# Arterial input function from PET image

Absolute quantitative PET studies require that the input function (IF), representing cumulative availability of the radiotracer in arterial plasma (AIF), is measured. Traditionally this is achieved via arterial cannulation. Image-derived input function (IDIF) is a noninvasive alternative to arterial blood sampling, but also associated with several problems that must be solved and methods well validated before using in clinical studies (Asselin et al., 2004; Zanotti-Fregonara et al., 2011; Christensen et al., 2014). IDIF can only be implemented with a minority of PET radiopharmaceuticals, and even then some blood samples usually need to be taken (Zanotti-Fregonara et al., 2011), unless some other form of calibration is possible (Christensen et al., 2014; Zanotti-Fregonara et al., 2014). Injection catheter can be used for venous blood sampling at late times (Hoekstra et al., 2000). Numerous research publications contain validation of a specific IDIF method for a specific study protocol, but the methods rarely have been applicable in other study protocols or research institutes without laborious revalidation.

Arterial blood curve (BTAC) is relatively easy to measure from heart cavities and ascending and descenting aorta because of their large size in humans (Henze et al., 1983; Weinberg et al., 1988; Gambhir et al., 1989; Ohtake et al., 1991; van der Weerdt et al, 2001; de Geus-Oei et al., 2006; Horsager et al., 2015), if those are visible in PET image. Geometrical model has been commonly used to account for the spillover effects in the heart. Quality control of LV cavity derived BTACs should be performed to prevent large errors (Hoekstra et al., 1999). Probably the most successful application is the method for quantification of myocardial perfusion using [15O]H2O (Iida et al., 1991 and 1992). When heart is not in the field of imaging, other large arterial blood pools that can be used to estimate arterial blood curve are abdominal aorta (Ohtake et al., 1991; Germano et al, 1992), femoral arteries (Lüdemann et al, 2006; Croteau et al., 2010), and common iliac arteries (Schiepers et al., 2008; Cho et al., 2010). Image reconstruction method may affect the quality of the IDIF; OS-EM can reduce noise, but cause bias, when compared to FBP (Feng et al., 2015).

If a region which could be used to extract decent AIF does not fit into the FOV of the PET scanner, a common practice in clinical PET studies is to first position the subject so that heart is in the FOV, and after the arterial peak has passed (usually after 10-20 min), bed is moved and the late scan of the region of interest is started; the initial BTAC is measured from small ROI placed in LV cavity of the heart, and it is combined with venous samples withdrawn during the late scan (Eary & Mankoff, 1998). With very short-lived radionuclides and standardized injection protocols, a repeated PET study can be performed, scanning first the heart for the input, and then the region of interest, using the input function from the first scan either directly or after scaling (Tolbod et al., 2018). In a more advanced (and expensive) setting, another PET scanner could be used to scan for example heart at the same time as the tissue uptake is measured for example in the brain (Iida et al., 1998). Also wrist scanners have been studied with the aim of noninvasive measurement of arterial blood curve from the radial artery (Aykac et al., 2001; Shokouhi et al., 2003; Kriplani et al., 2007a, 2007b).

Suboptimal reconstruction methods may lead to substantial bias in estimated IDIF (Boellaard et al., 2001). Arterial inflammation, for example in chronic kidney disease, may lead to IDIF overestimation, if the radiopharmaceutical is avidly taken up by inflammatory cells (for example [18F]FDG) or arterial calcifications (for example [18F]F-).

IDIF methods at their best can provide the arterial blood curve, which for most radiopharmaceuticals need to be further converted to plasma curve and corrected for circulating label-carrying metabolites (Nahmias et al., 2000; Mourik et al., 2009).

## Carotid artery

In brain PET studies the blood curve is estimated from carotid arteries or other intra-cranial blood vessels, but because of large partial volume effect and proximity of large veins the results may be poor and require a few blood samples for calibration. Different approaches like factor analysis, non-negative matrix factorization (Kim et al., 2001), independent component analysis (ICA) (Naganawa et al., 2005; Chen et al., 2007), cluster analysis, and applying MRI (Fung et al., 2010; Fung & Carson, 2013; Iguchi et al., 2013; Su et al., 2013; Lyoo et al., 2014; Mabrouk et al., 2014; Simončič & Zanotti-Fregonara, 2015; Jochimsen et al., 2016; Khalighi et al., 2018; Kang et al., 2018) have been used to overcome these problems. Patient motion must be minimal or corrected for (Mourik et al., 2011). Hahn et al 2012 have proposed using linear discriminant analysis (LDA) to delineate vessels from the image. Integrated PET-MRI allows MR angiography for segmenting the carotid arteries and monitoring subject movement (Islam et al., 2017; Su et al., 2017; Sundar et al., 2019).

Mean diameters of internal carotid artery and common carotid artery are 5.11±0.87 mm and 6.52±0.98 mm in men, and 4.66±0.78 mm and 6.10±0.80 mm in women (Krejza et al., 2006). Croteau et al (2010) measured carotid diameter from CT image, and used phantom based recovery coefficient and spill-in factors to correct carotid blood curves. Similar approach was used by Feng et al (2012).

Schain et al. (2013) identified the voxels belonging to the carotid by computation of the Pearson product-moment correlation coefficient between a seeding region and voxels in a larger region (excluding voxels in the seeding region). First, coordinates of the highest local maximum are automatically extracted from time frame where the carotids are most clearly visible. Coordinates are provided to the MATITK Connected Threshold Segmentation method to obtain a seeding region. Seeding region is dilated to obtain the subset mask. The final voxels contributing to the IDIF are extracted using the Pearson correlation method. The extracted curve is then scaled to blood radioactivity using blood samples (Bahri MA et al., 2017), or geometric transfer matrix approach (Bastin et al., 2020) which has been used for partial volume correction (Rousset et al., 1998).

## Small animals

IDIF methods in small-animal studies are especially important, because reliable and frequent blood sampling may not be possible (Laforest et al., 2005). Heart cavity and vena cava (Yee et al., 2005; Moerman et al., 2011; Lanz et al., 2014; MacAskill et al., 2019) can be used, if appropriately validated. Vena cava is problematic, if radiopharmaceutical was injected into tail vein. In FDG mice studies, about 2 min p.i., vena cava provides more reliable AIF than heart cavity (Thorn et al., 2013; Thackeray et al., 2015). Blood samples taken from the tail or femoral artery could be combined with initial data from the LV cavity (Shoghi & Welch, 2007; Wong et al., 2011). Initial BTAC from LV cavity could also be combined with scaled TAC of the liver (Tantawy & Peterson, 2010).

Thresholding has been used to generate ROI in the lumen of the left ventricle of the heart in mice PET studies (Verhaeghe et al., 2018). Clustering methods can be helpful in automating IDIF estimation from mice PET images (Zheng et al., 2011). Integrated PET-MRI helps to perform partial volume correction for mouse heart (Evans et al., 2015). Factor analysis of rat or mouse heart can separate the TACs of myocardium and blood (Wu et al., 1996; Laforest et al., 2005; Herrero et al., 2006; Kim et al., 2006). Modelling of the combined kinetic information from myocardial muscle and LV cavity is another option to extract the input function (Fang & Muzic Jr, 2008; Kudomi et al., 2011; Xiong et al, 2012; Li et al., 2015). Gated PET imaging (Locke et al., 2011; Mabrouk et al., 2012; Zhong & Kundu et al., 2013a and 2013b; Evans et al., 2015) can improve the separation of myocardial muscle from the cavity.

Kinetics of urine radioactivity in the whole bladder can be used in deriving input function in FDG PET studies (Wong et al., 2008, 2013).

### The liver

Perfusion in the liver is high, and blood-to-hepatocyte transfer is practically unlimited for most radioligands; therefore radioactivity concentration in the liver follows relatively well the BTAC. [18F]FDG concentration in the liver has been suggested to be an suitable substitute for BTAC in small animal studies (Green et al., 1998; Yu et al., 2009; Tantawy & Peterson, 2010) and even in diagnostic PET (Torizuka et al., 1995).

## Effect of time frames

After bolus administration of the radioligand, the radioactivity concentration in the arterial blood changes rapidly. To accurately follow the kinetics of the input_function, blood sampling should be frequent in the initial phase of the study. Compartmental model fitting is reliable only when the kinetics of the input function and tissue data are accurately measured. However, the in vivo measurement of radioactivity requires relatively long time frames to achieve sufficient count statistics. The longer the time frames, the less kinetic information can be collected, but the measured concentrations are less noisy.

As the peak of the input curve is usually very sharp (on purpose), it seems to be flattened when measured as an average during PET frames. The effect is pronounced when the peak time is divided between two adjacent time frames, in comparison to when the peak resides mostly during a single time frame:

Unlike compartmental models, graphical analysis methods, such as Patlak plot, are not affected by long time frames, if frame durations are taken into account in calculation of the AUCs.

Detecting the position of the blood vessel in the image is usually (depending on the radiopharmaceutical) only possible right after the administration, at the time of the blood peak. Towards the end of the study, the activity concentration in the surrounding tissue reaches and often exceeds the activity in the vessel. Therefore the detection of the blood vessel may not be possible from late PET scans. Even in dynamic scan, if the initial time frames are long, the blood peak may not be visible in the image data. Additionally, the obtained blood TAC may look like the peak was missed (Figure 2), while the AUCs of the TAC may still be correct and usable in Patlak plot.

## Simple techniques

### Locating the artery in the dynamic image

Summing of only the first few frames of the dynamic image reveals the position of large arteries. Locating the arterial VOI can be automated by calculating for each pixel the difference between mean activity during first few minutes and during the end frames, and then finding a fixed-sized VOI where this value is at its maximum (Backes et al., 2009).

Seeded region growing and cluster analysis have also been used to identify arterial VOIs (Liptrot et al., 2004; Mourik et al., 2008). Pairwise correlations between image voxels can be used to identify pixels with similar kinetics (Schain et al., 2013).

### Correcting vessel activity for PVE

VOI drawn on a small vessel contains activity of blood and surrounding tissue (background) because of the partial volume effect (PVE). If VOI is small, then part of the blood activity is spread outside of the VOI, but if VOI is large, then we can assume that no blood activity is spread outside of it. In that case, the activity concentration in the VOI is the weighted sum of arterial and background concentrations (CA and Cbg, respectively)

, where the weighting factor fv is the fractional volume of the vessel inside the VOI. Backes et al (2009) assumed for [18F]FLT that the ratio of background-to-arterial concentration can be described by exponential function with rate constant k:

, and thus the true arterial concentration could be calculated from equation (Backes et al., 2009):

Hackett et al (2013) tested this and other models for the background concentration, and, with [18F]FLT, reversible one-tissue compartment model gave the lowest AICc:

Additionally, they noted that arterial blood TAC could be well fitted with a seven-parameter function. The model that consists of the two compartmental model parameters and seven function parameters was then fitted to the TAC of the carotid ROI. Objective function contained also difference between estimated and measured blood activity at 1-3 sampling points; at least two blood samples were needed to get a good IDIF (Hackett et al., 2013).

## Alternative methods to retrieve model input from image data

Model-based input function is based on the assumption that the input function is common to all tissue regions in the image, and can be solved from the data.

Population-based input function (PBIF) is based on the individual scaling of a radiopharmaceutical- and population-specific input curve (Zanotti-Fregonara et al, 2013). For example injected dose and subject mass can be used in scaling, or a venous blood sample.

Reference tissue input models have been developed to replace arterial plasma input with a reference tissue, when available.

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Updated at: 2020-01-30
Created at: 2010-03-14
Written by: Vesa Oikonen