Coincidence timing

MTBC mean time between coincidence (time)... 

Smith GE, McPhee KA 1987 Performance on a coincidence timing task correlates with intelligence. Intelligence 11 161-167... 

Wright MJ, Smith GA, Geffen GM, Geffen CB, Martin NG 2000 Genetic influence on the variance in coincidence timing and its covariance with IQ a twin study. Intelligence, in press... 

They differ from the kernels it (ti, ..., r ) of the Volterra series only by a faster signal decay with increasing time arguments [Bliil]. For coinciding time arguments the crosscorrelation function is the sum of the n-dimensional impulse-response function h with the impulse-response functions hm of lower orders m < n. The stochastic impulse-response functions h are the kernels of an expansion of the system response y(t) similar to the Volterra series (4.2.4) but with functionals orthogonalized for white-noise excitation x t) [Bliil, Marl, Leel, Schl], This expansion is known by the name Wiener series, and the h are referred to as Wiener kernels. 

More recently, D. Emin [24] developed an altemative analysis of activated hopping by introducing the concept of coincidence. The turmeling of an electron from one site to the next occurs when the energy state of the second site coincides with that of the first one. Such a coincidence is insured by the thermal deformations of the lattice. By comparing the lifetime of such a coincidence and the electron transit time, one can identify two classes of hopping processes. If the coincidence time is much larger than the transit time, the jump is adiabatic the electron has time to follow the lattice deformations. In the reverse case, the jump is non-adiabatic. 

Figure 3.1. (a) True coincidence events (b) Random coincidence events detected by two detectors connected in coincidence along the dotted line. The two 511-keV photons originated from different positron annihilations, (c) Scattered coincidence events. Two scattered photons with little loss of energy originating from two annihilation events may fall within PHA window and also within coincidence time window to be detected as a coincidence event by two detectors. 

A PET study begins with the injection or inhalation of a radiotracer, followed by scanning. When the radiotracer decays, it emits a positron that travels a short distance and annihilates with an electron (Eig. 5.1). Annihilation produces two 511-keV photons, which propagate at approximately 180° apart These photons can be detected within a short time window called the coincidence time window (-10 ns). Many such events are summed to provide the distribution of the radiotracer. Radio-tracer transport, washout and retention can be monitored by PET and, if cah-brated, the PET images can yield quantitative estimates of the amount of radiotracer... 

The detection rate in the start detector is r the detection rate in the stop detector The probability that the stop detector detects a photon in the coincidence time interval, At, after a start photon is = r At. Therefore the coincidence rate is... 

FIGURE 4.4 Schematic diagram of a coincidence time-of-flight mass spectrometer. In contrast to current TDCs, the TPHC is a single-stop device that outputs pulses, whose amplitudes are proportional to flight times and are assigned to an appropriate channel by a PHA. 

Thus the standard error of is larger than V(Tj, j) and increases with the rate of random events. Any procedure that reduces randoms, such as better shielding of extraneous radiation or reduction in the coincidence time window (Eqn [4]), will lower this uncertainty. The resultant standard error is conventionally described by the noise equivalent count (NEC) which is defined as follows. The fractional error of is V(T,ot + 2R)/T,<,r If a number (NEC) of hypothetical counts are collected (free of background) the fractional error is (VNEC)/NEC = 1/VNEC. Equating this to the fractional error of gives... 

Aj = number of photons left unscattered after distance T along the LOR = original number of photons c = speed of light Eq, Ef= initial and final energy of scattered photon f= fraction of FOV subtended by the object Wg = rest mass of the electron N = total number of counts (trues) = number of resolution elements = number of unscattered photons at x P = number of prompt events r = detector radius R = number of random events, detector ring radius S = total number of scattered events t = detector width (axial thickness) T = distance along LOR, coincidence time window ... 

Vi. Correction of random and scattered coincidences. Random coincidences can be corrected by two simple procedures. One is by using the delayed coincidence measurement with the same time window and the other, mentioned earlier, is by estimating random coincidences using Eq. (34). As stated above, random coincidences can be reduced either by minimizing the coincidence time window or by reducing the activity. 

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