Analytic derivation of pinhole collimation sensitivity for a general source model using spherical harmonics.
Pinhole collimators are widely used for single photon emission computed tomography (SPECT) imaging of small organs and animals. There has also been renewed interest in using pinhole arrays for clinical cardiac SPECT imaging to achieve high sensitivity and complete data sampling. Overall sensitivity of a pinhole array is critical in determining a system's performance. Conventionally, a point source model has been used to evaluate the sensitivity and optimize the system design. This model is simple but far from realistic. This work addresses the use of more realistic source models to assess the sensitivity performance of pinhole collimation. We have derived an analytical formula for pinhole collimation sensitivity with a general source distribution model using spherical harmonics. As special cases of this general model, we provided the pinhole sensitivity formulae for line, disk and sphere sources. These results show that the point source model is just the zeroth-order approximation of the other source models. The point source model overestimates or underestimates the sensitivity relative to the more realistic model. The sphere source model yields the same sensitivity as a point source located at the center of the sphere when attenuation is not taken into account. In the presence of attenuation, the average path length of emitted gamma rays is 3/4 of the radius of the sphere source. The calculated sensitivities based on these formulae show good agreement with separate Monte Carlo simulations in simple cases. The general and special sensitivity formulae derived here can be useful for the design and optimization of SPECT systems that utilize pinhole collimators.
Li
Yu-Sheng
YS
Department of Diagnostic Radiology, Rush University Medical Center, Chicago, IL 60612, USA. Yusheng_Li@rush.edu
Oldendick
James E
JE
Chang
Wei
W
D000388:Air; D007091:Image Processing, Computer-Assisted; D008962:Models, Theoretical; D009010:Monte Carlo Method; D015899:Tomography, Emission-Computed, Single-Photon / Q000295:instrumentation*; D014867:Water
D014867:Water
J Nucl Med. 2006 Apr;47(4):595-602
16595492
IEEE Trans Nucl Sci. 2009 Oct 6;56(5):2659-2671
23885129
IEEE Trans Med Imaging. 2001 Aug;20(8):730-41
11513024
J Nucl Med. 2006 Nov;47(11):1884-90
17079823
Phys Med Biol. 1967 Oct;12(4):489-500
6061848
Phys Med Biol. 2004 Oct 7;49(19):4543-61
15552416
Phys Med Biol. 2006 Oct 7;51(19):4923-50
16985279
Phys Med Biol. 2009 Jan 21;54(2):207-25
19088387
Phys Med Biol. 1963 Jun;8:165-82
13932556
Phys Med Biol. 2005 Nov 21;50(22):R45-61
16264248
Phys Med Biol. 1994 Mar;39(3):425-37
15551591
Phys Med Biol. 2004 Oct 7;49(19):4579-92
15552418
Med Phys. 2006 Apr;33(4):997-1004
16696476
IEEE Trans Med Imaging. 2002 Aug;21(8):878-87
12472261
Med Phys. 1997 Nov;24(11):1701-9
9394277
Phys Med Biol. 2005 Oct 7;50(19):4609-24
16177493
J Nucl Med Technol. 2008 Dec;36(4):207-12
19008286
Phys Med Biol. 2009 Mar 21;54(6):1469-82
19218734
J Nucl Med. 2008 Jul;49(7):1080-9
18552149
IEEE Trans Med Imaging. 2004 Jun;23(6):750-63
15191149
Phys Med Biol. 2007 May 7;52(9):2567-81
17440253
Eur J Nucl Med Mol Imaging. 2007 Feb;34(2):151-61
17143647
J Nucl Med. 1994 Feb;35(2):342-8
8295008