Why Perfusion and Shunting Need Separate Model Inputs
Cirrhosis can change how much blood perfuses functional liver tissue and how much drug-bearing blood bypasses that tissue through portosystemic pathways. These changes are related but not interchangeable. Lower perfusion changes the flow available to carry drug through the liver; shunting diverts a fraction of incoming drug away from hepatic extraction. A model that represents only lower hepatic clearance can therefore miss a change in first-pass escape, while a model that represents only shunting can miss reduced delivery through the perfused route.
The purpose here is to isolate these two effects. Assume, for the calculations, that the unbound fraction in blood and intrinsic hepatic clearance are fixed. This is a simplifying comparison, not a claim that they remain unchanged in cirrhosis. The earlier material on translating disease phenotypes into PBPK changes and on Child-Pugh and MELD scores provides context for describing impairment; a score does not, by itself, determine hepatic blood flow or shunt fraction.
This aggregate definition treats the bypassed fraction as drug that reaches the systemic circulation without hepatic extraction on that pass. It is suitable when the model has one effective inflow and one bypass fraction. If the portal vein and hepatic artery have different routes or shunt fractions, represent their flows and routing separately rather than applying one aggregate fraction indiscriminately. A shunt fraction is a model input describing routing, not a direct measure of liver function.
Well-Stirred Liver With an Explicit Bypass Route
For the perfused liver route, the well-stirred assumption is that incoming drug mixes rapidly and uniformly with drug in the liver before leaving in the outflow. Elimination is linear in unbound drug concentration; \(f_u\) and \(CL_{int}\) are treated as constant over the concentration range. The liver receives flow \(Q_L\), not \(Q_H\), because the bypassed flow does not enter the modeled hepatic tissue.
Let \(C_{in}\) and \(C_{out}\) be blood concentrations entering and leaving the perfused liver route. The rate entering minus the rate leaving equals the hepatic elimination rate. Under the well-stirred assumption, that elimination rate is \(f_u CL_{int} C_{out}\). Therefore:
Rearranging gives the fraction of drug escaping unchanged from the perfused route, \(C_{out}/C_{in}\), and the extraction fraction on that route:
The bypassed fraction escapes extraction on that pass. Combining bypass and perfused routes gives hepatic availability \(F_H\), the fraction of drug entering this hepatic inflow that reaches systemic blood without being removed by the liver on that pass. The corresponding hepatic clearance from systemic blood is the flow through the perfused route multiplied by its extraction fraction.
These equations separate three quantities that are easy to conflate. \(Q_H\) describes total inflow before bypass; \(Q_L\) describes flow reaching the modeled liver; and \(F_H\) describes escape from hepatic removal. \(CL_H\) describes hepatic removal of drug presented from systemic blood. Less delivery to liver tissue does not automatically mean less systemic exposure by a fixed amount: exposure also depends on route of administration and all other clearance pathways.
Worked Effects of Flow and Shunting
Worked Example: Separating Reduced Flow From Increased Shunting
Consider a hypothetical drug with \(f_u CL_{int}=20\) L/h. In a reference condition, let \(Q_H=100\) L/h and \(f_{sh}=0\). In a hypothetical cirrhosis scenario, let \(Q_H=60\) L/h and \(f_{sh}=0.25\). Hold all other parameters fixed. Calculate \(Q_L\), \(CL_H\), and \(F_H\), and compare the combined scenario with lower flow alone.
In the reference condition, \(Q_L=(1-0)(100)=100\) L/h. Thus:
For lower flow alone, keep \(f_{sh}=0\) but use \(Q_H=60\) L/h. Then \(Q_L=60\) L/h, \(CL_H=60(20)/(60+20)=15.00\) L/h, and \(F_H=60/(60+20)=0.7500\). Reduced flow alone lowers hepatic clearance and also lowers hepatic availability in this example: less extraction occurs during the liver pass.
For the combined scenario, \(Q_L=(1-0.25)(60)=45\) L/h. Therefore:
Relative to lower flow alone, adding shunting lowers hepatic clearance from 15.00 to 13.85 L/h and raises hepatic availability from 0.7500 to 0.7692. Yet compared with the reference condition, the combined scenario has lower \(F_H\), because the reduction in perfused flow is substantial. The directions of the two changes must be interpreted against the chosen comparator.
Worked Example: Isolating the Effect of a Shunt
For a second hypothetical drug, let \(Q_H=80\) L/h and \(f_u CL_{int}=40\) L/h. Compare no shunting with \(f_{sh}=0.30\), keeping total inflow and intrinsic clearance fixed. Assume hepatic clearance is the only systemic clearance and compare IV AUC, for which \(AUC=Dose/CL_H\).
With no shunting, \(Q_L=80\) L/h. The hepatic clearance and availability are:
With \(f_{sh}=0.30\), \(Q_L=(1-0.30)(80)=56\) L/h. Thus:
For the same IV dose, the AUC ratio is \(26.67/23.33=1.143\). Under the stated hepatic-only clearance assumption, shunting increases IV AUC by about 14.3% by reducing hepatic clearance. For an oral dose, shunting can also raise the fraction escaping first-pass hepatic removal. That oral effect is not represented by the IV calculation.
Worked Example: Extraction Changes the Size of the Flow Effect
Compare a low-extraction hypothetical drug with \(f_u CL_{int}=5\) L/h and a high-extraction hypothetical drug with \(f_u CL_{int}=300\) L/h. For each drug, use \(Q_H=100\) L/h with no shunting as the reference, then use \(Q_H=60\) L/h and \(f_{sh}=0.20\). Calculate clearance and hepatic availability for the two conditions.
For the low-extraction drug, the reference values are \(CL_H=100(5)/(100+5)=4.762\) L/h and \(F_H=100/105=0.9524\). In the altered condition, \(Q_L=0.80(60)=48\) L/h, so \(CL_H=48(5)/(48+5)=4.528\) L/h and \(F_H=0.20+0.80(48/53)=0.9245\).
For the high-extraction drug, the reference values are \(CL_H=100(300)/(100+300)=75.00\) L/h and \(F_H=100/400=0.2500\). In the altered condition, \(Q_L=48\) L/h, so \(CL_H=48(300)/(48+300)=41.38\) L/h and \(F_H=0.20+0.80(48/348)=0.3103\).
The results illustrate why extraction characteristics matter when interpreting a flow change. The high-extraction drug has a larger absolute decrease in hepatic clearance and a larger increase in hepatic availability. The low-extraction drug has high hepatic availability in both conditions, so the same routing change produces a smaller absolute change in \(F_H\). These are model-based comparisons with intrinsic clearance held fixed, not predictions for every drug in cirrhosis.
From Hepatic Availability to Systemic Exposure
For a linear oral model, a useful bookkeeping relation is \(AUC_{oral}=Dose \times F_a \times F_g \times F_H/CL_{total}\), where \(F_a\) is the fraction absorbed, \(F_g\) is the fraction escaping gut loss, and \(CL_{total}\) is total systemic clearance. This relation assumes these factors are defined consistently for the model. It shows why hepatic availability and clearance should be calculated separately: shunting can affect both, while hepatic impairment can also affect other inputs that have deliberately been held fixed here.
In the special case of no shunting and hepatic-only systemic clearance, \(F_H=Q_H/(Q_H+X)\) and \(CL_H=Q_HX/(Q_H+X)\), where \(X=f_u CL_{int}\). Their ratio is \(F_H/CL_H=1/X\). Thus, under these restrictive assumptions, changing flow alone changes both terms but does not change oral AUC for a fixed dose. This cancellation does not mean flow is irrelevant: it changes hepatic extraction and IV clearance, and it need not hold when there is shunting, extrahepatic clearance, or changing absorption and gut availability.
With shunting, the bypass fraction contributes to \(F_H\), but the bypassed flow does not contribute to \(CL_H\) in this model. Consequently, the cancellation generally fails. In a PBPK implementation, route the bypassed drug directly to the systemic circulation and the remaining inflow to the liver compartment. That structure allows hepatic delivery, hepatic extraction, and systemic exposure to arise from the same mass-balanced routing assumptions.
Diagnostics, Alternatives, and Limitations
Check the model structure and its outputs before interpreting a prediction. First, confirm \(0 \leq f_{sh} \leq 1\), \(Q_H>0\), \(Q_L=(1-f_{sh})Q_H\), and \(CL_H \leq Q_L\). The last condition follows because the extraction fraction cannot exceed one. Also check \(0 \leq F_H \leq 1\). If a simulated shunt causes drug to disappear rather than reach the systemic route, the mass balance is wrong. If a bypass fraction is applied both to flow and again as an additional clearance reduction, the same effect may have been counted twice.
A flow-only model can be a reasonable simpler alternative when there is no evidence to support a separate bypass pathway and the question concerns aggregate hepatic clearance. It cannot, by itself, represent a bypass-specific contribution to first-pass escape. A shunt-only adjustment may represent bypass routing but leaves perfusion through the liver unchanged unless \(Q_H\) or the hepatic compartment is also modified. An explicit routing model is more informative when oral and IV observations, or other route-specific evidence, need to be explained together.
Available exposure data may not uniquely identify \(Q_H\), \(f_{sh}\), and \(CL_{int}\): different combinations can produce similar clearance or oral availability. Do not infer a precise shunt fraction from an exposure change alone without adequate information and a defensible model. A lumped model also omits spatial heterogeneity, distinct portal and arterial routing, and other disease-related changes. If those details matter to the prediction, the simple aggregate equations are insufficient. Keep the interpretation limited to the changes actually represented; here, binding, functional liver mass, and enzyme capacity are held fixed.
Check Your Understanding
Answer each question, then compare with the solutions below.
- A hypothetical model has \(Q_H=50\) L/h, \(f_{sh}=0.20\), and \(f_u CL_{int}=10\) L/h. What is \(Q_L\)?
- For the same model, calculate \(CL_H\).
- For the same model, calculate \(F_H\). What fraction escapes through the bypass route alone?
- Why can lower flow and increased shunting have different effects on oral hepatic availability?
Solutions. 1. \(Q_L=(1-0.20)(50)=40\) L/h. 2. \(CL_H=40(10)/(40+10)=8.000\) L/h. 3. \(F_H=0.20+0.80(40/50)=0.8400\); the bypass route contributes 0.20, or 20% of incoming drug, to escape. 4. Lower flow changes extraction on the perfused route, whereas shunting adds a fraction that bypasses hepatic extraction. Their combined effect depends on extraction and on the comparison condition, so neither should be substituted for the other.