Figure 1.
Our spatially resolved model is based on mass balance equations from physiologically based pharmacokinetic modeling as well as organ and vascular geometry obtained by in vivo imaging. The combined model allows a detailed simulation of hepatic distribution and metabolization to accurately describe spatio-temporal effects underlying first-pass perfusion in the liver.
Figure 2.
Conceptual two-dimensional sketch of our liver perfusion model.
The homogenized hepatic space HHS is supplied and drained by the supplying vascular systems SVS and the draining vascular system DVS, respectively. The blood flow through the SVS summarizes the contributions of both supplying systems (hepatic artery and portal vein). The blood is hereafter transferred to the HHS along the terminal edges of the supplying vascular tree (dashed lines). After blood has passed through the HHS, flow into the draining vascular tree (hepatic vein) occurs again along its terminal edges (dashed lines). The HHS itself locally consists of several subspaces, the sinusoidal subspace (combining red blood cells and the plasma subspace), the interstitial subspace, the cellular subspace, and the remaining subspace. An actual 3D vascular geometry is shown in Figure 3. The SVS and DVS roots are connected to the rest of the body by the total blood flow in the liver. In the vascular structures, only 1D advection with given velocities per edge take place. In the HHS, 3D advection (according to a 3D flow velocity vector field) as well as exchange between the HHS subspaces and metabolization (according to PBPK model parameters) are considered simultaneously.
Figure 3.
From in vivo scans to vascular geometry.
Based on an in vivo micro-CT scan (a) of a mouse, vascular structures (b) in the liver are segmented and skeletonized. The supplying and draining vascular systems (SVS and DVS) are shown in red and blue, respectively. Furthermore, the liver is segmented and decomposed in lobes shown in different colors in (c). An algorithmic procedure is used to determine physiological vascular structures (d) with the desired level of detail, in our case leaf nodes (end points) for each of the two trees are used.
Table 1.
PBPK parameters for the compounds considered.
Figure 4.
Visualization of pathophysiological states (steatosis, -induced necrosis) in the spatially resolved liver model.
The images show the distribution of lipid in our steatotic model with homogeneous lipid accumulation throughout the whole liver (a, b) and different heterogeneous distributions (c, d) in the left lateral lobe and the remaining lobes. The average lipid accumulation over the whole liver is the same in both steatosis cases. The lipid accumulation is assumed to change the distribution and metabolization behavior according to Equation 9. The liver volume affected by -induced necrosis is shown in dark at the bottom (e, f). In each case, a volume rendering (a, c, e) and one coronal slice through the model liver (b, d, f) is shown along with the vascular structures.
Figure 5.
PBPK model establishment and parameter identification.
Pharmacokinetic simulations of an intravenous dose of midazolam of per kg body weight (left) and an oral dose of spiramycin of
per kg body weight (right) are shown. The PBPK simulations (red lines) were compared to experimental data (green asterisks) for midazolam [66] and spiramycin [67] in mice.
Figure 6.
Results of the single pass perfusion of CFDA SE (outflow concentrations).
For perfusion by CFDA SE, the large plot (left) shows the outflowing CFDA SE concentration in the healthy state of the isolated mouse liver model and the two steatotic states for a CFDA SE inflow during seconds. For comparison, results for a PBPK simulation are shown as well. The four small plots (right) show the mean CFDA SE concentrations in the four subspaces of the homogenized hepatic space as well as the ranges between 5th/95th and 25th/75th percentiles, respectively, to illustrate the ranges of the concentrations in the spatially resolved model. The PBPK simulation results, shown for comparison, in contrast yield one value for each compartment at any given time point, representing only mean values.
Figure 7.
Results of the spatio-temporal perfusion simulations of CFDA SE in the liver.
The volume renderings show the distribution of CFDA SE in the mouse liver for the healthy state at different time points, showing the first pass of perfusion (), the distribution phase (
) and the wash out (
).
Figure 8.
Influence of spatially heterogeneous lipid distributions on CFDA SE concentrations in steatosis.
A comparison (b) of the CFDA SE concentrations at in the heterogeneous steatotic state (a) to the healthy state of the isolated mouse liver (see Figure 7) shows higher concentrations of the lipophilic tracer throughout the steatotic liver model. The difference (c) between the heterogeneous and homogeneous steatotic states exhibits higher CFDA SE concentrations (red spots) outside the left lateral lobe with higher lipid accumulation in the homogeneous case, see Figure 4. Notice that the color scales are different. This clearly shows that spatial resolution is indispensable for accurate modeling. For a clearer visualization of the concentration differences in the HHS volume, we omitted the vascular structures in the volume renderings (b and c).
Figure 9.
Simulations with a spatially resolved model for midazolam.
The large plot (left) shows the outflowing midazolam concentrations for the healthy state and the pathological states for a midazolam inflow during seconds. For comparison, results for simulations with a PBPK model are shown as well. The four smaller plots (right) show the total amounts contained in the subspaces of the liver, using the same lines and colors. Here, a difference between healthy and pathological states can be observed. In case of
-induced necrosis, higher outflow concentrations are predicted whereas they are lower in the steatotic cases. In particular, the outflow concentration as well as the amounts contained in the plasma and the interstitium also show a difference of up to
,
, and
percent, respectively, between the homogeneous and heterogeneous steatotic states (marked by arrows).
Figure 10.
Results for the metabolization of spiramycin and comparison to experimental data from an isolated perfused liver.
The plot shows the outflow rates of spiramycin from our single pass perfusion model for a spiramycin inflow during minutes compared to experimental data from an isolated perfused liver [32]. While the experimental values were measured in a healthy liver, we also show simulation results for the steatotic states. The volume renderings show the total spiramycin concentration for four time points after the end of the inflow (
minutes).