Weight =

Css =

DOSE =

Tinf = 0.5

Vd =

K elimination =

TAU =

Change in Time =

Patient identifier =

This is the Css equation for first order elimination only. It is used to determine volume of distribution and possible dosage modifications. K elimination must first be determined with a different template. (Half-Life and Ke)

- Weight: the patient's weight

- Css: the steady state concentration in mg/Liter or mcg/mL [This can be any steady-state concentration (peak, trough, Cpmax, or C time - see notes below.]

- DOSE: the mg dose of medication given

- Tinf: the duration of the medication dose infusion (in hours)

- Vd: the apparent volume of distribution (in Liters/kg)

- K elimination: the elimination rate constant (in "/hr")

- TAU: the frequency of dose administration (in hours)

- Change in Time: the number of hours from the end of the dose infusion to Css

- Patient identifier: You may add initials or a name to the results to help you identify whose they are. This identifier will be included when you email results. This may also be left blank.

K elimination must be determined first with the "Half-life and ke" template. This equation is most commonly used to determine the volume of distribution using a reported measured concentration as Css.

***This equation will allow you to use the reported peak or trough values without having to extrapolate to solve for Cpmax or Cpmin. It does not require Css to be the true Cpmax or Cpmin. The user can insert for Css the value for any reported steady-state concentration (or the value for Cpmax or Cpmin - if that is your preference).

The value inserted for Change in Time is the number of hours from the end of the dose infusion until the measured concentration. When using Cpmax for Css, the Change in Time would be zero. The equation can also be used to find a new maintenance dosing regimen. To find the new value for CssTrough, input for Change in Time the value of (TAU - Tinf) and solve for Css. To find the new CssPeak, set Change in Time = 0.5hrs (if your normal practice is to draw peak levels 30 minutes after the end of the infusion) and solve for Css.

NOTE********** Clinicians very familiar with pharmacokinetic evaluation of routine vancomycin and aminoglycoside peak and trough levels may only need two equations:

Half-Life and ke along with Concentration Steady-State to find ke, T 1/2, Vd, the new dosage and interval, and the new concentrations achieved with this new dosage.

The steps are as follows:

1. Determine k elimination and T 1/2 using

Half-Life and ke template.

2. Open the Concentration Steady-State equation and insert for Css the value of the measured trough (pre) level. Insert the values for DOSE, Tinf, K elimination", weight, TAU, and Change in Time (when the Css value is the pre or trough the Change in Time is the number of hours from the completion of the previous dose infusion until the time that the pre level was drawn).

3. Tap on the "=" to solve for Vd

4. Change Css to the new VALUE that you want to achieve (making sure to alter Change in Time to reflect the number of hours after the end of the dose infusion that you want to achieve this VALUE), and change TAU if necessary, then Solve for DOSE.

5. Continue to alter Css, DOSE, or TAU and solve for the remaining variable until you determine a regimen that achieves the PRE and POST levels that you want - ALWAYS making sure that the value input for Change in Time accurately reflects the number of hours from the end of the dose infusion to the Css that would be drawn.

Amikacin umol/L x 0.585 = mCg/mL

Caffeine umol/L x 0.194 = mCg/mL

Gentamicin umol/L x 0.478 = mCg/mL

Phenobarbital umol/L x 0.232 = mCg/mL

Tobramycin umol/L x 0.468 = mCg/mL

Vancomycin umol/L x 1.449 = mCg/mL

CB is a 35kg 8 year old child who is started on Gentamicin 70 mg IV Q 8 hours. The first dose is at 1100 on 12/20 and infused over 30 minutes. The next dose is given at 1900 on 12/20, with the third dose given at 0300 0n 12/21. A Pre level drawn 30 minutes before the third dose was 0.7 mg/L. A Post level drawn 30 minutes after the third dose finished infusing was 5.0 mg/L. You believe that the levels are at steady-state based on the dosage given and the patient's age and renal function. Your goal for the Post level is ~ 8 mg/L with a Pre level goal of < 1 mg/L. From using the Half-life and ke template, you determine that this patient's k elimination is 0.302 and half-life is 2.3 hours based on a change in time of 6.5 hours. What is this patient's volume of distribution?

How should you modify the dose to achieve levels within your goal range? Input the following:

- Weight: 35 kg

- Css: 5 mg/L

- DOSE: 70mg

- Tinf: 0.5 hrs

- K elimination: 0.302

- TAU: 8 hrs

- Change in Time: 0.5 hrs

The calculator solves for Vd giving a value of 0.35 L/kg.

If you believe that this value sounds reasonable for your patient, then proceed to answer this question: How should you modify the dose to achieve levels within your goal range?

Re-input the following:

- Css: 8 mg/L

And then tap the "?" symbol next to DOSE to find the new dose needed to achieve your desired Post level of 8 mg/L. The calculator gives an answer of 112 mg.

To make this a more reasonable dose to measure, modify this to 110 mg and now tap the "?" symbol next to Css to find the Post level that will occur with 110 mg Q 8 hours. The calculator gives an answer of 7.9 mg/L.

To find what the new Pre value will be on this dose, re-input the following:

- Change in Time: 7.5 hrs

Now tap "?" symbol next to Css. The calculator gives an answer of 0.9 mg/L for the new Pre level.

Your calculations suggest that CB's dose may be changed to 110 mg every 8 hours to achieve a Post level of ~ 8 mg/L and a Pre level 0f 0.95 mg/L.

If you wanted a lower Pre value:

- TAU: 12 hrs

- Change in Time: 0.5 hrs

- Css to 8 mg/L

Tap "=" next to DOSE to find what dose given every 12 hours would give the desired Post level. The calculator would give the answer of 119.7 or ~ 120 mg.

Finally, modify:

- DOSE: 120 mg

- Change in Time: 11.5 hrs

Tap the "=" symbol next to Css to find that the new Pre level on 120 mg every 12 hours would be 0.3 mg/L.

Weight

Css

DOSE

Tinf

Vd

K elimination

TAU

Change in Time

Patient identifier

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