Yesterday in Bremen, my long-time friend Prof. Roberto Ferraresi of Milano made an offhand remark that has been bouncing around my head ever since. Small artery disease, he said, is relatively easy to spot on an angiogram — because it doesn’t look like nature.
He’s right. And the reason he’s right is Benoit Mandelbrot.
The vascular tree is one of the cleanest fractals biology ever produced. Lungs, river deltas, lightning, ferns, coastlines, the bronchial tree, the pedal arch — all are self-similar across scales, the small repeating the shape of the large. Murray’s law, written in 1926, is the engineering rule that makes it work: at each bifurcation, the cube of the parent radius equals the sum of the cubes of the daughters. Follow that rule down a few generations and you get a tree. Break it and you get noise.
Healthy human microcirculation has a measurable fractal dimension. In the retina — the most accessible window we have to small vessel beds — it sits around 1.7 by box-counting. In diabetes, hypertension, CADASIL, and a growing list of microvascular diseases, that number falls. The vasculature gets sparser, gappier, less complex; lacunarity rises. OCT-A studies now show the deep capillary plexus loses fractal dimension before clinical retinopathy is visible. The tree thins before the leaves fall.
This is why your eye knows. When you flick through a normal pedal angiogram, the foot looks like a delta, a fern, a piece of weather. When you flick through a foot with severe SAD, you are looking at a pruned tree in February — recognizable not by what is there, but by the absence of the pattern that should be there. Roberto and Joe Mills’ SAD/MAC scoring system is, in part, a clinical instrument for grading that loss of self-similarity. The question “how bad is the small vessel disease?” is, geometrically, “how much fractality has been eaten?”
Two implications worth chewing on.
First, fractal dimension and lacunarity are quantifiable. We measure them in retinas. We could measure them in feet. Imagine a one-number summary of a pedal angiogram — a complexity index — that correlates with healing, with limb salvage, with mortality. The math is sitting there waiting for us.
Second, this is exactly the kind of weird-ideas-and-weird-people territory I love. Mandelbrot died fifteen years ago and never thought about diabetic feet. Murray published in 1926 and never thought about CLTI. But put a podiatric surgeon, an interventional cardiologist from Milan, an OCT-A engineer, and a fractal mathematician in the same room and you might come out with a tool we badly need.
If it doesn’t look like a tree, a river, or a lightning bolt — something is wrong. The eye knew it. Now we just have to teach the math to keep up.
— DGA
#Fractals #Microcirculation #SmallArteryDisease #SAD #CLTI #DiabeticFoot #LimbSalvage #Angiogram #Mandelbrot #MurraysLaw #Ferraresi #Bremen #EWMA2026
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