Determination of the Attenuation Map in Emission Tomography

(A) Narrow-beam attenuation as function of source depth in cylindric water phantom for photons of different energies of interest in nuclear medicine imaging. Lower energy photons suffer more attenuation than higher energy photons for any given source depth. (B) Same as A for 140 keV and different attenuating media. Lung tissue allows greater transmission, soft tissue allows intermediate amount of transmission, and bone allows least transmission for equal tissue thicknesses. Source depth is not useful parameter in coincidence imaging. Therefore, curves shown reflect singles detection.

Illustration of reconstruction artifacts resulting from lack of attenuation correction for uniform distribution of activity in cylindric phantom. (A) Reconstructed image without attenuation correction. (B) Uniform attenuation map. (C) Same slice as in A after applying attenuation correction. Note loss of activity at center of cylinder on noncorrected image (A) and recovery of uniform activity distribution after attenuation correction (C).

Acquisition geometry illustrates attenuated radon transform showing original 2D attenuation map μ(x,y) and activity distribution f(x,y), and 1D projection data p(s,φ), reflecting photon attenuation and activity distribution in patient, and projection data recorded in 1 view of imaging detector, respectively. P denotes projection operator.

(A) Principle of FBP reconstruction algorithm. Activity distribution is recovered from measured projection data in 2 steps: filtering—projections are filtered by ramp filter; then—backprojection—contribution to image volume of each of filtered projections is computed. (B) Iterative approach is based on process of matching measured projections to calculated projections. Calculated projections are determined from initial reconstruction and are compared with measured data. Difference between 2 datasets is used to correct calculated projections. Procedure is repeated until some predefined error level has been reached.

Illustration of main differences between attenuation correction schemes for SPECT and PET on transmission image in thorax region of patient. (A) In SPECT, most widely used algorithm on commercial systems calculates attenuation factor e^−μa(e^{(−∫₀aμ(x)dx)} for nonuniform attenuating media) for all projection angles and assigns average attenuation factor to each point within object along all rays. Procedure can be repeated iteratively and adapted to nonuniform attenuating media. (B) In PET, attenuation correction factors are independent of location of emission point on LOR and are therefore given directly by factor e^−μ(a+b)(e^{(−∫₀a+bμ(x)dx)} for nonuniform attenuating media) for each projection.

Different configurations of transmission scanning geometries for SPECT. (A) Sheet source. (B) Scanning line source. (C) Fixed line source and converging collimation. (D) Point or line source and asymmetric fanbeam collimation. (E) Multiple line sources where source size is proportional to relative activity of source. (F) Point source and septal penetration of parallel collimation.

Different configurations of transmission scanning geometries for hybrid SPECT/PET cameras. (A) Symmetric point source and fanbeam geometry that truncate imaged object. (B) Offset point source covering entire field of view where flux of radiation includes center of rotation for sampling to be complete. (C) Two scanning point sources translating axially and located far enough to side so that flux of radiation does not include center of rotation. Truncation is avoided by lateral movement of bed and 360° rotation. (D) Multiple point sources inserted between existing septa and placed along line parallel to axis of rotation near edge of 1 camera. Septa provide axial collimation for sources so that transmission system operates in 2D offset fanbeam geometry.

Different configurations of transmission scanning geometries for PET. (A) Ring sources of positron-emitting radionuclide measuring transmission in coincidence mode. (B) Rotating positron-emitting rods measuring transmission in coincidence mode. (C) Single-photon source producing coincidence events between known source position and photons detected on opposing side of detector ring. (D) Fixed positron-emitting rod (left) or single-photon (right) sources on rotating, partial-ring scanner.

Illustration of fuzzy clustering segmentation algorithm on clinical whole-body study at thorax level. (A) Reconstructed image from low-statistics transmission scanning. (B) Corresponding segmented transmission image into 3 clusters to extract specific areas of differing attenuation such as air, lungs, and soft tissue. (C) Final attenuation map obtained by assigning known attenuation coefficients and weighted averaging and adding-up high-quality transmission image of scanner bed obtained from high-statistics scan. (Reprinted with permission of (88).)

Illustration of improvement in image quality using segmented attenuation correction. (A) Reconstructions using measured attenuation correction. (B) Reconstructions using fuzzy clustering-based segmented attenuation correction. Note that images reconstructed with segmented attenuation correction are less noisy and show more uniform uptake of tracer. (Reprinted with permission of (88).)

SPECT image of patient with neuroblastoma using ¹³¹I-metaiodobenzylguanidine (¹³¹I-MIBG). (Left) Images reconstructed with FBP and with iterative ML-EM reconstruction including attenuation correction (AC) and both attenuation correction and correction for collimator response (AC + Collim.). (Right) Correlated CT scan in same anatomic region (CT), functional image (SPECT), and fused images show radionuclide image superimposed in color on correlated CT scan (Fused). (Reprinted with permission of (130).)

FBP reconstructions without attenuation correction of clinical 3D brain PET images presented in different planes. Noncorrected image tends to depress reconstructed activity at center of brain.