Dosage Calculation - Mass/Time - IV mL Rate Questions

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Mass/Time - IV mL Rate Questions

Give an order in quantity of mass per time, determine the necessary IV flow rate in mL/hr based on the given mass per volume. These types of problems are often used in critical care nursing.

Formula:

$$\boxed{\frac{\mathbf{Ordered\; Per\; Hour}}{\mathbf{Have}}x\mathbf{Volume\; (mL)}=\mathbf{Y(Flow\; Rate\; in\; mL/hr)}}$$

Example: Give patient 500 mg of dopamine in 250 mL of D5W to infuse at 20 mg/hr. Calculate the flow rate in mL/hr.

$$\frac{\mathbf{Ordered\; Per\; Hour}}{\mathbf{Have}}x\mathbf{Volume\; (mL)}=\mathbf{Y(Flow\; Rate\; in\; mL/hr)}$$

$$\frac{\mathbf{20\; mg/hr}}{\mathbf{500\; mg}}x\mathbf{250\; mL}=\boxed{\mathbf{10\; mL/hr}}$$

Alternatively 500 mg = 250 mL
Therefore, 20 mg/hr = 250 mL/500 mg x 20 mg/hr = 10 mL/hr

Example: Aggrastat at 12.5 mg in 250 mL is prescribed to be infused at a rate of 6 mcg/kg/hr in a patient who weighs 100 kg. At what flow rate in mL/hr will you set the pump?

$$\frac{\mathbf{Ordered\; Per\; Hour}}{\mathbf{Have}}x\mathbf{Volume\; (mL)}=\mathbf{Y(Flow\; Rate\; in\; mL/hr)}$$

The first step is to convert the order per time to the amount required for this particular patient. This is a Dosage By Weight Question. 6 mcg/kg/hr is a dosage in terms of kg.

$$\mathbf{Weight\; in\; Kg}x\mathbf{Dosage\; Per\; Kg}=\mathbf{Y(Required\; Dosage)}$$

$$\mathbf{100\; Kg}x\mathbf{6\; mcg/kg/hr}=\mathbf{600\; mcg/hr}$$

Convert 600 mcg/hr to mg/hr.
    mcg → mg → g → kg    ( ÷ by 1,000 )
    600 ÷ 1,000 = 0.6 mg/hr

$$\frac{\mathbf{0.6\; mg/hr}}{\mathbf{12.5\; mg}}x\mathbf{250\; mL}=\boxed{\mathbf{12\; mL/hr}}$$

Alternatively 12.5 mg = 250 mL
Therefore, 0.6 mg/hr = 250 mL/12.5 mg x 0.6 mg/hr = 12 mL/hr

Question (22): (From Ngee Ann Polytechnics Dosage Calculation Worksheet)
ORDER: I/V Dopamine 5 mcg/kg/min. Dilution - 200 mg/100 mL Normal Saline. Patient Weight: 50 kg.
Calculate: __________ mL/hr = 5 mcg/kg/min.

$$\frac{\mathbf{Ordered\; Per\; Hour}}{\mathbf{Have}}x\mathbf{Volume\; (mL)}=\mathbf{Y(Flow\; Rate\; in\; mL/hr)}$$

The first step is to convert the order per time to the amount required for this particular patient. This is a Dosage By Weight Question. 50 kg is the weight in kg and 5 mcg/kg/min is a dosage in terms of kg.

1 min Dosage = 5 mcg/kg
1 hour Dosage = 5 mcg/kg x 60 = 300 mcg/kg
5 mcg/kg/min = 300 mcg/kg/hr

$$\mathbf{Weight\; in\; Kg}x\mathbf{Dosage\; Per\; Kg}=\mathbf{Y(Required\; Dosage)}$$

$$\mathbf{50\; Kg}x\mathbf{300\; mcg/kg/hr}=\mathbf{15,000\; mcg/hr}$$

Convert 15,000 mcg/hr to mg/hr.
    mcg → mg → g → kg    ( ÷ by 1,000 )
    15,000 ÷ 1,000 = 15 mg/hr

$$\frac{\mathbf{15\; mg/hr}}{\mathbf{200\; mg}}x\mathbf{100\; mL}=\boxed{\mathbf{7.5\; mL/hr}}$$

Alternatively 200 mg = 100 mL
Therefore, 15 mg/hr = 100 mL/200 mg x 15 mg/hr = 7.5 mL/hr

Question (23): (From Ngee Ann Polytechnics Dosage Calculation Worksheet)
ORDER: I/V Dopamine 1 mcg/kg/min. Patient Weight: 50 kg.
Calculate: Amount of Dopamine in 100 mL diluent to deliver 1 mL/hr = 1 mcg/kg/min

The first step is to convert the order per time to the amount required for this particular patient. This is a Dosage By Weight Question. 50 kg is the weight in kg and 1 mcg/kg/min is a dosage in terms of kg.

1 min Dosage = 1 mcg/kg
1 hour Dosage = 1 mcg/kg x 60 = 60 mcg/kg
1 mcg/kg/min = 60 mcg/kg/hr

$$\mathbf{Weight\; in\; Kg}x\mathbf{Dosage\; Per\; Kg}=\mathbf{Y(Required\; Dosage)}$$

$$\mathbf{50\; Kg}x\mathbf{60\; mcg/kg/hr}=\mathbf{3,000\; mcg/hr}$$

Convert 3,000 mcg/hr to mg/hr.
mcg → mg → g → kg ( ÷ by 1,000 )
3,000 ÷ 1,000 = 3 mg/hr

$$\frac{\mathbf{Ordered\; Per\; Hour}}{\mathbf{Have}}x\mathbf{Volume\; (mL)}=\mathbf{Y(Flow\; Rate\; in\; mL/hr)}$$

$$\frac{\mathbf{3\; mg/hr}}{\mathbf{Amt.\; of\; Dopamine}}x\mathbf{100\; mL}=\mathbf{1\; mL/hr}$$

$$\mathbf{Amt.\; of\; Dopamine}=\frac{\mathbf{3\; mg/hr}x\mathbf{100\; mL}}{\mathbf{1\; mL/hr}}=\boxed{\mathbf{300\; mg}}$$

Alternatively,
To deliver, 1 mL = 3 mg of Dopamine
Therefore, 100 mL diluent = 3/1 x 100 = 300 mg of Dopamine

Question (24): (From Ngee Ann Polytechnics Dosage Calculation Worksheet)
Patient Weight: 50 kg.
Calculate amount diluent for 200 mg Dopamine to deliver 1 mL/hr = 1 mcg/kg/min (Dosage).

The first step is to convert the order per time to the amount required for this particular patient. This is a Dosage By Weight Question. 50 kg is the weight in kg and 1 mcg/kg/min is a dosage in terms of kg.

1 min Dosage = 1 mcg/kg
1 hour Dosage = 1 mcg/kg x 60 = 60 mcg/kg
1 mcg/kg/min = 60 mcg/kg/hr

$$\mathbf{Weight\; in\; Kg}x\mathbf{Dosage\; Per\; Kg}=\mathbf{Y(Required\; Dosage)}$$

$$\mathbf{50\; Kg}x\mathbf{60\; mcg/kg/hr}=\mathbf{3,000\; mcg/hr}$$

Convert 3,000 mcg/hr to mg/hr.
mcg → mg → g → kg ( ÷ by 1,000 )
3,000 ÷ 1,000 = 3 mg/hr

$$\frac{\mathbf{Ordered\; Per\; Hour}}{\mathbf{Have}}x\mathbf{Volume\; (mL)}=\mathbf{Y(Flow\; Rate\; in\; mL/hr)}$$

$$\frac{\mathbf{3\; mg/hr}}{\mathbf{200\; mg}}x\mathbf{Volume\; of\; diluent\; (mL)}=\mathbf{1\; mL/hr}$$

$$\mathbf{Volume\; of\; diluent\; (mL)}=\mathbf{1\; mL/hr}x\frac{\mathbf{200\; mg}}{\mathbf{3\; mg/hr}}=\boxed{\mathbf{66.7\; mL}}$$

Alternatively,
To deliver, 3 mg of Dopamine = 1 mL
Therefore, 200 mg of Dopamine = 1/3 x 200 = 66.7 mL of diluent

Question (25): (From Ngee Ann Polytechnics Dosage Calculation Worksheet)
ORDER: I/V adrenaline 0.02 mcg/kg/min. Dilution - 1.5 mg/50 mL. Patient Weight: 50 kg.
Calculate: __________ mL/hr = 0.02 mcg/kg/min.

$$\frac{\mathbf{Ordered\; Per\; Hour}}{\mathbf{Have}}x\mathbf{Volume\; (mL)}=\mathbf{Y(Flow\; Rate\; in\; mL/hr)}$$

The first step is to convert the order per time to the amount required for this particular patient. This is a Dosage By Weight Question. 50 kg is the weight in kg and 0.02 mcg/kg/min is a dosage in terms of kg.

1 min Dosage = 0.02 mcg/kg
1 hour Dosage = 0.02 mcg/kg x 60 = 1.2 mcg/kg
0.02 mcg/kg/min = 1.2 mcg/kg/hr

$$\mathbf{Weight\; in\; Kg}x\mathbf{Dosage\; Per\; Kg}=\mathbf{Y(Required\; Dosage)}$$

$$\mathbf{50\; Kg}x\mathbf{1.2\; mcg/kg/hr}=\mathbf{60\; mcg/hr}$$

Convert 60 mcg/hr to mg/hr.
    mcg → mg → g → kg    ( ÷ by 1,000 )
    60 ÷ 1,000 = 0.06 mg/hr

$$\frac{\mathbf{0.06\; mg/hr}}{\mathbf{1.5\; mg}}x\mathbf{50\; mL}=\boxed{\mathbf{2\; mL/hr}}$$

Alternatively 1.5 mg = 50 mL
Therefore, 0.06 mg/hr = 50 mL/1.5 mg x 0.06 mg/hr = 2 mL/hr

Congratulations: You have completed the Dosage Calculation Worksheet From Ngee Ann Polytechnics.

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Reference
[1] Advanced Formatting, Ry’s MathML Tutorial, http://rypress.com/tutorials/mathml/advanced-formatting.
[2] MathML, Presentation MathML, https://en.wikipedia.org/wiki/MathML.
[3] MathJax in Blogger (II), Posted on Tuesday, 12 July 2011, http://irrep.blogspot.sg/2011/07/mathjax-in-blogger-ii.html
[4] MathJax, http://docs.mathjax.org/en/latest/start.html
[5] MathML Fundamentals (Colours), W3C recommendation, http://www.w3.org/TR/MathML/chapter2.html

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