if preferred, but present clearly, title, label, and number the plot.

• 3. Interpolate patient serum concentrations from Fig 1 and complete Table 3.

• 4. Using a semi-log plot (Fig 2) of Log concentration against time (Table 3), determine C0, the concentration at time = 0, and the half-life (t ½). Use either excel or linear paper if preferred, but present clearly, title, label, and number the plot.

Table 2: Data for calibration plot
TT NoConc (mMole/L) from Table 1Abs (Arb)
1?0.153
2?0.405
3?0.731
4?1.176
Table 3: Patient (data) Extrapolated from calibration plot
Sample (Hour)Abs (Arb)Conc mMole/L (determined)
10.711?
160.556?
360.341?
720.126?

• 5. Include copies of your graphs (Fig 1 & Fig 2). Minimum ½ page A4 for each graph / legend.

• 6. Summarise your findings: Complete Table 4, using the equations outlined.

Complete Table 4: PK results from your calculations

This list provides a “calculations check”!

Table 4Equations usedEnter your values here, tand report as “Table 4”
1C2 = C1. V1/V2Values set out in Table 1 & 2.
 Li standards (from stock, C1)Used to create calibration plot (Fig 1).
  Used to interpolate patient Li concentrations from Abs.
2C0 = intercept= ……………….. , from semi-log plot (Fig 2)
3t ½ = time for C0 to halve= ……………….., from semi-log plot (Fig 2)
4V = D/C0                 *= ………………..
5K = 0.693 / t ½= ………………..
6Cl = K.V= ………………..
7L.D. = Target [=0.9] . V / F [=1]= ………………..
8Rinf = Css [=0.9] . Cl= ………………..

* Dose given (D) prior to sampling plasma at four time points (1, 16, 32 and 72hrs).

Dose given (D) mMole
Patient dataDose
260
648
1048
1354
1569

• 7. Finally, answer the following questions, and submit via Canvas:

1. What advice would you give were the Css plasma levels achieved from your Rinf as follows:

a) 0.65 mmoles/L:

……………….. ……………….. ……………….. ……………… ………………

b) 0.95 mmoles/L:

……………….. ……………….. ……………….. ……………… ………………

c) 1.1 mmoles/L:

……………….. ……………….. ……………….. ……………… ………………

2a. Explain briefly how Atomic Absorption works; hint – who’s Law / what is proportional to what?

……………….. ……………….. ……………….. ……………… ………………

2b. What alternatives are available for measuring Li ions in solution?

……………….. ……………….. ……………….. ……………… ………………

3. What condition is treated with Lithium?

……………….. ……………….. ……………….. ……………… ………………

A note on the therapeutic window for Lithium therapy

This dosing simulation works towards a Li target of 0.9mmole/L and within a dose range (1.1-0.7mmole/L) that is consistent with indications (use) and toxicity, reproduced here; and the therapeutic range of 0.6 mEq/L-1.2 mEq/L (0.6 mmols/L-1.2 mmols/L, reported by Tietz NW (Ed): Clinical Guide to Laboratory Tests, 3rd ed. W. B. Saunders, Philadelphia, PA, 1995 https://www.allinahealth.org/CCS/doc/Thomson%20Consumer%20Lab%20Database/49/150195.htm

Semi-log graph paper is included – else use Excel:

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