Diffusion, dialysis and clearance

Companion to chapters 4, 10 and 17 of Human Biology for the Medical Maker: Foundations of biology, Kidneys, gut, and hormones and Treatment and life-support devices. It covers chapter 4’s exit criterion of calculating a diffusion time with units, and its question on why cells sit within about 100–200 μm of a capillary.

Educational — not a medical device. Not for diagnosis, treatment, monitoring or dosing. Simulation only: dialysis figures here are orientation, "not settings, doses, or targets" for anybody, and dialysis equipment is firmly for clinical teams.

How to use it

Diffusion time. Pick a distance (type it or drag the log-scale slider) and a diffusion coefficient; the time follows t ≈ x²/2D. With chapter 4’s D = 2 × 10⁻⁹ m²/s for oxygen in water: 10 μm ≈ 25 ms, 100 μm ≈ 2.5 s, 1 mm ≈ 4 min, 1 cm ≈ 7 h. The log–log plot marks those four points and the 100–200 μm band within which most cells sit from a capillary. Below it, surface ÷ volume = 3/r for a sphere: a bacterium (r 0.5 μm) has 6 μm⁻¹, a 20 μm-diameter human cell 0.3 μm⁻¹.

Fit D from data. Chapter 4’s exercise: a drop of food colouring on gelatin or agar, photographed over a day. Paste one "distance, time" pair per line (commas, tabs, spaces or semicolons; a header line and # comments are fine), choose the units, and the tool fits distance against √time and reports D = slope² ÷ 2 — or ÷ 4 for spread across a surface, ÷ 6 from a point in a block. Tick the intercept option when the drop starts with a size of its own. A line that does not parse is reported by number, never skipped.

Dialyser clearance. K = Q_b × (C_in − C_out) ÷ C_in and Kt/V. Chapter 17’s example: 300 mL/min, urea 30 → 9 mmol/L gives K = 210 mL/min, K × t ≈ 50 L over 4 hours, and Kt/V ≈ 1.2 with 42 L of body water. Then a week of clearance: kidneys filtering 120 mL/min continuously handle ≈ 1,200 L of plasma a week, a dialyser at 200 mL/min for 12 hours ≈ 144 L (chapter 10). Last, the general relationship for one dialyser: clearance against blood flow, counter- and co-current, with the extraction per pass marked at 250, 350 and 450 mL/min — clearance rises with flow but with diminishing returns, because the fraction removed per pass falls.

Co- vs counter-current. An animated exchanger — blood above, dialysate below, shading for concentration — with the concentration profiles along the fibre. Counter-current keeps a gradient along the whole length; co-current lets the streams converge, capping clearance at Q_bQ_d ÷ (Q_b + Q_d). Press Pause to stop the animation (it starts paused if your system asks for reduced motion).

Inputs outside each calculator’s range are rejected with a message, never clamped. Every value carries its unit.

Limits

t ≈ x²/2D is an order-of-magnitude rule for diffusion in one dimension, with no consumption along the way; tissue that uses oxygen as it diffuses fares worse.
A dye front is a colour threshold, not a root-mean-square distance, and depends on how much dye you used and how you photograph it; treat a fitted D as an order of magnitude.
The dialyser curves use the Michaels (1966) mass-transfer model with a single, illustrative KoA, a fixed dialysate flow and no ultrafiltration, recirculation or access effects. They show the shape of the relationship, not any real dialyser’s performance.
Kt/V here is the simple product K × t ÷ V; clinical Kt/V uses formulas that account for urea generation, ultrafiltration and rebound.
The book’s dialysis exercise (chapter 17) is being corrected. As printed, outlet concentrations of 40%, 35% and 30% of inlet at blood flows of 250, 350 and 450 mL/min give clearances of 150, 227.5 and 315 mL/min — each step buying more than the last, with extraction rising as flow rises. A fixed dialyser does the opposite: extraction falls as blood flow rises. The tool therefore shows the general relationship rather than building that exercise in.
Chapter 10 calls a creatinine clearance of 120 mL/min "a normal GFR"; this tool uses the figure only as the book’s orientation value for weekly totals and does not label any value normal.

Sources: chapter 4 (diffusion times, oxygen D, surface to volume, the agar exercise), chapter 10 (clearance, weekly totals, countercurrent dialysis, the bench dialysis-tubing exercise), chapter 17 (dialyser clearance and Kt/V example), appendix C (dialysate flow ~500–800 mL/min); A. S. Michaels, "Operating parameters and performance criteria for hemodialyzers and other membrane-separation devices", Trans Am Soc Artif Intern Organs 12:387–392 (1966).

Related: test lung and breathing mechanics, heart, vessels and oxygen, thermal design, statistics (more curve fitting).

Share link (under the title) copies a URL that reopens this tool exactly as you have it — every tab’s inputs, including pasted data, with the current tab selected. Opening such a link replaces the inputs this browser had saved for the tool. Link to a tab with its name after #: /tools/diffusion-exchange/#exchanger (or #time, #fit, #dialyser).

How to use it

Limits

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