Orthogonal Assay Validation for Spatial Multi-omics (2D)

Platform A

Noise (σ) 0.10

Systematic bias 0.00

Platform B

Noise (σ) 0.08

Systematic bias 0.00

Cross-platform validation

Pearson r (A vs. B, measured)

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R²

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Positions (n)

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How it works

A single spatial-omics platform can't validate itself. Here two independent measurement platforms (e.g. spatial transcriptomics and an orthogonal protein assay like IHC) each scan the same grid of tissue positions, measuring a related biological signal. Each platform's readout is the true underlying biology plus its own noise and systematic bias — the two error sources are never shared, because the platforms use unrelated chemistry.

A(x,y) = gainA·truth(x,y) + biasA + N(0, σA)
B(x,y) = gainB·truth(x,y) + biasB + N(0, σB)
r = Σ(Aᵢ−Ā)(Bᵢ−B̄) / √[Σ(Aᵢ−Ā)²·Σ(Bᵢ−B̄)²]

The engine never compares either platform back to the hidden truth field — real experiments don't have access to it either. Instead it computes the real Pearson correlation directly between the two actual noisy measurements, position by position, exactly as a real cross-platform validation study does. A high r means the two independent technologies agree, which is the standard evidence that platform A's signal is real biology and not technical artifact; a low r flags platform-specific noise or bias.

Noise (σ) — each platform's own random measurement error at every position. Raising either platform's noise decorrelates it from the ground truth and from the other platform, so the measured A-vs-B correlation drops — with zero access to the truth field itself.
Systematic bias — a constant offset added to every reading from one platform (miscalibration). A pure offset shifts the scatter cloud but barely dents the correlation on its own, because Pearson r is offset-invariant — noise, not bias, is what erodes agreement.
Heatmaps — each panel is min–max normalized independently so its own spatial pattern stays visible regardless of gain/bias/noise.
Scatter plot — every point is one tissue position's (A, B) pair. A tight diagonal cloud is high r; a round cloud is r near 0.

Platform A

Platform B

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