Hepatic blood flow using [¹⁵O]H₂O and dynamic PET

[¹⁵O]H₂O bolus model

The analysis method of hepatic blood flow (actually perfusion) is based on one-tissue compartment model, modified to account for the dual input of the liver, consisting of hepatic artery and portal vein (Taniguchi et al., 1993, 1996a, and 1999; Kudomi et al., 2008; Slimani et al., 2008; Kiss et al., 2009; Rijzewijk et al., 2010). Although appropriate radiowater model for liver requires both inputs, it does not necessarily mean that the portal perfusion (f_PV) can be reliably quantified, especially in non-invasive studies where tracer concentration curve of portal vein is not measured but estimated in the model (Ziegler et al., 1996; Becker et al., 2005; Rijzewijk et al., 2010).

**Figure 1.** Compartmental model for radiowater in the liver.

Radiowater concentration in the volume of interest, as measured with PET, (C_PET(t)), is the volume fraction weighted sum of concentrations in the blood (C_B(t)) and liver tissue, (C_T(t)):

$C_{PET}(t) = (1 - V_B) \times C_{T}(t) + V_B \times C_{B}(t)$

Blood concentration is a weighted sum of concentrations in the arterial and portal blood (C_A and C_PV), with the arterial and portal blood flows (f_A and f_PV) as the weighting factors:

$C_{B}(t) = \frac{f_A C_{A}(t) + f_{PV} C_{PV}(t)}{f_A + f_{PV}}$

Since radiowater is an inert tracer with reversible kinetics, the concentration curve of the portal vein blood is assumed to be simply the arterial blood delayed and dispersed in the gastrointestinal tract (GI):

$C_{PV}(t) = k_{GI} C_{A}(t - \Delta t) \otimes e^{-k_{GI} t}$

Concentration of radiowater in the tissue is described with the one-tissue compartmental model with the two input functions; p is the partition coefficient of water in the tissue:

$\frac{dC_{T}(t)}{dt} = f_A \times C_{A}(t) + f_{PV} \times C_{PV}(t) \ - \frac{f_A + f_{PV}}{p} \times C_{T}(t)$

Based on this model, liver tissue data can be simulated using program sim_wliv.

If the impact of venous blood, including portal vein, on vascular volume fraction is ignored, that is, V_B is assumed to represent arterial blood volume only and marked with V_A, then a simple multilinear equation for estimating the model parameters:

$C_{PET}(T) = V_{A} C_{A}(T) + \left[ (1-V_{A})f_A + V_A k_2 \right] \int\limits_{0}^{T} C_{A}(t)dt \ + \left[ (1-V_{A})f_{PV} \right] \int\limits_{0}^{T} C_{PV}(t)dt \ - k_2 \int\limits_{0}^{T} C_{PET}(t)dt$

, where k₂=(f_A+f_PV)/p.

Liver tumours

In tumours of the liver, most of the blood is supplied by the portal artery (Breedis & Young, 1954; Ackerman, 1972). Therefore, perfusion in liver tumours can be analyzed using only the usual arterial input (Taniguchi et al., 1996b; Yamaguchi et al., 2000; Kunishima et al., 2002; Fukuda et al., 2004).

Steady-state approach should not be applied, because the partition coefficient of water in tumours is not known (Yamaguchi et al., 2000).

Arterial blood data

Blood data from on-line sampler

Arterial blood data, collected using on-line sampling system, must be calibrated and corrected for physical decay, dispersion, and time delay. It is recommended that regional tissue TAC from the liver is used in time delay correction.

Extraction of arterial blood data from PET image

Instead of using ABSS, arterial blood TAC can be extracted from the dynamic image. The procedure is very reliable if CT or MR images are available and the point spread function of PET image is known (full width at half maximum, FWHM, in mm). If no CT or MR images are available, then the program eabaort may need to be validated for the specific PET scanner. With modern PET scanners the image resolution is good enough for using the blood TAC from small ROI drawn into abdominal aorta without any correction for partial volume effect.

Delay correction may not be needed for arterial input that is extracted from abdominal aorta, but for the portal vein input estimation the delay is an important parameter.

Analysis method in TPC

Extracting the input function simultaneously with the model fitting is performed by N Kudomi using software written by him.

If arterial blood curve is available, then the model presented above can be used, and regional liver TTACs can be fitted using fit_wliv. However, the quality of PET data may not allow accurate estimation of all model parameters. Especially, the estimates for V_B have very high variability and do not affect the fitted curve, but introduce high variability to the other parameters (see an example in Figure 2). The dual-input in hepatic radiowater models is known to lead to problems with parameter identifiability (Becker et al., 2005). Therefore, V_B should be constrained to a fixed value, for example to 0; although the total blood volume in the liver is high, only the arterial fraction of blood from hepatic artery is kinetically distinguishable in radiowater data. Spleen data could be used to add information to the model (Taniguchi et al., 1999).

Radiowater model fitted to liver TTAC — **Figure 2.** Radiowater model was fitted using fit_wliv to liver TTAC (black) using as input function the blood TAC from ROI drawn on heart LV cavity (red). In this example *V_B* was either fixed to zero (blue) or left unconstrained. With both settings for the *V_B* similar fit quality was obtained, although the fitted *V_B* was 47%. With *V_B=0* the estimated model parameters were *f_A=0.82 mL/(min*mL)*, *f_PV=3.10 mL/(min*mL)*, *p=0.86 mL/mL*, *k_GI=1.26 min^-1*, and the delay time between LV cavity blood and liver was 13 s and the additional delay time in portal vein was 16 s.

Literature

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Fukuda K, Taniguchi H, Koh T, Kunishima S, Yamagishi H. Relationships between oxygen and glucose metabolism in human liver tumours: positron emission tomography using ¹⁵O and ¹⁸F-deoxyglucose. Nucl Med Commun. 2004; 25: 577-583. doi: 10.1097/01.mnm.0000126627.01919.1d.

Kiss J, Naum A, Kudomi N, Knuuti J, Iozzo P, Savunen T, Nuutila P. Non-invasive diagnosis of acute mesenteric ischaemia using PET. Eur J Nucl Med Mol Imaging 2009; 36: 1338-1345. doi: 10.1007/s00259-009-1094-0.

Kudomi N, Slimani L, Järvisalo MJ, Kiss J, Lautamäki R, Naum GA, Savunen T, Knuuti J, Iida H, Nuutila P, Iozzo P. Non-invasive estimation of hepatic blood perfusion from H₂¹⁵O PET images using tissue-derived arterial and portal input functions. Eur J Nucl Med Mol Imaging 2008; 35: 1899–1911. doi: 10.1007/s00259-008-0796-z.

Miyazaki S, Murase K, Yoshikawa T, Morimoto S, Ohno Y, Sugimura K. A quantitative method for estimating hepatic blood flow using a dual-input single-compartment model. Br J Radiol. 2008; 81(970): 790-800. doi: 10.1259/bjr/52166324.

Shiomi S, Iwata Y, Sasaki N, Morikawa H, Tamori A, Habu D, Takeda T, Nishiguchi S, Kuroki T, Ochi H. Assessment of hepatic blood flow by PET with¹⁵O water: correlation between per-rectal portal scintigraphy with⁹⁹Tc^m-pertechnate and scintigraphy with ⁹⁹Tc^m-GSA. Nucl Med Commun. 2000; 21: 533-538. doi: 10.1097/00006231-200006000-00006.

Slimani L, Kudomi N, Oikonen V, Järvisalo M, Kiss J, Naum A, Borra R, Viljanen A, Ferrannini E, Savunen T, Nuutila P, Iozzo P. Quantification of liver perfusion with [¹⁵O]H₂O-PET and its relationship with glucose metabolism and substrate levels. J Hepatol. 2008; 48: 974-982. doi: 10.1016/j.jhep.2008.01.029.

Taniguchi H, Kunishima S, Koh T. The reproducibility of independently measuring human regional hepatic arterial, portal and total hepatic blood flow using [¹⁵]water and positron emission tomography. Nucl Med Commun. 2003; 24: 497-501. doi: 10.1097/00006231-200305000-00003.

Winterdahl M, Keiding S, Sørensen M, Mortensen F, Viborg F, Alstrup AKO, Munk OL. Tracer input for kinetic modelling of liver physiology determined without sampling portal venous blood in pigs. Eur J Nucl Med Mol Imaging 2011; 38(2): 263-270. doi: 10.1007/s00259-010-1620-0.

Ziegler SI, Haberkorn U, Byrne H, Tong C, Schosser R, Krieter H, Kaja S, Richolt JA, Lammertsma AA, Price P. Measurement of liver blood flow using oxygen-15 labelled water and dynamic positron emission tomography: limitations of model description. Eur J Nucl Med. 1996; 23: 169-177. doi: 10.1007/BF01731841.

Tags: Perfusion, Radiowater, Liver

Updated at: 2023-03-25
Created at: 2015-02-04
Written by: Vesa Oikonen

Hepatic blood flow using [15O]H2O and dynamic PET

[15O]H2O bolus model