Question

q3. determine the bsa of a patient who weighs 31 lb with a height of 26 inches using the bsa formula.

Explanation:

The BSA (Body Surface Area) formula for children (or patients with weight in pounds and height in inches) is usually the Mosteller formula or the Du Bois formula. The Mosteller formula is simpler: \( \text{BSA (m}^2\text{)} = \sqrt{\frac{\text{height (in)} \times \text{weight (lb)}}{3131}} \) (or sometimes \( \frac{\text{height (cm)} \times \text{weight (kg)}}{3600} \), but we need to adjust units if using metric. However, since the problem gives height in inches and weight in pounds, we'll use the version for imperial units: \( \text{BSA (m}^2\text{)} = \sqrt{\frac{\text{height (in)} \times \text{weight (lb)}}{3131}} \) or sometimes the formula is \( \text{BSA (m}^2\text{)} = \frac{\sqrt{\text{height (cm)} \times \text{weight (kg)}}}{60} \), but let's confirm the correct formula for imperial units. Wait, actually, the standard Mosteller formula is \( \text{BSA (m}^2\text{)} = \sqrt{\frac{h(\text{cm}) \times w(\text{kg})}{3600}} \). So first, we need to convert inches to cm and pounds to kg.

Step 1: Convert height to cm

Height = 26 inches. Since 1 inch = 2.54 cm, so \( 26 \times 2.54 = 66.04 \) cm.

Step 2: Convert weight to kg

Weight = 31 lb. Since 1 lb = 0.453592 kg, so \( 31 \times 0.453592 \approx 14.061352 \) kg.

Step 3: Apply the Mosteller formula

\( \text{BSA} = \sqrt{\frac{h \times w}{3600}} \), where \( h = 66.04 \) cm, \( w = 14.061352 \) kg.

First, calculate \( h \times w \): \( 66.04 \times 14.061352 \approx 928.61 \)

Then divide by 3600: \( \frac{928.61}{3600} \approx 0.2579 \)

Then take the square root: \( \sqrt{0.2579} \approx 0.5078 \) m². Wait, but that seems high for a child? Wait, maybe the formula is different. Alternatively, the Du Bois formula: \( \text{BSA (m}^2\text{)} = 0.007184 \times w^{0.425} \times h^{0.725} \), where \( w \) is in kg and \( h \) is in cm. Let's try that.

Step 3 (Alternative): Use Du Bois formula

\( w = 14.061352 \) kg, \( h = 66.04 \) cm.

First, calculate \( w^{0.425} \): \( 14.061352^{0.425} \approx e^{0.425 \times \ln(14.061352)} \approx e^{0.425 \times 2.644} \approx e^{1.123} \approx 3.074 \)

Then \( h^{0.725} \): \( 66.04^{0.725} \approx e^{0.725 \times \ln(66.04)} \approx e^{0.725 \times 4.189} \approx e^{3.037} \approx 20.83 \)

Then multiply by 0.007184: \( 0.007184 \times 3.074 \times 20.83 \approx 0.007184 \times 64.04 \approx 0.460 \) m². Hmm, still a bit high? Wait, maybe the patient is a child, so maybe the formula is different. Wait, the problem says "using the BSA formula"—maybe it's the formula for children: \( \text{BSA (m}^2\text{)} = \frac{\text{weight (lb)} \times \text{height (in)}}{3131} \) (this is a simplified formula for imperial units, sometimes used). Let's try that:

\( \text{BSA} = \sqrt{\frac{31 \times 26}{3131}} = \sqrt{\frac{806}{3131}} \approx \sqrt{0.2574} \approx 0.507 \) m². So that's consistent with the Mosteller formula after unit conversion. So the BSA is approximately 0.51 m² (rounded to two decimal places) or 0.507 m².

Wait, let's check the formula again. The standard Mosteller formula is \( \text{BSA (m}^2\text{)} = \sqrt{\frac{h(\text{cm}) \times w(\text{kg})}{3600}} \). So:

h = 26 in = 26 * 2.54 = 66.04 cm

w = 31 lb = 31 * 0.453592 ≈ 14.061 kg

Then \( \frac{66.04 \times 14.061}{3600} = \frac{928.6}{3600} ≈ 0.2579 \)

Square root of 0.2579 ≈ 0.5078 m² ≈ 0.51 m².

So the steps are:

1. Convert height to cm: 26 * 2.54 = 66.04 cm

1. Convert weight to kg: 31 * 0.453592 ≈ 14.061 kg

1. Apply Mosteller formula: \( \sqrt{\frac{66.04 \times 14.061}{3600}} ≈ 0.51 \) m²

Answer:

The BSA of the patient is approximately \( \boldsymbol{0.51} \) m² (or more precisely \( \approx 0.508 \) m²).