Evaluation of Hepatic Fibrosis with Portal Pressure Gradient in Rats

Abstract

MRI has the potential of providing a noninvasive assessment of liver pathology. This work introduces a portal pressure gradient (PPG) model derived from fluid mechanics, where the PPG is proportional to the average velocity and inversely proportional to the vessel area in the upper part of portal vein. Using a phase-contrast spoiled gradient echo sequence, the PPG model was verified in a phantom study and was tested in an animal study using 35 rats with various degrees of hepatic fibrosis induced by carbon tetrachloride (CCl₄). Histological examination was conducted to determine the severity of hepatic fibrosis. The fibrosis score monotonically increased with the duration of CCl₄ treatment. The PPG was highly correlated with nonzero fibrosis scores (r² = 0.90, P < 0.05). There was a significant difference between control and cirrhosis groups (P < 0.0006, α < 0.0018). The difference between control and fibrosis (noncirrhosis) groups (P < 0.002, α < 0.006) was also significant. Without the administration of any contrast agent, the MRI-PPG approach shows promise as a noninvasive means of evaluating liver fibrosis.

Chronic liver injury induces liver fibrosis and its endpoint, liver cirrhosis, is one of the leading causes of morbidity and mortality worldwide (1). Liver fibrosis occurs as a consequence of the increased accumulation of hepatic extracellular matrix (ECM) in response to various liver injuries (2). The accumulated ECM generates the capillarization of sinusoids (3), which are specialized capillaries in the liver with low-pressure channels formed by the plates of hepatocytes, and decreases the permeability of channels in hepatic microcirculation (4), which in turn raises the resistance to the portal venous flow. Thus, a hemodynamic pressure gradient change occurs in the portal vein (PV) when liver fibrosis occurs.

The current gold standard for staging liver fibrosis is the histopathological analysis of biopsy samples, but this approach is invasive and has several limitations, including sampling errors and risks of complications such as bleeding and infection (5). It is also inappropriate for longitudinal assessment of the liver status, which is of particular concern in evaluating the response to antifibrosis drug therapy.

A hepatic venous pressure gradient (HVPG) method has previously been proposed as an alternative for evaluating liver cirrhosis and portal hypertension. This method involves measuring the difference between sinusoidal pressure and intraabdominal pressure with a balloon catheter positioned in the hepatic vein (6). The procedure is less invasive than the direct measurement of portal venous pressure, but there is still an emerging need to develop a noninvasive imaging method for a safe and reliable assessment of liver fibrosis.

MRI has already shown utility in the detection of liver pathology (7). It permits imaging of the whole liver within a breathhold with flexible image contrast characteristics (8). Unlike CT, MRI involves no ionizing radiation exposure. Published data has also shown that MRI-measured hepatic flow parameters are more accurate than Doppler ultrasonography (9). In terms of assessing liver fibrosis noninvasively, magnetic resonance elastography (MRE) has shown promise by measuring the elasticity of the liver tissue using the displacement induced by mechanical waves, and a linear correlation between liver stiffness and fibrosis extent has been revealed in an animal model (21). MRE is also performed in patients with chronic liver disease with validated accuracy and high sensitivity (22,23). The quantification of hepatic perfusion parameters with dynamic contrast-enhanced MRI (DCE-MRI) and the assessment of hepatic fat content with MR spectroscopy, Dixon and IDEAL, also show promise in both animal and human work (10,37,38). This study investigated the utility of a portal pressure gradient (PPG) model based on fluid mechanics in combination with MRI to assess liver fibrosis noninvasively. Using phase contrast MRI (PC-MRI), the PPG was measured in rats with various degrees of hepatic fibrosis and the results were compared with the histological data.

THEORY

The complicated, highly nonlinear Navier Stokes equation in fluid mechanics can be simplified to Poiseuille flow when the flow is laminar, steady state, and fully developed (11). A fully developed flow region is where the boundary layer merges at the centerline and viscous effects extend to the entire cross-section so that the velocity profile no longer changes with increasing distance. The velocity profile is parabolic for laminar, steady-state, fully developed flow and the pressure gradient in the direction of flow satisfies the following equation:

$$\frac{dp}{dx}=v/\left(\pi R^3\right)\cdot \left(8\mu \pi \right)=8\mu \pi \left(\frac{v}{A}\right)$$ [1]

where μ is the dynamic viscosity of the fluid and can be assumed to be a constant in general, v is the average flow velocity, and A is the cross-sectional area of the vessel. For the phantom study, μ = 1.002 × 10⁻³ N · s/m² (water at 20°C) (11); for the animal study, μ = 3.5 × 10⁻³ N · s/m² (rat blood at 37°C) (24,25).

For the internal tube flow, if the dimensionless Reynolds number, which can be interpreted as the ratio of the inertial and viscous forces (Re = ρvD/μ, where ρ is the density of the fluid; D is the diameter of the tube), is below 2300, then the flow is laminar (11). If dv/dt = 0 (the flow velocity does not change with the time), then the flow is steady-state. If dv/dx = 0 (the velocity profile does not change along the flow direction), then the flow is fully developed.

Equation [1] is the PPG model, where the PPG is a constant multiplied by (v/A) for the laminar, steady-state, and fully developed flow. Since v and A can be obtained using PC-MRI (12–14), the PPG value can be achieved noninvasively.

MATERIALS AND METHODS

All MRI experiments were performed on a 1.5 T Siemens Sonata Imaging System (Erlangen, Germany) using a phased-array wrist coil (4 channels, USA Instruments, Aurora, OH). A single slice was identified perpendicular to the flow direction by referring to the coronal, sagittal, and transverse scout images acquired using trueFISP. A Siemens FLASH phase contrast sequence (fl_pc) was applied to obtain the velocity and area measurement (see details below). A three-point phase unwrapping method (15) was applied in order to increase the velocity-to-noise ratio (VNR), where three interleaved velocity encoding (Venc) gradients rather than the usual two were used: 0, a low Venc for high sensitivity, and a high Venc that is larger than the maximum velocity to aid in unwrapping the phase.

For the data analysis process, complex raw data were obtained and both the magnitude and phase images were reconstructed (32) using a three-point phase unwrapping algorithm (15) written in MatLab (MathWorks, Natick, MA). The vessel area A was measured from the magnitude image. The pixel-by-pixel velocity v_i was obtained from the phase image and the average velocity v was obtained using v = (Σv_i · A_i)/(N · A_i), where A_i was the area of each pixel, and N was the number of the pixels within the vessel area. The pressure gradient was represented by calculating (v/A) using the PPG model.

Phantom Study

The phantom study had two purposes: 1) to validate the accuracy, repeatability, and sensitivity of the velocity and area measurement using PC-MRI; and 2) to verify the PPG model quantitatively.

The phantom consisted of a plastic tube (8-mm or 6-mm inner diameter with 1-mm wall thickness), a peristaltic pump (Omega Engineering, Stamford, CT), a flow meter (King Instrument, Garden Grove, CA; accuracy ±2%) and a water reservoir (Fig. 1). We measured the volume rate (Q) using the flow meter and the mean flow velocity (v) was calculated using the volume rate divided by the tube area (A): v = Q/A. Two catheters were inserted to measure the pressure invasively, the distance between which was much larger than the hydrodynamic entry length (11) so that the disturbance they introduced to the system could be ignored.

FIG. 1.

Graph shows the setup of the phantom.

Since the average velocity was one-half of the maximum velocity in Poiseuille flow (11) and the average flow velocity was 5–24 cm/s, the maximum velocity ranged from 10 to 48 cm/s. Therefore, the low/high Venc was chosen as 10/50 cm/s. For the purpose of maximizing the signal, the flip angle was chosen to equal the Ernst angle (16), which was ≈15° in both the phantom and animal studies. In order to minimize the phase error, TE was set to 11 ms and the corresponding shortest TR was 61 ms. The field of view (FOV) was 128 × 128 mm² and the matrix size was 256 × 256, yielding an in-plane resolution of 0.5 × 0.5 mm². There were more than seven pixels along the diameter of the tube to reduce the partial volume error within the tube (17). Other scan parameters were: NEX = 3, slice thickness = 5 mm, and total scan time ≈25 sec.

The velocity measurement was repeated five times with the same scan parameters to check the repeatability. To study the sensitivity of slice selection, a tilt slice was chosen 5–30° off the perpendicular direction. In order to cross-check the accuracy of velocity measurement using PC-MRI, the average velocity was also measured through the flow-meter. In order to cross-check the pressure gradient measurement to verify the PPG model, the pressure gradient was also obtained by calculating (p1-p2)/Δx, where p1 and p2 were measured through mechanical pressure sensors and Δx was the distance between the two sensors.

Animal Study

The animal research protocol was approved by the local Institutional Animal Care and Use Committee. A total of 35 male Wistar rats (Charles River Laboratories, Wilmington, MA) were studied. Among them, eight were control and 27 were treated with intraperitoneal (IP) injection with carbon tetrachloride (CCl₄) mixed with vegetable oil (25 microl CCl₄+150 microl oil, Fisher Scientific, Pitts-burgh, PA) at a frequency of three times per week for 2–16 weeks to induce hepatic fibrosis (19). There were n = 6 rats treated for 2–3 weeks, n = 12 treated for 6–8 weeks, n = 9 treated for 11–16 weeks. Other data on these rats have been previously published (37).

The rats underwent MRI 1–2 days after the last dose of CCl₄ treatment. All the rats were anesthetized by subcutaneous injection of ketamine (80 mg/kg; Fort Dodge Animal Health, Fort Dodge, IA) plus xylazine (10 mg/kg; J. A. Webster, Sterling, VA) prior to MRI examination. In order to minimize the prandial effect to assure the portal venous flow was nonpulsatile and steady-state, the food was removed from the rats’ cage 2 hr before the MRI scan (20).

During MRI scanning a single slice was selected perpendicular to the upper part of the PV by referring to the coronal, sagittal, and transverse scout images acquired using trueFISP (one example shown in Fig. 4a). The landmark region within which the slice was prescribed had a length of ≈10 mm and was located above the entrance of the splenic vein in the upper part of PV. The portal venous flow in this region satisfied the laminar, steady-state, and fully developed conditions, such that the PPG could be calculated by measuring the average portal venous flow velocity v and the vessel area A.

FIG. 4.

a: The sagittal view of a rat: the liver, PV, and inferior vena cava (IVC) are clearly shown; the landmark was the upper part of PV (≈10 mm), where the flow satisfied the laminar, steady-state, and fully developed conditions. A single slice was chosen perpendicular to PV within the landmark. b: The reconstructed magnitude image where the vessel area was measured. c: The reconstructed phase image using the three-point phase unwrapping method where the velocity was measured. The IVC and PV were bright and the aorta was dark, which meant the flow direction was opposite to each other.

The fl_pc sequence that was optimized in the phantom study was used in rats: TR/TE = 45/9.7 ms, flip angle = 15°, FOV ≈120 × 120 mm² (512 × 512 matrix), NEX = 12, Venc = 10/50 cm/s, total scan time ≈5 min, slice thickness = 2.6 mm. Magnitude and phase images were reconstructed from raw data as shown in Fig. 4b,c.

Immediately after MRI the rats were sacrificed via IV injection of a supersaturated solution of potassium chloride and the liver samples of the rats were collected and stained with Masson’s trichrome to quantify the collagen content. A semiquantitative fibrosis score ranging from 0–5 was assigned to each rat according to the amount of collagen deposition: 0 (normal, absent of collagen deposition), 1 (minimal, <10% collagen), 2 (mild, 10–20% collagen), 3 (moderate, 20–30% collagen), 4 (marked, 30–40% collagen), and 5 (severe, >40% collagen). The livers were also evaluated for cirrhosis if there were nodular regeneration, bridging fibrosis, and diffuse involvement in the samples.

Rats were categorized for statistical analysis by weeks of CCl₄ treatment and further classified according to their fibrosis scores. The rats were also categorized into control, fibrosis (noncirrhosis), and cirrhosis groups. For statistical comparison, a Student’s t-test was conducted with unequal variance. The pairwise correlations were examined by calculating the Pearson correlation coefficient (p). For multiple pairwise comparisons, a Bonferroni correction was conducted by adjusting the significance level (α): α = p/N, where N is the number of comparison. Each comparison was judged significant only if P < 0.05 or α < 0.05/N (25).

RESULTS

Phantom Study

The velocity profile obtained in the phantom study is shown in Fig. 2a, and this was very close to the theoretical parabolic shape under the laminar, steady-state, and fully developed flow conditions. The pixel-by-pixel velocity had a small error (≈6%) in the central area and a large error at the edge (≈20%) (17) (Fig. 2a). Using the flow meter as a cross-check, the MRI-measured average velocity v had an error <5%. The repeatability of the average velocity measurement was within 5% and the repeatability of the tube area measurement was within 6%, hence the repeatability of the pressure gradient (represented by v/A) was calculated to be within 12%. Using the pressure sensors as a cross-check for the pressure gradient measurement, we found the PPG-MRI measured pressure gradient had an error less than 12%, as shown in Fig. 3. The PPG model was verified according to the linear relationship between the pressure gradient and (v/A), where a slope equal to 8πμ (Fig. 3) was observed.

FIG. 2.

Bars: standard deviation (STD). a: Graph shows one example of the velocity profile in the phantom (diameter D = 8 mm) acquired using PC-MRI with TR/TE = 61/11 ms, flip angle = 15°, resolution = 0.5 × 0.5 mm², NEX = 3, slice thickness = 5 mm, Venc = 10/50 cm/s, total scan time ≈25 sec. The MRI-measured average velocity v_MRI = 9 cm/s with the repeatability error ≈5%; flow meter measured average velocity v_real = 8.8 cm/s (< the 5% repeatability error of the MRI measurement). b: Phase velocity images for Venc = 10 cm/s, Venc = 50 cm/s, and the three-point method (Venc = 10/50 cm/s) of the phantom in color using the same scan parameters as (a). v_MRI = 19 cm/s and v_real = 21.0 cm/s. Phase wrapping is observed in the low Venc image (b1), large noise is observed in high Venc image (b2), and three-point image has lower noise than high-Venc image and no phase wrapping (b3). c: Graph shows one example of the velocity profile in the rat’s PV (diameter D = 2 mm) acquired using PC-MRI with TR/TE = 45/9.7 ms, flip angle = 15°, resolution = 0.25 × 0.25 mm², NEX = 12, slice thickness = 2.6 mm, Venc = 10/50 cm/s, total scan time ≈5 min. The MRI-measured average velocity v = 6 cm/s with the repeatability error ≈8%.

FIG. 3.

Phantom data shows the pressure gradient was proportional to (v/A). The slope of D = 8 mm and D = 6 mm was approximately equal to 8πμ, which verified the PPG model in Eq. [1]. Bars = STD.

Theoretically, if the slice tilts by an angle θ, the average velocity becomes v · cosθ and the area becomes A/cosθ, then the error of the pressure gradient is proportional to (1-cos²θ) = sin²θ and the error propagation is proportional to (sinθ/cos³θ) · σ_θ, where σ_θ is the uncertainty of tilt measurement. But the real error of MRI measurement was larger than the theoretical error, especially for large tilt angles, because of partial volume effects within a voxel. For instance, when θ = 5°, the real error was 2.7% and the theoretical error was sin²θ = 0.8%; but when θ = 30°, the real error was propagated to 41%, although the theoretical error was sin²θ = 25%. Based on the experimental results, the oblique angle should be less than 15° off the perpendicular direction where the error of pressure gradient measurement was around 11% (less than the 12% repeatability error). This showed the importance of the perpendicularity of the slice orientation.

The phantom flow satisfied the laminar, steady-state, fully developed conditions. The flow was laminar because Re < 2000; the flow was steady-state because a steady-state pump was used; finally, the flow was fully developed because the velocity profile acquired using PC-MRI did not vary with the axial position.

Animal Study

The velocity profile of the rat’s upper PV within the landmark region showed an approximately parabolic shape (Fig. 2c). Compared to the phantom data, the pixel-by-pixel velocity measurement in rats had larger errors due to the larger noise in vivo. The repeatability of the average velocity V was within 8% and the repeatability of the vessel area A was within 7%, hence the repeatability of PPG was within 16%. The upper part of the portal venous flow in both the healthy and diseased rats satisfied the laminar, steady-state, and fully developed conditions with Re < 2000 and it was observed that the flow velocity profile did not vary with the time or axial position.

All the nine rats in the 11–16-week group had histological changes indicating cirrhosis, including nodular regeneration and bridging fibrosis, shown in Fig. 5. The 18 rats in the 2–3-week and 6–8-week groups had fibrosis without cirrhosis and the entire untreated control group was normal.

FIG. 5.

Graphs show the histology of the rats’ liver in the control, 2–3-week, 6–8-week, and 11–16-week groups, respectively: Masson’s trichrome-stained sections of liver for collagen (blue/green) from CCl₄-induced injury. The degree of fibrosis increases from normal in control rats (upper left) to minimal in the 2–3-week group (upper right), to mild and moderate in the 6–8-week group (bottom left), and finally to marked and severe in the 11–16-week group (bottom right). Rats in the 6–8-week group (bottom left) had the most significant fatty change (steatosis) within hepatocytes. Rats in the 11–16-week group (bottom right) had nodular hepatocellular regeneration (NR), marked fibrosis (*) that bridged hepatic lobules and pronounced biliary hyperplasia (BH), which indicate cirrhosis. Scale bars = 200 μm.

For fibrosis score (FS) assignment, all the eight rats in the control group were normal (FS = 0); all the six rats in the 2–3-week group had minimal fibrosis (FS = 1); among the 12 rats in the 6–8-week group, six had mild fibrosis (FS = 2) and six had moderate (FS = 3) fibrosis scores; among the nine rats in the 11–16-week group, two had marked fibrosis (FS = 4) and seven had severe fibrosis (FS = 5).

The fibrosis score was highly correlated with and monotonically increased with the duration of CCl₄ treatment (r = 0.99, P < 0.05) (Fig. 6a). The PPG monotonically decreased with the duration of CCl₄ treatment (Fig. 6b). When compared with the control group, the fibrosis (noncirrhosis) group had a significantly lower PPG score (P < 0.002, α < 0.006), as did the cirrhosis group (P < 0.0006, α < 0.002). Nevertheless, the difference between the fibrosis (noncirrhosis) and cirrhosis groups was not significant (significance level α ≈0.05), shown in Fig. 6c. Since PPG of the control was significantly different from that of the diseased groups, we plotted the PPG vs. nonzero fibrosis scores and found that PPG was highly correlated with fibrosis score (r² = 0.90, P < 0.05) (Fig. 7a). Since the average velocity v and the vessel area A were both acquired, the portal flow rate Q = v · A was also calculated and the difference between control, fibrosis (noncirrhosis), and cirrhosis groups was tested and this showed no significant difference (control vs. cirrhosis: P ≈0.3; control vs. fibrosis (noncirrhosis): P ≈0.5). For the rats with marked fibrosis scores (FS = 4), the difference from early, moderate, or severe fibrosis was not significant. However, rats presenting with early fibrosis (FS = 1 and 2) and moderate fibrosis (FS = 3) had significantly different PPG scores from the severe fibrosis (FS = 5) group (Fig. 7b).

FIG. 6.

Bars: standard error of the mean (SEM). a: Graph shows the fibrosis score monotonically increased with the time of CCl₄ treatment in rats and the fibrosis score was highly correlated with the duration of the treatment (r = 0.99, P < 0.01). b: Graph shows the PPG monotonically decreased with the duration of the CCl₄ treatment in rats. c: Graph shows the PPG of control, fibrosis (noncirrhosis), and cirrhosis group: the PPG in the control group was significantly higher than the fibrosis (noncirrhosis) group (P < 0.0006, α < 0.0018); the PPG in the control group was also significantly higher than the cirrhosis group (P < 0.0002, α < 0.0006). However, the difference between fibrosis and cirrhosis groups was not very significant (α ≈0.05).

FIG. 7.

a: Graph shows a linear relationship between PPG and nonzero fibrosis scores in fibrosis rats (r² = 0.90, P < 0.05, with 95% confidence interval). b: Graph shows the PPG of early fibrosis (FS = 1 and 2) and moderate fibrosis (FS = 3) was significantly different from that of severe fibrosis (FS = 5). Bars: SEM.

DISCUSSION

A fluid mechanics PPG model using phase contrast MRI data was verified in a phantom and tested in 35 rats with different degrees of liver fibrosis without the administration of any contrast agent. Our results show that the MRI-PPG technique had good repeatability and accuracy.

The PPG is a different measure from the more common portal pressure (PP) (18) and hepatic venous pressure gradient (HVPG) (6) measurements, which are often used clinically but are both invasive. Portal pressure is a measure of the absolute value of pressure in the portal vein, in units of mmHg. Normal PP is 5–10 mmHg, while portal hypertension is defined as anything above 12 mmHg. HVPG measures the difference between the sinusoidal pressure (WHVP) and the free hepatic venous pressure (FHVP), which represents the pressure difference between the PV and the intraabdominal vena cava. PPG, on the other hand, shows the change in pressure in the portal vein along the flow direction (dp/dx≈Δp/Δx) in units of Pascal/meter (1 Pascal = 0.0075 mmHg). It decreases with the progression of liver fibrosis because the pressure drop per unit length is reduced due to the increased resistance in the liver. The PPG can be represented by (v/A) in units of cm⁻¹s⁻¹ for laminar, steady-state, and fully developed flow. The advantages of the PPG approach include that it is noninvasive and does not need an independent reference point.

Using a three-point PC-MRI method did improve VNR, especially in vivo. The additional gain in VNR is proportional to the square root of (high Venc/low Venc) (15), which was ≈2.2 in the animal study. The disadvantage of the three-point PC-MRI was the 33% increase in scan time. This is an important consideration when such studies are conducted in humans, where the total scan time should be within a breathhold (≈20 sec) in order to minimize motion artifacts.

The histopathological changes observed in the animal study were consistent with published results for rats (19). For the control rats without CCl₄ treatment, there was no sign of abnormal collagen deposition; for the 2–3-week treated rats, minimal fibrosis was observed; for 6–8-week group, a mild to moderate fibrosis was observed; for the 11–16-week group, a marked to severe fibrosis and signs of cirrhosis were observed (Fig. 5).

There are several limitations to the PPG model. First, the PPG results are sensitive to the slice orientation. As the ultimate goal is to apply this model to humans, one challenge lies in the complicated vessel orientation of the human PV. The determination of the slice orientation can be difficult even with clear sagittal, coronal, and transverse images for reference. This problem can be solved by applying the three-directional velocity encodings (33) with high-resolution, thin-slice acquisitions. The single-directional encoding method includes zero-encoding and velocity-encoding gradients, while the three-directional encoding method includes zero gradients and the encoding gradients in x, y, and z axis (0, Venc-x, Venc-y, and Venc-z), so the total scan time will be twice as much as the single-directional encoding, but this approach permits velocity vector mapping in an arbitrary direction and independent of the slice selection, thus eliminating some of the errors that arise if the slice is not perpendicular to the flow direction.

Second, the model requires laminar, steady-state, and fully developed flow in the upper part of the PV. Fortunately, the upper part of the portal venous flow in both healthy and diseased rats in our study satisfied these conditions. In order to apply the PPG model to humans, the portal venous flow in humans must satisfy these conditions. Since the maximum Reynolds number is far less than 2000 based on the vessel size and average velocity in the portal vein (27,28), the portal venous flow is likely laminar. We selected the upper 4-cm of the portal vein at the entrance to the liver as a landmark, and in humans this section has no branches, so the flow can be assumed to be steady-state and this is supported by other work as well (29,30). Because blood flow is non-Newtonian, it is very difficult to calculate the hydrodynamic entrance length to determine whether the flow is fully developed (11). However, it is still true that the lower the flow velocity and the larger the vessel diameter, the slower boundary layers merge at the centerline, thus the less fully developed the flow. Generally speaking, the most severe patient has the lowest flow velocity and the largest PV diameter. In a preliminary human study, we observed fully developed portal venous flow in three patients with biopsy-proven severe fibrosis (F4) without ascites or collaterals (31). Among them, the lowest flow velocity and the largest PV diameter (v = 10 cm/s and D = 15 mm) is already at the extreme level in the reported patients (27,28), yet the velocity profiles were independent of the axial distance, suggesting the portal venous flow was fully developed. Overall, we cannot apply the proposed model to turbulent flow, or to pulsatile flow, such as the portal flow immediately after food intake (20), or to abnormal vascular structure such as in patients with collaterals or ascites. Because the severity of fibrosis can reduce the average velocity of portal flow and increase the vessel diameter, this may lead to failure to maintain the fully developed flow condition, thus making application of this method in severely fibrotic patients problematic. However, this limitation is perhaps acceptable, as the diagnosis of cirrhosis is usually obvious in patients with these symptoms.

There was a significant difference for control vs. fibrosis (noncirrhosis) and control vs. cirrhosis groups. However, the difference between the fibrosis (noncirrhosis) and cirrhosis groups was not significant. The portal flow rate (Q = v · A) did not show a significant difference in control vs. fibrosis and control vs. cirrhosis groups, suggesting that simply measuring flow is insufficient. PPG was also highly correlated with nonzero fibrosis scores (r² = 0.90, P < 0.05, with 95% confidence interval), which supports the feasibility of MRI-PPG as a potential tool for evaluating hepatic fibrosis. Furthermore, the early fibrosis (FS = 1 and 2) and moderate fibrosis (FS = 3) rats had significantly different PPG from severe fibrosis (FS = 5) rats. However, for marked fibrosis rats (FS = 4), no significant difference from early fibrosis or severe fibrosis was observed, probably because the sample size (n = 2) was too small.

In summary, the MRI-PPG model may be a useful clinical tool for the noninvasive evaluation of liver fibrosis. Other approaches such as MRE have shown recent promise in human studies (22,34–36) and may provide complementary data to the PPG approach presented here. While offering high accuracy to evaluate hepatic fibrosis, MRE is somewhat more complicated to perform, as it requires a transducer to transmit mechanical waves and sometimes multiple transducers are recommended to achieve more uniform penetration of shear waves (23). The analysis is also complicated as an inversion algorithm is needed to process the wave images (21), but the analysis for the PPG approach also requires more additional steps than the more conventional imaging approaches. These approaches, together with MR measures of fat content and perfusion parameters (37,38) with potential indication of liver tissue inflammation, may soon provide a comprehensive assessment of liver status.