Dual blood supply to the liver

Quantitative studies of the liver are complicated by its dual input function. Blood supply from hepatic artery has the same tracer concentration as all other arteries, with very sharp curve peak in case of bolus administration of the tracer. However, most of the blood supply to the liver comes via portal vein; tracer is first distributed to the intestines, spleen, pancreas, and gallbladder, and as a result the concentration peak is dispersed, delayed, and possibly affected by the metabolic processes in the splanchnic organs: depending on the tracer, AUC and/or the fraction of label-carrying metabolites may be different in arterial blood and portal vein.

Since the tracer concentration in hepatic aorta is the same as in any artery, it can be measured as usual, but concentration in portal vein cannot be sampled noninvasively, and not at all in human studies. Small size and respiratory movement make it difficult to retrieve portal vein concentration reliably from dynamic PET image; in human [¹¹C]palmitate study both arterial and portal input could be derived from the image (Gormsen et al., 2018).

In animal studies samples can be taken also from the portal vein. Blood flow (mL/min) in hepatic aorta (f_HA) and portal vein (f_PV) can be measured noninvasively (although not very precisely) using Doppler ultrasound method. Dual input function for liver can then be calculated as blood flow weighted average of arterial, C_A, and portal vein, C_PV, concentration curves (Brix et al., 2001; Munk et al., 2001; Iozzo et al., 2007; Keiding, 2012):

${C}_{dual}(t) = \frac{f_{HA}}{f_{HA}+f_{PV}} C_A(t) + \frac{f_{PV}}{f_{HA}+f_{PV}} C_{PV}(t)$

Program liverinp can be used to combine C_A(t) and C_PV(t) using the previous equation.

The fraction of flow via portal vein in dogs has been estimated to be 0.65-0.85 and in sheep ∼0.8 (Katz & Bergman, 1969). In rats, the portal vein fraction has been estimated to be 0.72±0.05 (Fleming et al., 1981). In rabbits the fraction was ∼0.79, as measured using microspheres (Materne et al., 2000). In pigs, ultrasound method has given fractions 0.83±0.03 (Iozzo et al., 2007), and 0.7, with range 0.6-0.9 (Winterdahl et al., 2012). In humans, CT-based assessment provided portal vein fraction 0.83 for healthy liver and 0.58 for liver tumours (Ng et al., 2012).

In human studies, the obvious approach has been to ignore the input via portal vein, and either validate that the results still are correct (Chen et al., 1991), or accept that the obtained results may be biased but correlate well with the physiological parameter of interest (Choi et al., 1994).

A more challenging approach is to estimate the portal vein concentration curve based on the arterial input by including additional compartment(s) and/or dispersion and delay parameters to the model (Choi et al., 1994; Taniguchi et al., 1996; Ziegler et al., 1996; Chen et al., 2004a and 2004b; Kudomi et al., 2008). Whole-body recirculatory model has been developed for [¹³N]NH₄⁺ and its metabolites in artery and portal vein (Weiss et al., 2002).

Classical n-compartmental model approximation for the delayed response is the one-parameter, transit-time model (DiStefano III, 2013, p 192), with transfer function

$h(t) = \frac{\beta^{n-1}}{(\beta + t)^{n}}$

and Munk et al (2003) applied the 2-compartmental model (n=2) for estimating the portal vein concentration:

$\begin{align*} &{C}_{PV}(t) = \int_{0}^{t} h(t-\tau) C_A(\tau) d\tau \\ &\text{, where} \\ &h(t) = \frac{\beta}{(\beta + t)^2} \end{align*}$

The discretely sampled arterial data and the impulse-response function, h(t), need to be interpolated to even sample times and sampling durations for calculation of the convolution integral. The value of each interpolated sample must represent the mean value during the (short) Δt: in practise this means that arterial data should be interpolated to the midpoint of the even intervals, and since the response function is an integrable function, its definite integral during Δt, divided by Δt, should be used. Resulting convolution integral on the other hand should be scaled by Δt; thus Δt is cancelled out. Thus, the response function values at time points T can be calculated from equation:

$\int_{T - \frac{\Delta t}{2}}^{T + \frac{\Delta t}{2}} (\frac{\beta}{(\beta + t)^{2}}) dt = \frac{\beta \times \Delta t}{(\beta + T - \frac{\Delta t}{2})(\beta + T + \frac{\Delta t}{2})}$

Program liverpv can be used for computing portal vein curve from arterial curve using these equations. Winterdahl et al (2011) measured the β values in pigs for [¹⁸F]FDG (0.50 min), [¹⁵O]H₂O (2.17 min), [¹⁵O]CO (0.10 min), [¹⁸F]FDGal (0.82 min), and [¹¹C]methylglucose (0.57 min). Later, β value in pigs has been determined for [¹¹C]CSar (13 s) (Sørensen et al., 2016).

measured and simulated PV in Pig 1 — **Figure 1.** Arterial and portal vein BTACs were measured using ABSS in pig studies after bolus infusion of radiowater (Kudomi et al., 2009); this figure shows the measured arterial (black) and portal (red) BTACs in 14 pigs, and the portal vein BTAC simulated using the impulse-response model (blue) by Munk et al. (2003) using *β=2.17 min* as reported by Winterdahl et al (2011).

measured and simulated PV in Pig 2 — **Figure 1.** Arterial and portal vein BTACs were measured using ABSS in pig studies after bolus infusion of radiowater (Kudomi et al., 2009); this figure shows the measured arterial (black) and portal (red) BTACs in 14 pigs, and the portal vein BTAC simulated using the impulse-response model (blue) by Munk et al. (2003) using *β=2.17 min* as reported by Winterdahl et al (2011).

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Tags: Liver, Dual-input, Portal vein, Transit time, Simulation

Updated at: 2022-02-21
Created at: 2015-02-05
Written by: Vesa Oikonen

Dual blood supply to the liver

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Literature