These methods are based on simply observing the MR signal changes that result from the passage of contrast agent through the liver parenchyma or liver tumor, but may not directly relate these to the contemporaneous change in the aorta or portal vein. Disease characterization is based on the fact that the perfused liver or tumor shows enhancement with the arrival of contrast agent and therefore perfusion can be estimated by the rate of tissue enhancement. Hence, most model-free approaches use parameters derived from the initial slope of the tissue signal intensity-time or contrast concentration-time curve (Figure 4).

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Figure 4 Schematic plot of gadolinium concentration-time curve in liver tissue obtained from a perfusion MRI study. The diagram illustrates how the maximum gradient for arterial perfusion (g_a) and portal perfusion (g_p) are derived (based on Miles et al[2]). Note that the peak splenic enhancement is used to define the transition between arterial and portal phase of liver parenchyma enhancement. The maximum slope after the peak splenic enhancement is used to define portal perfusion.

One semi-quantitative index that can be calculated using the model-free approach is the HPI. The HPI was first proposed by Miles et al[2]. HPI refers to the proportion of hepatic perfusion that is derived from the hepatic artery, and it can be calculated using the following formula: arterial perfusion/arterial perfusion + portal venous perfusion). Miles et al[2] have used the time to peak in the splenic enhancement curve to distinguish between the arterial and portal venous phases of the liver. Liver arterial perfusion is then estimated by the maximum slope in the liver enhancement curve before the splenic peak, divided by the peak aortic enhancement (Figure 4). Correspondingly, liver portal venous perfusion is estimated by dividing the maximum slope in the liver enhancement curve after the splenic peak by the peak aortic enhancement (Figure 4).

Blomley et al[3] have further refined calculation of portal venous perfusion by removing the contribution of the hepatic artery from the liver contrast concentration-time curve by subtracting from it a scaled splenic contrast concentration-time curve. This is because the spleen is predominantly supplied by the aorta and not by the portal vein. Using the arterially subtracted liver contrast concentration-time curve, the portal venous perfusion is estimated by dividing the maximum slope of the arterially subtracted liver curve by the peak portal enhancement. This more direct method of estimating portal vascular contribution has also been advocated by Tsushima et al[19]. However, liver arterial perfusion can be estimated in a similar way as proposed by Miles et al[2].

The key advantage of using model-free approaches is that they are relatively easy to derive and do not require complex computation.

Applying tracer kinetic modeling enables quantitative vascular information to be extracted from temporally sampled MRI data, when the passage of contrast medium through the liver parenchyma or tumor is observed over time. Generally, an assumption is made that the imaged voxel contains a supplying impermeable artery that leads to a permeable capillary that leaks tracer (gadolinium contrast) into the interstitial space (Figure 5). The tracer is cleared from the voxel via an impermeable vein. However, the vessels and the interstitial space are beyond the resolution of the MRI scanner to directly image. What is measured by the MRI scanner is the average concentration of the tracer at any one time (reflected by the measured signal intensity) within the image voxel, which changes as contrast medium courses through.

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Figure 5 Schematic diagram illustrating a dual-input dual-compartment tracer kinetic model. Dual blood supply carrying gadolinium contrast molecules (blue spheres) from the hepatic artery (F_A) and portal vein (F_PV) enters the hepatic sinusoids (intravascular space). From here, the contrast molecules can leak outwards into the Space of Disse (interstitial space). Using a dual-input, dual compartment tracer kinetic model allows the estimation of intravascular properties (e.g. blood flow, F), as well as characteristics of the interstitial space (e.g. PS).

Tracer kinetic modeling uses mathematical curve fitting to describe the tissue contrast concentration-time curves. If the contrast concentration-time curve of the vascular supply is known (arterial input function), subsequent mathematical operations by convolution or deconvolution allow quantitative vascular parameters to be derived that best fit the tumor or tissue contrast concentration-time curves. Such an approach could be applied to tumor and non-tumor tissues, although the mathematical and pathophysiological assumptions may be different for each. Using one particular kinetic model (e.g. distributed parameter model), quantitative parameters such as hepatic arterial flow, portal venous flow, fraction of total flow contributed by hepatic artery, capillary permeability-surface area product (PS), percentage of intravascular space (v₁), percentage of interstitial space (v₂), and mean transit time (MTT) are derived. However, depending on the mathematical model applied and physiological assumptions made, variants of such quantitative parameters are obtained. Hence, when applying tracer kinetic modeling to clinical studies, it is important to state the choice of kinetic model employed at the outset. Currently, there is no consensus as to which kinetic model is best suited to evaluate the liver, and development of an international consensus in this area would be welcomed.

It has been observed that a hypervascular tumor (usually a tumor with a larger vascular space relative to the interstitial space) shows a pattern of rapid arterial enhancement followed by washout, whereas a hypovascular tumor (usually a tumor with a larger interstitial space relative to the vascular space) shows progressive enhancement. These observations could also be explained by considering tracer kinetic modeling.

A hypervascular tumor is predominantly supplied directly by hepatic arterial neovessels. As the intravascular space is relatively larger than the interstitial space, the average concentration imaged by the voxel predominantly reflects changes in the intravascular space. In such lesions, there is rapid and strong enhancement in the arterial phase. However, in the equilibrium phase, the contrast redistributes to the interstitium and the rest of the body. This reduces the concentration of tracer in the tumor vascular space and is visualized as contrast wash-out within the voxel.

A hypovascular tumor may be supplied by the hepatic artery and the portal vein. As the interstitial space is relatively larger than the intravascular space, the averaged contrast medium concentration within the image voxel predominantly reflects changes in the interstitial space. Hence, there is faint enhancement in the arterial phase as contrast agent diffuses into the relatively large interstitial space. With continued blood flow in the portal venous phase, more contrast medium diffuses outwards and the concentration in the interstitium increases. In the equilibrium phase, although the tracer concentration in the vascular space has reduced due to redistribution to the rest of the body, it is still higher than the concentration in the tumor interstitium. Hence, there may even be a net efflux of contrast medium into the interstitium in the equilibrium phase, and such a tumor may demonstrate a pattern of progressive enhancement.

Clearly, the above explanations could be simplistic, as other measurement factors determine the degree of tumor enhancement. Nevertheless, these descriptions can help us to appreciate how the pathophysiological differences in different disease processes could account for their imaging behavior.

Several kinetic models are currently in use for the assessment of liver perfusion. A detailed mathematical analysis of these is beyond the scope of this review. Kinetic models applied to the liver vary according to the physiological assumptions made, and can broadly differ in the following ways.

Single-input vs dual-input: Single-input models assume that the vascular input is derived from the hepatic artery only, whereas dual-input models assume that the vascular input is derived from both the hepatic artery and the portal vein. Dual-input models are more physiological, although in tumors, where the blood supply in highly arterialized, assumption of a single vascular input may suffice to approximate the vascular behavior.

Single-compartment vs dual-compartment: Single compartment models assume that the contrast is confined to only one compartment (i.e. vascular space), whereas dual compartment models assume that there is dynamic distribution of contrast between two compartments (i.e. the vascular space and the interstitial space). Single-compartment models are computationally simpler and could be applied as an approximation for the normal liver, because the Space of Disse communicates freely with the sinusoids. Dual-compartment models are computationally more demanding but may give a better reflection of the microcirculation of the diseased liver, resulting from tumor or cirrhosis[4,20] (Figure 6).

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Figure 6 Schematic diagram illustrating the key difference between a single-compartment model (A) and a dual-compartment tracer kinetic model (B). Using a single-compartment model, only the vascular compartment is considered and kinetic properties related to this (e.g. blood flow, F) can be estimated. The behavior of the normal liver can be approximated by a single-compartment model. Using a dual-compartment model, kinetic properties that describe the interstitial space (e.g. PS) can be quantified in addition. In disease states (e.g. liver cirrhosis and tumors), the vascular behavior of these tissues are better described using a dual-compartment model.

Conventional compartment (CC) model vs distributed parameter (DP) model: In several kinetic models, the assumption is made that there is instantaneous mixing or equilibrium of the contrast medium along the entire course of a vessel. We term these as CC models. One example of a CC model is Toft’s model[21]. Another approach takes into account a concentration gradient within the vascular space. This approach is called the DP model. CC models are simpler to implement and computationally easier to solve but make more assumptions about the microcirculation. By comparison, DP models are more complex, which attempts to make fewer assumptions about the microcirculation, but are computationally more intensive and require higher temporal resolution data to derive meaningful results.

Derived microcirculatory parameters: Generally, dual compartment models are necessary to extract parameters that describe the interstitial space, e.g. v₂, PS and extraction fraction (EF) using the DP model; or extracellular extravascular volume using the Toft’s model. Such parameters cannot be derived using a single-compartment model. Single compartment models allow for estimates of blood flow, volume of distribution and mean transit time.

Clearly, the choice of the kinetic model depends on many factors including local expertise, available software to perform the perfusion analysis, understanding of the disease pathophysiology, MRI measurement technique applied, and the quality (spatial and temporal resolution) of the MRI data. At the time of writing, only a few commercial softwares are available to undertake such analyses, and many research groups are therefore reliant on self-scripted software for data evaluation. Not surprisingly, this has led to disparate efforts in developing analysis tools, which are often institution-specific and non-standardized. The lack of standardization in the methodologies applied for data analysis is an acknowledged issue by researchers in the field, and there is fortunately increasing international efforts towards the harmonization and standardization of imaging acquisition and data analysis. Such developments are paramount for the wider clinical adoption of the technique and institution-vendor partnerships are being developed to address such challenges.

Some of the kinetic modeling approaches that have been applied in the published literature are summarized in Table 2.

Model-free approach: Several studies have demonstrated the potential of perfusion imaging to detect changes in the liver of patients at risk of liver metastases. Totman et al[22] have shown that there is a difference in the portal perfusion index (PPI) between patients with and without cancer. Leggett et al[1] have observed that the HPI is elevated in patients with overt metastases compared with those without metastases. In another study, Tsushima et al[23] have found that the normal looking liver in a patient with liver metastases shows a reduction in the PPI, which suggests that there is potential for using liver perfusion studies to detect microscopic metastases. These cross-sectional imaging observations have been corroborated by nuclear scintigraphy studies[24,25]. Despite the reported relationship between high HPI and low PPI with increased likelihood of liver micrometastases in patients with cancer, few studies have had longitudinal follow-up to validate the subsequent development of macroscopic liver metastases. For example, in the study by Leggett et al[1], follow-up data were only available in eight patients, of which three who subsequently developed macroscopic liver metastases showed decreased portal perfusion. Although there is great potential to use liver perfusion studies to detect or predict microscopic liver metastases, more work involving longitudinal studies is required to establish its clinical role (Figure 7).

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Figure 7 A middle-aged man with colorectal liver metastases to the liver. A: T1-weighted axial MR image demonstrates a hypointense liver metastasis in the right liver lobe (arrow); B: HPI map (calculated by the method described by Miles et al[2]) overlaid on the T1-weighted image shows increased HPI within the metastasis, typical of malignant disease.

Meijerink et al[26] have found functional liver perfusion maps to be helpful supplements to the routine radiological diagnosis of liver metastases. Compared with routine four-phase CT, total-liver-volume CT perfusion studies with calculation of the HPI increased the sensitivity of metastases detection to 89.2% from 78.4% and specificity to 82.6% from 78.3%. Four out of a total of 37 metastases were detected with the help of perfusion maps. Perfusion CT maps increase the conspicuity of metastatic disease because of the increased perfusion at the tumor rims, which makes liver metastases appear larger, thus facilitating the detection of smaller lesions.

Model-based approach: There have been few studies using a model-based approach for evaluating liver metastases. Cuenod et al[27] have applied a dual-input single-compartment model in rats and have observed that the presence of micrometastases in an apparently macroscopically normal liver resulted in a 34% decrease in portal blood flow and a 25% increase in the MTT for blood to pass through the liver. The changes were similar for macrometastases but more marked.

Koh et al[20] have employed a dual-input dual-compartment DP model in three patients with liver metastases for a technical validation study. Using the particular model, they found that the normal liver had near zero interstitial space volume and PS (which may be explained by the large fenestrae allowing free contrast medium exchange between the Space of Disse and the liver sinusoids), and that liver metastases have a non-zero and finite interstitial space volume and PS. Using this quantitative technique, there is an increase in the arterial fraction (arterial flow/sum of arterial and portal flow) to the metastases, although the portal flow remains significant (Figure 8). These observations of the difference in kinetic modeling behavior between the normal liver and liver metastases are supported by histopathological observations reported by Liu and Matsui[12]. Thus, the dual-input dual-compartment DP model appears to have the potential to characterize microcirculatory pathophysiology but larger studies are required to confirm the initial findings.

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Figure 8 Parameteric maps of a patient with colorectal metastases derived from a dual-input, dual-compartment, DP tracer kinetic model. F (blood flow), α (arterial fraction, or % hepatic arterial flow from total hepatic blood flow), F_A (hepatic arterial blood flow), F_PV (hepatic portal venous blood flow), t₀ (contrast arrival time), t₁ (MTT), v₁ (fractional intravascular volume), v₂ (fractional interstitial volume), E (extraction fraction), PS (permeability-surface area product). Note that in the two liver metastases demonstrated (outlined in pink), the lesions were characterized by lower total blood flow, but higher arterial fraction and fractional interstitial volume.

Model-free approach: Abdullah et al[28] have studied the differences between colorectal metastases and HCC and have found no significant difference in HPI between the two malignant entities. However, there is an increase in arterial flow, portal flow, and total blood flow in HCC compared to colorectal metastases. The distribution volume is also observed to be higher in HCC.

Model-based approach: Fournier et al[29] have applied the dual-input single-compartment model in a rat HCC model and have found that HCC is characterized by higher arterial flow and lower portal flow.

Sahani et al[30] have employed a single-input dual-compartment DP model in patients with HCC and have found that blood flow, blood volume and PS are higher in well-differentiated HCC compared with moderately or poorly differentiated HCC, which suggests that such vascular quantification could yield information on tumor grade.

Koh et al[4] have used the dual-input dual-compartment DP model in four patients with HCC and have measured the fractional interstitial space and associated extravasation parameters (PS and extraction ratio). HCC is characterized by increased arterial flow, increased total blood flow, as well as early contrast agent arrival time. The early arrival of contrast agent is postulated to be related to arteriogenesis and direct tumor supply by branches of the hepatic artery. Tumor vascularity (fractional intravascular volume) was higher for two out of four patients. Portal venous flow decreased but remained significant. The derived microcirculatory parameters were supported by histopathological findings of arteriogenesis in HCC[15,31]. Together with other imaging modalities such as diffusion-weighted MRI, MR perfusion imaging has the potential to contribute significantly to the multi-parameteric functional assessment of the liver to improve the diagnosis and characterization of HCC[32].

Anti-angiogenic agents have emerged as a class of antitumor agents that target tumor vasculature. The rationale of anti-angiogenic therapy is based on the observation that tumors require new blood vessels for growth and survival. Based on the diffusion distances of oxygen and nutrients, tumor cells cannot survive if they are further than 2 mm from a blood vessel. Thus, effective anti-angiogenic therapy acts by depriving a growing tumor of its nutrients, and can thus curb the growth of the primary tumor as well as its metastasis.

However, current methods of assessing efficacy of chemotherapy, such as the Response Evaluation Criteria in Solid Tumors (RECIST), are based on observing a decrease in tumor size[33]. Effective anti-angiogenic therapy often manifests as lack of tumor growth rather than decrease in tumor size because the therapy is not cytotoxic. Hence, there is a need for a reliable response biomarker to assess the efficacy of such therapy.

The challenge for a reliable response biomarker holds true for HCC that is treated by local tumor ablation. Ablated tumor differs from viable tumor in its blood supply. Previous international consensus conferences have recommended that the RECIST criteria be modified for HCC to assess only the viable tumor[34-36]. Viable tumor is defined as tumor that shows enhancement in the arterial phase. Thus, MR perfusion imaging also has the potential to provide valuable functional information that can be used to distinguish viable tumor from necrosis in HCC[37].

Model-free approach: Wang et al[38] have analyzed the arterial uptake slope in MR liver perfusion studies of patients with HCC treated with thalidomide. They have found that there was a greater decrease in the peak enhancement, maximum enhancement, and slope of enhancement in patients without disease progression compared to those who progressed on treatment. Miyazaki et al[39] have applied HPI to assess the efficacy of anti-angiogenic therapy in patients with liver metastases and have found a median 15% decrease in HPI at 28 d after anti-angiogenic treatment in patients who responded to treatment. In another study, Meijerink et al[40] have evaluated liver HPI and have found that HPI decreased in liver tumor treated with combination anti-angiogenic therapy with AZD2171 and gefitinib. However, most of these studies involved relatively small numbers of patients, and more studies are therefore required to establish whether MR liver perfusion indices can serve as a reliable response biomarker for anti-angiogenic drug therapy.

Meijerink et al[41] also have evaluated HPI for assessing local recurrence in liver metastases treated with RFA. The authors have found that an increase in HPI parallels disease recurrence detection by ¹⁸fluorodeoxyglucose positron emission tomography.

Model-based approach: There are few published studies that have applied a model-based approach for the evaluation of treatment response in hepatic malignancy. Chen et al[42] have studied the effects of transarterial chemo-embolization using a dual-input dual-compartment DP model and have found that the hepatic arterial fraction, hepatic arterial perfusion, and hepatic blood volume are significantly reduced by effective embolization. These indices could also help to indicate the presence of viable tumor. The potential of using model-based approaches for assessing the effects of anti-angiogenic or antivascular treatment is currently being investigated (Figure 9).

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Figure 9 Parametric maps of efflux constant (Ktrans), extravascular extracellular space (Ve) and arterial perfusion fraction before (top row) and after (bottom row) anti-angiogenic therapy obtained using a dual-input, single-compartment, conventional compartment model (after Materne et al[46]). Note multiple metastases in the liver, which are largely hypovascular but show increased arterial perfusion at the edge of the lesions. The metastases also show moderate Ve. After treatment with anti-angiogenic drug, arterial perfusion is reduced at the tumor rims, also with a decrease in tumor Ve. The Ktrans in the left lobe of the liver is also decreased, which may reflect drug effects on microscopic disease.

Model-free approach: Increase in hepatic arterial perfusion and decrease in portal venous perfusion have been reported in perfusion scintigraphy studies in patients with liver cirrhosis[43]. Miles et al[2] and Blomley et al[3] also have found an increase in HPI and decreased PPI respectively in cirrhotic liver.

Model-based approach: Guan et al[44] have applied a dual-input dual-compartment DP model in rats treated with diethylnitrosamine. As diethylnitrosamine induces a continuum of hepatitis, hepatic fibrosis and eventually cirrhosis, a gradual increase in hepatic arterial flow and MTT are observed across these groups, accompanied by a corresponding gradual decrease in blood volume and blood flow.

Koh et al[4] have utilized a dual-input dual-compartment DP model and have found that cirrhotic livers return a measurable fractional interstitial space, whereas normal liver shows a near-zero fractional interstitial space. In another study, Hashimoto et al[5] have applied a dual-input dual-compartment DP model and have found that the hepatic arterial fraction increases with the extent of fibrosis and cirrhosis.

The use of a single-compartment kinetic model has also been found to be useful for the assessment of liver cirrhosis.

Annet et al[6] have investigated a dual-input single-compartment CC model and have found that the microcirculatory parameters derived from such a technique correlate with the severity of cirrhosis and portal pressure. The measured portal pressure, a reflection of the degree of portal hypertension, is correlated with the calculated portal fraction, portal perfusion and MTT. Furthermore, the severity of cirrhosis as assessed by Child-Pugh class has been found to correlate with portal fraction, portal perfusion, arterial perfusion and MTT. Cirrhotic livers have shown an increase in arterial perfusion, decrease in portal perfusion, decrease in total blood flow, and an increase in MTT.

These findings can be corroborated with other published studies. In an earlier study by Van Beers et al[7], a cutoff threshold of 22.6 s for the MTT in the liver enabled the diagnosis of liver cirrhosis to be made with a sensitivity and specificity of 81%. In another study, Hagiwara et al[8] have used a dual-input single-compartment CC model and have found that there was an increase in the arterial blood flow, arterial fraction, distribution volume, and MTT in patients with advanced hepatic fibrosis. Receiver operating curve analysis has shown that the MTT, distribution volume and arterial flow are good predictive parameters with an area under the receiver operating characteristic curves that ranges from 0.791 to 0.824, and reported sensitivity of 76.9%-84.6% and specificity of 71.4%-78.5%. Thus, MR liver perfusion appears to be a promising method for the non-invasive diagnosis of liver cirrhosis and for assessing the severity of the condition.