Nephron Loss & Hyperfiltration — 2D Lattice Model

Disease Drivers

Underlying insult (diabetes / hypertension) 2.0%/yr

Hyperfiltration injury sensitivity 1.2×

RAAS blockade (ACEi/ARB therapy) 0%

Simulation speed 4 yr/s

Kidney Function

Total GFR

100 mL/min

Nephrons remaining

100%

CKD stage

Years elapsed

0.0

Single-nephron GFR

1.00×

Annual loss rate

2.0%/yr

How it works

Every cell in the left panel's lattice is one nephron. When N(t) of the original N₀ survive, the survivors partially compensate by raising their own filtration rate — the Brenner hyperfiltration hypothesis (Brenner et al., 1982):

SNGFR(t) = SNGFR₀ · (N₀ / N(t))^k        (k ≈ 0.45, partial compensation)
GFR_total(t) = SNGFR(t) · N(t) = GFR₀ · (N(t) / N₀)^(1-k)

Because k < 1, total GFR still falls as N falls — compensation is never complete. Worse, the elevated single-nephron pressure that drives hyperfiltration itself injures the glomerulus, adding a feedback term to each nephron's annual failure hazard:

hazard(t) = insult_rate + sensitivity · max(0, SNGFR/SNGFR₀ − 1) · (1 − RAAS_blockade)

Underlying insult — the baseline damage rate from diabetes, hypertension, or another chronic disease.
Hyperfiltration injury sensitivity — how strongly each surviving nephron's own compensatory overwork accelerates its neighbours' demise.
RAAS blockade — ACE inhibitors / ARBs relax the efferent arteriole and lower intraglomerular pressure, blunting the hyperfiltration-driven term without touching the baseline insult.

The right-hand strip chart plots total GFR, the single-nephron hyperfiltration ratio, and the instantaneous hazard rate against simulated years, so you can watch the feedback loop unfold as a trajectory, not just as a dying lattice. CKD stages follow the KDIGO GFR bands: G1 ≥ 90, G2 60–89, G3a 45–59, G3b 30–44, G4 15–29, G5 < 15 mL/min/1.73m².

Kidney failure (CKD stage G5) — dialysis or transplant required

Healthy nephron Hyperfiltering (stressed) Sclerosed / lost

Nephron Loss and Compensatory Hyperfiltration — 2D Lattice Model