A connected dose profile.

Use spatial correlation to reconstruct dose along the biopsy, predict withheld segments and quantify the profile's uncertainty.

A fitted semivariogram beside the reconstructed dose profile for one biopsy.A fitted semivariogram beside the reconstructed dose profile for one biopsy. Shown: Spatial correlation.

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A fitted semivariogram beside the reconstructed dose profile for one biopsy.

Nearby positions inform the dose profile.

Learn how dose varies with distance along each core. That spatial relationship turns uncertain local estimates into a continuous profile with model-based uncertainty.

Interpretation. This example estimates an underlying dose profile. Its uncertainty bands do not describe a more certain physical biopsy location.

Test the profile on withheld sections.

Fit the model without one stretch of the core, then compare predictions there with the simulated dose estimates left out of the fit.

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Three held-out folds for biopsy 6: train-only semivariograms beside predictions for the withheld dose estimates.Three held-out folds for biopsy 6: train-only semivariograms beside predictions for the withheld dose estimates. Shown: (a) Fold 1 prediction.

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Three held-out folds for biopsy 6: train-only semivariograms beside predictions for the withheld dose estimates.
Blocked prediction

Predict a section left out.

Fit the model without one stretch of the core. Then compare its predictions with the dose estimates withheld from the fit.

Study scope. Predictions are tested against withheld simulated dose estimates, not independent measurements in tissue.

From possible locations to a dose profile.

First, simulate plausible biopsy locations and map their doses. Gaussian process regression (GPR) then combines those estimates with the spatial relationship along each core to estimate its dose profile and uncertainty.

Analysis pipeline from simulated dose summaries through spatial correlation fitting to dose profiles, uncertainty and prediction checks.

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Analysis pipeline from simulated dose summaries through spatial correlation fitting to dose profiles, uncertainty and prediction checks.

Retain the differences between cores.

Dose trends and their spatial scales vary. Each core gets its own fitted relationship rather than a single shared dose profile.

Four biopsy dose profiles with different trends, uncertainty bands and axis ranges.Four biopsy dose profiles with different trends, uncertainty bands and axis ranges. Shown: Biopsy 3.

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Four biopsy dose profiles with different trends, uncertainty bands and axis ranges.

Spatial correlation narrows uncertainty in the estimated profile.

Across 27 biopsies, the median within-biopsy reduction from Monte Carlo standard deviation to latent GP posterior standard deviation was 59.1%.

Interpretation. The comparison is between location-induced dose spread and uncertainty in the estimated underlying profile. It does not mean 59.1% less physical location error.

Cohort uncertainty comparison with a summary of kernel, residual and blocked-prediction checks.Cohort uncertainty comparison with a summary of kernel, residual and blocked-prediction checks. Shown: Cohort uncertainty.

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Cohort uncertainty comparison with a summary of kernel, residual and blocked-prediction checks.

What do the narrower bands describe?

Simulated dose spread describes how the assignment changes with position. The model instead estimates an underlying, or latent, dose profile using relationships between neighbouring positions.

Simulated and modelled dose standard deviations and their ratio along two biopsy cores.

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Simulated and modelled dose standard deviations and their ratio along two biopsy cores.

Check the modelling assumptions.

Compare covariance models and residual patterns alongside the earlier prediction tests.

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Residual mean versus SD for exponential, Matern 1.5, Matern 2.5 and RBF covariance kernels.

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Residual mean versus SD for exponential, Matern 1.5, Matern 2.5 and RBF covariance kernels.
Sensitivity analysis

Compare the assumptions.

Different covariance models describe how neighbouring positions relate. Similar-looking fits do not settle the choice: held-out prediction errors matter too.

Interpretation. Model choice combines these fit checks with held-out prediction tests.

Connect dose with tissue measurements.

Use the profiles to study tissue response in its dose context and support biopsy-level QA. Further evaluation needs independent observations, additional cohorts and checks on the assumed location uncertainties.

Research status. Internal prediction tests do not establish dose accuracy in living tissue or clinical benefit.

AAPM 2026 poster

Conference version of the study. Its 58.2% mean reduction and the paper's 59.1% median describe different summaries.

AAPM 2026 · Gaussian process dose modelling

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AAPM 2026 · Gaussian process dose modelling

Study resources

Medical Physics · 2026 · Published

Gaussian Process Regression of HDR Prostate Biopsy Dose for Improved Modelling of Localization-Induced Uncertainty

M. Muscat, J. Crook, A. Jirasek, J. Andrews, N. BeckerPublication link forthcoming

Research software

BiopsyContext dose mapping and biopsy-specific Gaussian process modelling.

The current BiopsyContext platform is developed privately, separate from these public research archives.