Time delay

Although the shape of radioactivity concentration curve is similar in all arteries (if dispersion is corrected), the measured radioactivity peak seems to arrive at different times in the tissue (PET) and in the blood samples, because of sample tubing and different distance and blood velocity in different arteries (Figure 1). This difference in tracer appearance times in blood (ATB) is sometimes small and can be ignored in the analysis of PET data. However, compartmental model analysis does not provide good fit unless delay correction is applied, even if delay time is only few seconds. If the first-pass extraction of the radiotracer is high, delay time must be accounted for to avoid biases. This is especially important in case of PET perfusion radiotracers such as radiowater (Herscovitch et al., 1983; Baron et al., 1989).

Blood curve is delayed and dispersed during its passage in arteries — **Figure 1.** After intravenous bolus infusion, venous blood that contains the radiotracer travels to the heart and lungs, causing delay and dispersion. When leaving from the left ventricle of the heart (black), radiotracer is well-mixed into the pumped blood volume, so that blood with similar concentration of radiotracer is distributed into the whole arterial network. Depending on the diameter and length of the arteries, blood TAC is more dispersed and delayed; short distance and high blood flow into the brain causes less dispersion and delay (red) than in the radial artery which is common blood sampling site (blue). Sampling apparatus may cause additional dispersion and delay to the measured blood TAC (green).
To retrieve correct input function for the brain, the measured blood TAC must be corrected for the delay and dispersion to match the blood TAC in the arteries of the brain.

Delay in input function is dependent on the distance and blood flow — **Figure 1.** After intravenous bolus infusion, venous blood that contains the radiotracer travels to the heart and lungs, causing delay and dispersion. When leaving from the left ventricle of the heart (black), radiotracer is well-mixed into the pumped blood volume, so that blood with similar concentration of radiotracer is distributed into the whole arterial network. Depending on the diameter and length of the arteries, blood TAC is more dispersed and delayed; short distance and high blood flow into the brain causes less dispersion and delay (red) than in the radial artery which is common blood sampling site (blue). Sampling apparatus may cause additional dispersion and delay to the measured blood TAC (green).
To retrieve correct input function for the brain, the measured blood TAC must be corrected for the delay and dispersion to match the blood TAC in the arteries of the brain.

Delay time can be slightly different in different parts of the same organ. Precise quantification may require pixel-by-pixel delay correction, as has been shown to be the case in brain studies of patients with unilateral arterial steno-occlusive lesions (Islam et al., 2017).

Notice that radiotracer often appears in the region of interest earlier than it appears in the measured blood or plasma curve, because of longer arterial distance to the blood sampling site. After time delay correction the arterial blood curve should start ascending 1-3 s before the tissue curve.

Time delay correction

Delay is usually estimated by fitting compartmental model to the initial phases of the data repeatedly with a range of time-shifted input curves, and selecting the delay time that provides the best fit (Iida et al., 1988). Linearization of the model will make this process fast (van den Hoff et al., 1993). A range of fixed blood volume can additionally used to increase reliability of the result (Kimura et al., 2004). Previously used slope method for estimating delay time is not as accurate as the fitting method (Iida et al., 1988; Meyer, 1989). Leading edge method, with pre-set trigger threshold of peak activity, is computationally very fast, and provides better results in whole body PET studies than no delay correction at all (Li et al., 2022).

In theory, Dispersion correction should be done before delay time correction, or simultaneously (Meyer, 1989), by adding delay and dispersion as additional parameter in compartmental model fitting (Meyer, 1989). However, blood volume and dispersion cannot be estimated independently. This can be utilized in time delay correction: dispersion actually does not affect the estimated delay time between input function and tissue curve, because vascular volume fraction accounts for the dispersion (Mourik et al., 2008). The time delay from left ventricular cavity of the heart to a peripheral artery correlates with the dispersion time constant between these sites (Iida et al., 1989); when arterial input function is derived from the PET image, this relationship could be used to correct the input function for dispersion at the region of interest.

What data do we need?

For delay correction, corrected blood curve measured using on-line detector and PET count rate curve (*.cr) are normally used.

It may be possible to use manually sampled blood or plasma curve instead of on-line detector data, if manual samples have been taken at 10-15 s intervals (at max), and the initial increasing phase of the curve contains several sampling points.

Also, the count rate curve can be replaced with regional TACs (see below) or "head curve", an average TAC from the dynamic image or sinogram made with imghead, if PET time frames are short enough (10-15 s or less) in the beginning of the PET scan.

Count rate curve must not be used in certain cases

If the heart, lungs or aorta is inside the PET image volume (or even close to it in 3D studies, in which the spill-over artefacts may be significant), then the use of count rate or head curve is discouraged: In the heart and large arteries the initial radioactivity concentration is relatively high and appears considerably sooner than in the tissue of interest. This may cause a bias of a few seconds in the estimated delay time. For example in perfusion studies of renal cortex and tumours in oral cavity, a region-of-interest TAC should be used in the delay time correction in place of count-rate curve.

Software

In most cases, the time delay correction is included in the ABSS data pre-processing scripts. Alternatively, certain model analysis software makes automatically or optionally also the time delay correction, for example fit_h2o.

If you need to do the time delay correction by yourself, you can use fitdelay. However, different radiopharmaceuticals may require specific settings for this program to work reliably.

In all cases, you must always visually check that time delay correction was successful!

If time delay is known from elsewhere, e.g. by visual inspection, the time delay can be corrected using tactime.

If it does not work

The most common reasons for failure in automatic delay correction are:

Outlier (very high value) in the beginning of the on-line detector curve; find and remove the outlier manually in a text editor or by using blozero.
Steady background before the appearance of actual tracer; remove the background using dftrmbkg, tacslope, or taccalc.
Initial bump in the count rate curve, sometimes caused by approaching injection syringe; set the values manually to zero.
The curves have different time units; check by looking at the first (time) column in the data files, and correct using tacunit.
Manual input curve has too few samples during the radioactivity build-up phase.
Old count rate or blood datafile does not contain sample times; check by looking at the datafile, and add the time column using addtimes.

Note that the failure is not always obvious, but is only seen as biased results, unless you check the correction by plotting fitted input curve and tissue curve together.

Do it only after metabolite correction

The fractions of authentic radiopharmaceutical and metabolites are measured at sample times that are relative to the sample times of the total plasma or blood curve. Therefore, the metabolite correction must be made before the sample times of plasma or blood curve are changed. Delay time could however be estimated from uncorrected data, since only the initial phase of it is used.

If you use fitdelay to make the delay correction, you can correct all plasma and blood curves belonging to the same study by entering the file names to the end of the command line.

Literature

Iida H, Higano S, Tomura N, Shishido F, Kanno I, Miura S, Murakami M, Takahashi K, Sasaki H, Uemura K. Evaluation of regional difference of tracer appearance time in cerebral tissues using [¹⁵O]water and dynamic positron emission tomography. J Cereb Blood Flow Metab. 1988; 8: 285-288. doi: 10.1038/jcbfm.1988.60.

Iida H, Kanno I, Miura S, Murakami M, Takahashi K, Uemura K. Error analysis of a quantitative cerebral blood flow measurement using H₂¹⁵O autoradiography and positron emission tomography, with respect to the dispersion of the input function. J Cereb Blood Flow Metab. 1986; 6: 536-545. doi: 10.1038/jcbfm.1986.99.

Islam MM, Tsujikawa T, Mori T, Kiyono Y, Okazawa H. Pixel-by-pixel precise delay correction for measurement of cerebral hemodynamic parameters in H₂¹⁵O PET study. Ann Nucl Med. 2017; 31: 283-294. doi: 10.1007/s12149-017-1156-5.

Kudomi N, Maeda Y, Sasakawa Y, Monden T, Yamamoto Y, Kawai N, Iida H, Nishiyama Y. Imaging of the appearance time of cerebral blood using [¹⁵O]H₂O PET for the computation of correct CBF. EJNMMI Res. 2013; 3(1): 41. doi: 10.1186/2191-219X-3-41.

Meyer E. Simultaneous correction for tracer arrival delay and dispersion in CBF measurements by the H₂¹⁵O autoradiographic method and dynamic PET. J Nucl Med. 1989; 30:1069-1078.

van den Hoff J, Burchert W, Müller-Schauenburg W, Meyer G-J, Hundeshagen H. Accurate local blood flow measurements with dynamic PET: fast determination of input function delay and dispersion by multilinear minimization. J Nucl Med. 1993; 34:1770-1777.

Tags: Input function, BTAC, PTAC, Delay correction, Dispersion, Countrate

Updated at: 2023-09-18
Written by: Vesa Oikonen