Regular polygon PET scanner geometry

This example shows how to create and visualize PET scanners where the LOR endpoints can be modeled as a stack of regular polygons.

import parallelproj.pet_scanners
import matplotlib.pyplot as plt

from array_utils import suggest_array_backend_and_device

# To use a specific backend and/or device, replace the None arguments, e.g.:
#   xp, dev = suggest_array_backend_and_device(backend="numpy", dev="cpu") or by setting xp and dev manually
xp, dev = suggest_array_backend_and_device(None, None)

Using array API: array_api_compat.torch, device: cpu

Define four different PET scanners with different geometries

RegularPolygonPETScannerGeometry can be used to create the geometry of PET scanners where the LOR endpoints can be modeled as a stack of regular polygons.

Here we create four different PET scanners with different geometries. Note that symmetry_axis can be used to define which of the three axis is used as the cylinder (symmetry) axis.

scanner1 = parallelproj.pet_scanners.RegularPolygonPETScannerGeometry(
    xp,
    dev,
    radius=65.0,
    num_sides=12,
    num_lor_endpoints_per_side=8,
    lor_spacing=4.0,
    ring_positions=xp.linspace(-4, 4, 3, device=dev),
    symmetry_axis=2,
)

scanner2 = parallelproj.pet_scanners.RegularPolygonPETScannerGeometry(
    xp,
    dev,
    radius=65.0,
    num_sides=12,
    num_lor_endpoints_per_side=8,
    lor_spacing=4.0,
    ring_positions=xp.linspace(-4, 4, 3, device=dev),
    symmetry_axis=1,
)

scanner3 = parallelproj.pet_scanners.RegularPolygonPETScannerGeometry(
    xp,
    dev,
    radius=400.0,
    num_sides=32,
    num_lor_endpoints_per_side=16,
    lor_spacing=4.3,
    ring_positions=xp.linspace(-70, 70, 36, device=dev),
    symmetry_axis=2,
)

scanner4 = parallelproj.pet_scanners.RegularPolygonPETScannerGeometry(
    xp,
    dev,
    radius=400.0,
    num_sides=32,
    num_lor_endpoints_per_side=16,
    lor_spacing=4.3,
    ring_positions=xp.linspace(-70, 70, 36, device=dev),
    symmetry_axis=0,
)

Obtaining world coordinates of LOR endpoints

RegularPolygonPETScannerGeometry.get_lor_endpoints() can be used to obtain the world coordinates of the LOR endpoints

# get the word coordinates of the 4th LOR endpoint in the 1st "ring" (polygon)
# and the 5th LOR endpoint in the 2nd "ring" (polygon)
print("scanner1")
print(
    scanner1.get_lor_endpoints(
        xp.asarray([0, 1], device=dev), xp.asarray([3, 4], device=dev)
    )
)
print("scanner2")
print(
    scanner2.get_lor_endpoints(
        xp.asarray([0, 1], device=dev), xp.asarray([3, 4], device=dev)
    )
)

scanner1
tensor([[-2., 65., -4.],
        [ 2., 65.,  0.]])
scanner2
tensor([[65., -4., -2.],
        [65.,  0.,  2.]])

Visualize the defined LOR endpoints

RegularPolygonPETScannerGeometry.show_lor_endpoints() can be used to visualize the defined LOR endpoints

fig = plt.figure(figsize=(8, 8), tight_layout=True)
ax1 = fig.add_subplot(221, projection="3d")
ax2 = fig.add_subplot(222, projection="3d")
ax3 = fig.add_subplot(223, projection="3d")
ax4 = fig.add_subplot(224, projection="3d")
scanner1.show_lor_endpoints(ax1)
scanner2.show_lor_endpoints(ax2)
scanner3.show_lor_endpoints(ax3)
scanner4.show_lor_endpoints(ax4)
fig.show()

Defining an open PET scanner geometry

The phis argument can be used to manually define the azimuthal angles of the polygon “sides”. This can be used to create open PET scanner geometries. Here we create an open geometry with 6 sides and 3 rings corresponding to a full geometry using 12 sides where 6 sides were removed.

open_scanner = parallelproj.pet_scanners.RegularPolygonPETScannerGeometry(
    xp,
    dev,
    radius=65.0,
    num_sides=6,
    num_lor_endpoints_per_side=8,
    lor_spacing=4.0,
    ring_positions=xp.linspace(-4, 4, 3),
    symmetry_axis=2,
    phis=(2 * xp.pi / 12) * xp.asarray([-1, 0, 1, 5, 6, 7], device=dev),
)

fig2 = plt.figure(figsize=(8, 8), tight_layout=True)
ax2a = fig2.add_subplot(111, projection="3d")
open_scanner.show_lor_endpoints(ax2a)
fig2.show()