Monolithic crystal PET detectors need to be calibrated before they are put into service. Existing calibration methods usually collect an extensive dataset of reference events and estimate the position of γ photon interaction for individual detectors, which makes the calibration for a complete system lengthy and impractical. This work presents a whole-system calibration method for the first time in order to design a practical PET system with monolithic crystal detectors. The method forms the reference dataset by scanning a point source at different known locations, without the mechanical collimation. Then a likelihood model is built to describe the direct estimation of the line of response(LOR), instead of the position of γ photon interaction. To achieve the maximum likelihood we finally developed a deep learning network that encodes the charactistics of the entire system and creates a mapping from the pairwise distributions of scintillation photons to the LOR positions. Monte Carlo simulation shows that the proposed method estimates the position of γ photon interactions with a median positioning error of 0.36 mm in the x-y direction, and 0.17 mm in the depth of interaction, for a PET system with 50 mm × 50 mm × 15 mm monolithic crystals. Compared to other method, the direct LOR estimation has higher accuracy and precision. It is able to locate the incident γ photons without mechanical collimations; and more importantly, it calibrates the whole PET system simultaneously in a few hours; unlike other calibration method that take hours for each detector.

GoRock’s DSL offers a flexible, composable framework for PET (Positron Emission Tomography) data analysis and visualization, particularly geared toward efficient event filtering, coordinate transformation, and Line of Response (LOR) handling. By simplifying complex operations into modular functions, GoRock enables users to focus on high-level data insights with minimal code.

Data can be loaded into GoRock using pre-defined system data classes, making it straightforward to set up PET event samples for various experiments:

from hotpot.data_analysis import CachedSystemData

# Load PET data samples for different scenarios
sample_15mm = CachedSystemData('/path/to/data_15mm.csv')
sample_20mm = CachedSystemData('/path/to/data_20mm.csv')
sample_25mm = CachedSystemData('/path/to/data_25mm.csv')

GoRock allows comprehensive visualization of the PET system and Lines of Response (LORs). This feature enables users to graphically compare real, inferred, and estimated LORs, facilitating visual inspection of data quality and positional accuracy.

import plotly.graph_objects as go

# Filter LOR indices based on specific criteria
indices = sample_15mm.estimated_lor_positions[sample_15mm.predicted_local_positions > 7.5].index[:10]

# Visualize the PET system and various LORs in 3D
fig = go.Figure([
    *image_system.to_plotly(),  # System visualization
    *real_lor_positions[indices].to_plotly_segment(marker=dict(color='gold', size=3)),
    *inferred_lor_positions[indices].to_plotly_segment(marker=dict(color='blue', size=3)),
    *predicted_lor_positions[indices].to_plotly_segment(marker=dict(color='green', size=3)),
    sources[indices].to_plotly(marker=dict(size=4, color='red'))
])
fig.show()

To ensure the validity of PET event data, GoRock provides an efficient filtering mechanism for events with Depth of Interaction (DOI) values beyond acceptable thresholds. This helps in focusing analysis on in-range events only.

import numpy as np

# Filter events by DOI thresholds for each sample
out_of_bound_sample_15 = sample_15mm[np.logical_or(
    sample_15mm.predicted_local_positions > 7.5,
    sample_15mm.predicted_local_positions < -7.5
)]

out_of_bound_sample_20 = sample_20mm[np.logical_or(
    sample_20mm.predicted_local_positions > 10,
    sample_20mm.predicted_local_positions < -10
)]

out_of_bound_sample_25 = sample_25mm[np.logical_or(
    sample_25mm.predicted_local_positions > 12.5,
    sample_25mm.predicted_local_positions < -12.5
)]

Coordinate transformation between the PET detector's local and global coordinate systems is essential for accurate positioning and event comparison. GoRock makes this transformation straightforward, allowing seamless alignment of detected and inferred event coordinates.

import numpy as np

# Stack and sort LOR data in both local and global coordinates
sorted_lor_positions = np.sort(
    np.stack([
        sample.real_lor_local.hstack().y, 
        sample.predicted_lor_local.hstack().y
    ], axis=1), 
    axis=0
)

1. Composable Functions
   GoRock’s DSL is highly modular, allowing for straightforward combination of visualization, filtering, and transformation functions.

2. Streamlined Data Handling
   With tools for efficient data loading, event filtering, and DOI validation, GoRock minimizes processing overhead, focusing on essential data insights.

3. Integrated Visualization
   The DSL integrates with Plotly to enable interactive 3D plotting of PET systems and LORs, enhancing data interpretation through graphical insights.

For more advanced examples and additional functionalities, visit the GoRock GitHub repository.