Gaussian Process Regression of HDR Prostate Biopsy Dose for Improved Modelling of Localization Induced Uncertainty
Abstract
Purpose
To develop a Gaussian process regression (GPR) framework that treats along-core HDR prostate brachytherapy dose as a spatially correlated signal, in order to denoise voxel-level dose and dose-uncertainty summaries used for Monte Carlo biopsy dose quality assurance and future dose-biology analyses.
Methods
We analysed 27 MR-US guided targeted biopsies from 15 HDR monotherapy patients. Each core was reconstructed as 1 mm voxels on the clinical HDR dose grid. For each biopsy we estimated an along-core semivariogram and fit a stationary covariance model to infer correlation length and noise variance, then used these parameters in a one-dimensional GPR model to smooth voxel dose and its standard deviation along the core. We compared nominal versus GPR-smoothed voxel means and standard deviations across the cohort and summarised percent reductions in voxel-wise and along-core integrated standard deviation.
Results
Cohort semivariograms yielded median along-core correlation lengths of about 17 mm, indicating that dose is strongly correlated within one to two centimetres. GPR had minimal impact on voxel mean dose but systematically reduced voxel standard deviations by about 60 percent on average, with interquartile ranges of roughly plus or minus 5 percent. The integrated standard deviation along each core was reduced by about 35 percent on median. These gains were most pronounced in steep gradient regions, where nominal per-voxel standard deviations were largest.
Conclusion
Modelling HDR biopsy dose as a correlated one-dimensional process and applying GPR smoothing produces more stable and physically plausible estimates of voxel dose uncertainty without biasing mean dose. Embedding this layer upstream of Monte Carlo localization propagation should sharpen biopsy-level robustness estimates and increase statistical power for dose-response and biomarker studies built on MR-US guided prostate biopsies.