Why Resting Flow Allocation Matters
A PBPK model needs more than an organ volume: it also needs a representation of how much blood reaches each tissue. At rest, systemic cardiac output is distributed unevenly. The kidneys and brain receive substantial flows, while the fraction reaching a particular tissue depends on its vascular supply and on how the body is represented in the model. These allocations affect the rate at which circulating drug can be delivered to modelled tissues.
This tutorial uses one illustrative resting allocation for a reference adult. It is a practical calculation scheme, not a universal physiological constant. Published values and reference tables differ with measurement methods, body size, definitions of tissue beds, and the conditions under which flow was measured. The earlier material on organ-flow fractions and flow conservation establishes the basic calculation; here the emphasis is on applying it to major resting systemic destinations and interpreting the accounting correctly.
A Representative Resting Allocation
The table gives a deliberately rounded reference allocation for an adult at rest. The categories are defined as systemic arterial destinations: each unit of systemic output is assigned once to the first bed it supplies. “Portal-drained gastrointestinal tissues” means the gastrointestinal and related tissues whose venous blood drains to the portal vein. “Hepatic artery” is listed separately because it supplies the liver directly from the systemic arterial circulation.
| Systemic arterial destination | Illustrative fraction | Flow if \(Q_{\mathrm{CO}}=5.00\) L/min |
|---|---|---|
| Brain | 14% | 0.700 L/min |
| Kidneys | 20% | 1.00 L/min |
| Myocardium | 5% | 0.250 L/min |
| Skeletal muscle | 20% | 1.00 L/min |
| Skin | 5% | 0.250 L/min |
| Adipose tissue | 5% | 0.250 L/min |
| Portal-drained gastrointestinal tissues | 20% | 1.00 L/min |
| Hepatic artery | 5% | 0.250 L/min |
| Other systemic tissues | 6% | 0.300 L/min |
| Total systemic arterial destinations | 100% | 5.00 L/min |
The percentages sum to 100%, making the categories a complete allocation of systemic output under this bookkeeping scheme. The values should be read as approximate reference inputs, not as exact shares in every healthy adult. For example, skeletal-muscle flow can vary considerably with muscle activity, and measured flow depends on the tissue boundaries used to define a bed.
The liver needs special care. Blood from the portal-drained gastrointestinal tissues reaches the liver after passing through those tissues. Thus, the example table assigns 1.00 L/min to the gastrointestinal destination and 0.250 L/min to the liver’s hepatic-artery supply. The liver’s total incoming flow is approximately the portal contribution plus the hepatic arterial contribution, or 1.25 L/min in this example. That 1.25 L/min is a valid liver inflow, but it is not an additional parallel share of cardiac output: the portal component has already been counted as flow to the gastrointestinal destination.
Worked Example: Calculating Flows at a Reference Cardiac Output
Suppose a hypothetical reference adult has a resting systemic cardiac output of 5.00 L/min. Calculate the flows to the brain, kidneys, and myocardium using the illustrative fractions.
For each bed, multiply the fraction, written as a decimal, by cardiac output:
For the brain, \(f_{\mathrm{brain}}=0.14\), so \(Q_{\mathrm{brain}}=0.14(5.00\ \mathrm{L/min})=0.700\ \mathrm{L/min}\). For the kidneys, \(f_{\mathrm{kidney}}=0.20\), so \(Q_{\mathrm{kidney}}=0.20(5.00\ \mathrm{L/min})=1.00\ \mathrm{L/min}\). For the myocardium, \(f_{\mathrm{myocardium}}=0.05\), so \(Q_{\mathrm{myocardium}}=0.05(5.00\ \mathrm{L/min})=0.250\ \mathrm{L/min}\).
These are modelled flows under the stated reference assumptions. They are not measurements from an individual and do not imply that each person has exactly these flows.
Why the Fractions Sum to One
The conservation check follows directly from the flow accounting. Assume a steady resting state, so there is no net accumulation of blood within the circulation over the time interval considered. Also assume the listed destinations form a complete, mutually exclusive partition of systemic arterial output: each unit of output is counted in one destination, and no destination is omitted. If there are \(k\) such destinations, conservation gives the following result.
This is an accounting identity under the stated assumptions. It is a useful diagnostic, but a sum of one does not prove that each fraction is physiologically accurate. A table could conserve total flow while allocating too much to one bed and too little to another.
Worked Example: Scaling the Allocation to a Different Cardiac Output
Consider a hypothetical adult with resting systemic cardiac output of 4.60 L/min. Use the same illustrative fractions to calculate kidney flow, portal-drained gastrointestinal flow, and total liver inflow.
Kidney flow is \(Q_{\mathrm{kidney}}=0.20(4.60\ \mathrm{L/min})=0.920\ \mathrm{L/min}\). Portal-drained gastrointestinal flow is \(Q_{\mathrm{GI}}=0.20(4.60\ \mathrm{L/min})=0.920\ \mathrm{L/min}\). Hepatic-artery flow is \(Q_{\mathrm{HA}}=0.05(4.60\ \mathrm{L/min})=0.230\ \mathrm{L/min}\).
Under the simplifying assumption that all flow leaving the portal-drained tissues reaches the liver through the portal vein, portal flow is 0.920 L/min. Total liver inflow is therefore \(Q_{\mathrm{liver,total}}=Q_{\mathrm{portal}}+Q_{\mathrm{HA}}=0.920+0.230=1.15\ \mathrm{L/min}\). This value is the liver’s incoming flow, not a new allocation to add to the systemic arterial destinations.
Checking a Flow Table
A flow table should be checked both numerically and conceptually. The numerical check asks whether the stated fractions or absolute flows add to the intended total. The conceptual check asks whether the entries describe parallel systemic destinations, serial inflows, or a mixture. This second check matters because flow through a series of organs can appear in more than one organ-specific inflow measurement.
Worked Example: Finding an Incomplete Allocation
A hypothetical draft model assigns 14% to brain, 20% to kidneys, 5% to myocardium, 20% to skeletal muscle, 5% to skin, 5% to adipose tissue, 20% to portal-drained gastrointestinal tissues, and 5% to the hepatic artery. What fraction remains for other systemic tissues?
Add the listed fractions: \(0.14+0.20+0.05+0.20+0.05+0.05+0.20+0.05=0.94\). The residual is \(1.00-0.94=0.06\), or 6%. At a hypothetical cardiac output of 5.00 L/min, this corresponds to \(0.06(5.00\ \mathrm{L/min})=0.300\ \mathrm{L/min}\).
The residual identifies an amount that must be assigned or otherwise explained; it does not identify which tissue category should receive it. If the modeller adds a 6% “other systemic tissues” category, the allocation sums to one. If no such category is intended, the table is incomplete or its entries use inconsistent definitions.
Assumptions, Alternatives, and Limitations
The simple calculation \(Q_i=f_iQ_{\mathrm{CO}}\) assumes the fraction and cardiac output refer to the same physiological condition and compatible definitions. For a resting distribution, the input should represent rest rather than exercise or another altered state. The categories must be defined consistently, and a percentage must be converted to a proportion before multiplication. If the output is in L/min, the resulting organ flows are in L/min.
There are several useful ways to represent flow, each answering a different question:
| Representation | What it provides | Main caution |
|---|---|---|
| Fraction \(f_i\) | A share of cardiac output assigned to a bed | Does not specify absolute flow without \(Q_{\mathrm{CO}}\) |
| Absolute flow \(Q_i\) | Flow in units such as L/min | Depends on the cardiac output used |
| Reference allocation | A coherent baseline for a model scenario | May not represent an individual or another condition |
| Organ-specific measurement | Flow estimated for a particular organ and measurement context | May use a different tissue definition or count a serial inflow |
A reference fraction table is convenient when constructing a baseline PBPK physiology, while absolute flows make the model’s perfusion inputs explicit. Individual measurements may be preferable when they are available and appropriate, but they do not automatically resolve differences in tissue definitions or in whether a reported flow is arterial supply or total organ inflow. The table also compresses within-organ heterogeneity into one value; it does not describe regional perfusion within an organ.
Common Mistakes and Diagnostics
- Using percentages as if they were decimal fractions. The calculation \(14(5.00)\) is not the brain flow for a 14% allocation. Convert 14% to 0.14 first: \(0.14(5.00)=0.700\) L/min.
- Adding liver total inflow to a complete systemic allocation. Portal blood has already passed through portal-drained tissues. Adding both the gastrointestinal flow and the full liver inflow as independent parallel flows double-counts that portal component.
- Treating a total of 100% as proof of correct physiology. A complete sum checks the accounting, not the accuracy of individual estimates. Compare values with their measurement basis and intended scenario.
- Mixing conditions or definitions. Combining a resting cardiac output with a flow fraction defined for another condition, or combining a hepatic-artery fraction with total liver inflow as though both were parallel destinations, can make an apparently precise table misleading.
- Ignoring units. Fractions are dimensionless; multiplying by cardiac output in L/min produces flow in L/min. A result in mL/min requires an explicit conversion: \(1\ \mathrm{L/min}=1000\ \mathrm{mL/min}\).
Check Your Understanding
Answer each question, then compare your reasoning with the solutions below.
- At a hypothetical resting cardiac output of 4.00 L/min, what brain flow follows from a 14% fraction?
- At a cardiac output of 5.00 L/min, what is the hepatic-artery flow under the illustrative allocation?
- Why should total liver inflow not be added as a separate parallel destination when portal-drained gastrointestinal flow is already included?
- A proposed allocation totals 97%. What does the remaining 3% establish, and what does it not establish?
- State one assumption required for the fractions in a systemic destination table to sum to one.
Solutions. (1) \(0.14(4.00\ \mathrm{L/min})=0.560\ \mathrm{L/min}\). (2) \(0.05(5.00\ \mathrm{L/min})=0.250\ \mathrm{L/min}\). (3) The portal component of liver inflow is blood that has already been counted as flow through portal-drained gastrointestinal tissues, so adding it again double-counts that flow. (4) Three percent is unallocated under the proposed accounting; it does not determine which tissue should receive it or show that the listed fractions are individually accurate. (5) For example, the listed destinations must form a complete, mutually exclusive partition of systemic arterial output under steady-state flow accounting.