Question 1 · Hard
A pathologist slices a resected spleen into parallel slabs 5 mm thick and places them in a large volume of 10% neutral buffered formalin, laid so that fixative reaches both cut faces of every slab. The laboratory procedure estimates formaldehyde penetration with Medawar's relation d = K√t, where d is the distance penetrated in millimeters, t is the time in hours, and K is taken as 0.78 for 10% formalin. Before scheduling the slabs for the overnight processor, the technologist estimates how long formaldehyde needs to reach the middle of each slab. The best estimate is:
- AAbout 10 hours
- BAbout 3 hours
- CAbout 5 hours
- DAbout 41 hours
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Answer: A · About 10 hours
Formalin enters each slab from both cut faces, so the middle lies 2.5 mm, half of the 5 mm thickness, from each surface. Rearranging d = K√t gives t = (d/K)², so t = (2.5 ÷ 0.78)² = 3.2² ≈ 10.3 hours. Using the full 5 mm thickness gives (5 ÷ 0.78)² ≈ 41 hours, stopping at d ÷ K without squaring gives 3.2 hours, and multiplying d² by K gives about 4.9 hours. Because the time rises with the square of the distance, halving slab thickness cuts the penetration time to a quarter. Penetration is also not the same as fixation: formaldehyde forms its cross-links slowly after it arrives, so the slabs need longer in formalin than this estimate alone.
- B: 3 hours is d ÷ K, without squaring the result.
- C: 5 hours comes from multiplying d² by K instead of squaring d ÷ K.
- D: 41 hours uses the full 5 mm thickness, but fixative enters from both faces.