Parametrization of the 511 kev respond in BGO/ LSO Crystals with respect to Spatial Resolution in PETR/CT Scans

Transcription

1 Univerity of Tenneee, Knoxville Trace: Tenneee Reearch and Creative Exchange Univerity of Tenneee Honor Thei Project Univerity of Tenneee Honor Program Parametrization of the 511 kev repond in BGO/ LSO Crytal ith repect to Spatial Reolution in PETR/CT Scan Daniel Chadick Mitchell Univerity of Tenneee - Knoxville Follo thi and additional ork at: Recommended Citation Mitchell, Daniel Chadick, "Parametrization of the 511 kev repond in BGO/LSO Crytal ith repect to Spatial Reolution in PETR/CT Scan" (2005). Univerity of Tenneee Honor Thei Project. Thi i brought to you for free and open acce by the Univerity of Tenneee Honor Program at Trace: Tenneee Reearch and Creative Exchange. It ha been accepted for incluion in Univerity of Tenneee Honor Thei Project by an authorized adminitrator of Trace: Tenneee Reearch and Creative Exchange. For more information, pleae contact trace@utk.edu.

2 Preliminary Report on Progre Chad Mitchell June 14, 2004 Focu: The procedure and figure contained herein ignify an attempt to quantify the noie equivalent count rate (NECR) performance of a particular poitron emiion tomography (PET) canner, argued againt the increaing eight of the patient canned. Progreion: The data collected fall into four et. Both phantom and patient data ere collected, a count per econd, uing to et of detection crytal (?pre-pico (LSD),?pico(?)). The phantom data acquired i baed upon the National Electrical Manufacturer Aociation tandard of performance, and ill be referred to a NEMA data. The NEMA data a the firt to be evaluated. Theory tate that the data acquired hould follo the general equation: T() = an ft() (1) R() pn. S2 f{) (2) Where T() ignifie the rate of true occurrence, R() ignifie the rate of random occurrence, a i a patient-related attenuation contant, p i a canner-related attenuation contant, :f( ) and ft () are lifetime fraction, and i the count rate detected. When plotted, the NEMA data appear a: NEMA True, prepico NEMA True, pico J. 2OOCOO.. 100CXXl y",u0219x R''''1. =- 700CXXl 6OOOJO 6OOOJO 400CXXl OOCOO 100CXXl -100CXXl O COOOOOO OOOOOlO 35OOOIlOO -100CXXl 1C1OCJ1XlOO OO OO 4CXlOOOOO OO IlEMA Random, prepico IlEMA Random, pico y = 1 E-09x R2 = y = 1 E-09x R2 = 1-2D0llWb E E+14 1E E+-15 2E E+-15 quared

3 Thee graph alo ho a linear regreion line through the firt fe point of the graph. Thi repreent the expected trend neglecting the decay factor naturally preent. The lope of thi expected trend correpond to the an and ~N for the NEMA data. Alo, the point at hich thi line croe the -axi repreent an intrinic count rate aociated ith the crytal in the detector itelf. For the reported true, thi i eaily een. For random, the intrinic count hould be (or be very cloe to) zero. Thi implie only random occurrence in the abence of a ource, hich i logically accurate. After finding an and ~N, thee parameter are ued to plot graph of the lifetime fraction. A imple rearranging of equation 1 and 2, coupled ith experimental data for value of true and random at given rate, allo one to derive a governing equation in the intereting range of value (-J Million - ~45 Million count). ft(), pre pico ft(), pico 0, , ~ 0,9 0,88 0, y '" x R2 = E 0,92 0, , , , o E+07 1,2E E+07 1,6E+07 0, ,.---.,.----,----,----, , o fr(), prepico fr(). pica 1,10E E+00.. g ,50E-01.; 8, j QEQ1-1 E a: Baed on the trend for thi particular detector, the equation can be approximated ftnn() = e (3) ftnp() = -6.22e (4) fnn() = 8e-17 S2-1 e (5) fnp() = 3e-17 S2-5e (6) The notation i of the form rj\), here i = (T)rue/(R)andom, j (N)EMAI(P)atient, and k (N)on-pico/(P)ico. No a general equation can be contructed for the occurrence of true and random. Since the equation for lifetime fraction are a function independent of the patient, they can be conidered the an1e function hen applying thee form to the patient data. Thi i very ueful, a the patient data only contain one data point for each bed poition (poition 3 ill be the only one ued). The attempt ill be to extract a curve by back-calculating and fitting a conitent curve to the provided data point.

4 Patient data can no be evaluated given a ingle point for the count rate, the number of true and random occurrence detected, the intrinic count rate of the detector, and the lifetime fraction. By extracting the (l' and ~P', a trend can be etablihed baed on patient eight: up TP() (7) ( - Sintrinic) ft () The reult of thee equation: Alpha VI eight, prepico Alpha VS. eight, pico 0,03 0,025 0,02 ~ 0, y = -4E-05x + 0,0292 ~ :: ~ 0, y = -3E-05x ~ '.'.,~ 0~1--~--~--~--~--~--~~ , eight,lb Alpha v. eight -- normalied to NEMA tandard - _ 0.8 c Co ti prepico pied '-Linear (prepico), - Linear (pico) 0.2 O+-----~------~------~----~------~----~------~ o t

5 Beta v. eight, prepico Beta v. eight, pico E E E a. = li 1.4E ,. ::::~~: E E E-09 1.lE E ~.. ~ ~ r-----r---, o eight,lb By thee graph, one can ee the trend in eight dependence for up. Hoever, pp ho very little change. Thi upport the idea that p i a machine-dependent contant, and ill not change ubtantially ith each patient. The equation for up and value for pp are: u PN ~ e-5 -(lb) (9) upp ~ e-5 -(lb) (10) ppn ~ E-09 (11) ppp ~ E-09 (12) Having acquired thee value, the equation for T() and R() for the patient become analytical. The bae are in experimental data, but ith no dependence on any factor except for theoretical count rate and eight. From thee equation, the peudo-necr (PNECR) curve can be calculated for a given patient eight. PNECR T P ()2 (13) [TP() + RP() ] The folloing graph ho a PNECR urface repreentation of eight beteen zero and 350 pound, at a count rate of 0 to 25 million count for pre-pico data, and 0 to 45 million count for pico data: 2E7 2.5E7 Surface vie, pre-pico 350 Surface vie, pico

6 o 40000~r"T"TTT"T'T1rrrrT'"'l"TTT"I"I'"1r"T"TTT"'T'T'T""""""T"T"T'i:;:r- S o o PNECR Max, pre-pico (at peak) PNECR Max, pico (at peak) Full trend, pre-pico Full trend, pico By differentiating thee equation, ith repect to rate, and etting it to zero, one can find a maximum for PNECR given all eight and rate. All olution et of thi equation give valid data for patient trial, ith validation of aumption. A urface repreentation of thi, ith the olid plane being all zeroe poible:

7 o. o. Ske urface, pre-pico 2.5E o. Ske urface, pica o o Planar interection, pre-pi co Planar interection, pica

8 A et of NECR curve can alo be calculated from the Excel data uing the catter fraction meaured from each individual patient. The maximum of thee can be determined and charted: Max NECR v. eight, pre-pice y = x Max NECR v. eight, pico y = x c:: u c::!i\! ~ z '" ~ '" co ::E eight, Ib eight,lb Aumption: Many aumption are required for the analyi of thi data. Much of the data i conidered to be formulaic, and the reult of any trend or pattern are conidered full and correct in the range of interet. NEMA data i taken to be true and beyond quetion. Patient data i aumed to be uniform, ith no difference except for eight. Thi include, but i not limited to, variation in: height, muculature, cardiovacular and overall health, recent meal, recent exertion, ite of interet, time elaped beteen injection and can, and hair color. Any and all contant are treated ith exactne or a an average value determined through peronal judgment baed upon data. All equation ere preerved fully until implementation, ith no dropping of extraneou term or reduction of order.

9 Concluion: Surpriingly, the data doe not agree ith the current convention. A patient eight increae, a reduction in radioactive tracer provide a better pacial reolution, rather than an increae in radiation. Thi reduce the random count to a manageable amount, and the background radiation ceae to overpoer the active true reading. Preumably, an increae in time i a more reaonable olution than an increae in doage.