Encoding Disease-Related Physiological Remodeling

Why Disease-Related Remodeling Needs Organ-Specific Encoding

A disease state can change the size, composition, and perfusion of different organs in different directions. One organ may enlarge while another atrophies; fibrosis can replace functional tissue without producing a proportional change in total organ volume; and regional blood flow can change even when cardiac output is stable. A PBPK population that applies one multiplier to every organ cannot represent these distinct changes.

The aim is to translate documented physiological observations into model inputs while keeping clear which values were measured and which are assumptions. This tutorial focuses on organ volumes, tissue composition, and perfusion. A physiological change does not by itself establish a change in enzyme abundance, transporter activity, or drug binding; those require their own evidence and model decisions.

Definition: For organ \(i\), let \(V_i\) be the modelled organ volume, \(Q_i\) its blood flow, and \(Q_{\mathrm{CO}}\) cardiac output. Let \(V_{ik}\) be the volume assigned to tissue component \(k\) within organ \(i\), and let \(w_{ik}=V_{ik}/V_i\) be that component's volume fraction. For a given organ, the fractions must satisfy \(\sum_k w_{ik}=1\). When organ flows cover the entire circulation, they must also satisfy \(\sum_i Q_i=Q_{\mathrm{CO}}\).

The index \(i\) identifies an organ and \(k\) identifies a component within that organ. Components should be defined so that they partition the volume being modelled rather than double-counting it. For example, parenchymal tissue, fibrotic tissue, and other extravascular tissue can be treated as disjoint components. If vascular volume is represented separately in the PBPK structure, it should not also be counted inside those tissue volumes.

The introductory material on age-related organ atrophy and blood flow provides the context for representing organ-specific physiological changes. Here the same discipline is applied to disease remodeling: use the organ-level evidence available, preserve the model's volume and flow definitions, and do not presume that all organs share a common disease multiplier.

Translate Measurements Before Changing Model Inputs

A report may give an absolute organ volume, a percentage difference from a reference group, a tissue fraction, an absolute blood flow, or a flow per unit tissue mass. These are not interchangeable. First identify what was measured, the units, the population and disease state, and whether the reported quantity is absolute or normalized. Then map it to the corresponding PBPK input.

If a documented volume ratio \(r_{V,i}\) is defined relative to a model reference value, the disease-state volume is \(V_i'=r_{V,i}V_i\). If tissue fractions are also documented, component volumes follow from \(V_{ik}'=w_{ik}'V_i'\). A changed fraction alone does not determine the total organ volume; an absolute volume or an explicit volume assumption is also needed.

Perfusion evidence needs the same care. An absolute flow in litres per minute can directly specify \(Q_i'\), subject to circulation-wide constraints. A flow fraction \(f_i\) is defined as \(Q_i/Q_{\mathrm{CO}}\), so converting it to absolute flow requires the corresponding cardiac output. A reported flow per unit tissue mass requires an appropriate mass denominator before it can be used as an organ flow.

Key distinction: A measured change in an organ's volume, composition, or flow is evidence about that physiological quantity. It is not automatically evidence that every parameter associated with the organ changes by the same percentage. In particular, volume scaling alone does not establish proportional scaling of intrinsic clearance, partitioning, or blood flow.

Worked Example: Encoding Fibrotic Remodeling of the Liver

Consider a hypothetical dataset for a model reference adult with liver volume \(V_{\mathrm{liv}}=1.50\) L and liver blood flow \(Q_{\mathrm{liv}}=1.50\) L/min. Suppose measurements for a defined fibrotic disease group support a liver volume 20% below that reference, a liver flow 30% below it, and the following disease-state tissue fractions: 0.70 parenchymal, 0.20 fibrotic, and 0.10 other extravascular tissue. These numbers are hypothetical and are used only to illustrate the encoding.

The organ-volume ratio is \(r_{V,\mathrm{liv}}=0.80\), so the disease-state volume is

V_{\mathrm{liv}}'=0.80(1.50\ \mathrm{L})=1.20\ \mathrm{L}.

The reported fractions sum to \(0.70+0.20+0.10=1.00\), so they partition the modelled volume. The component volumes are

V_{\mathrm{par}}'=0.70(1.20)=0.840\ \mathrm{L},\qquad V_{\mathrm{fib}}'=0.20(1.20)=0.240\ \mathrm{L},\qquad V_{\mathrm{other}}'=0.10(1.20)=0.120\ \mathrm{L}.

Their sum is \(0.840+0.240+0.120=1.200\) L, as required. The 30% flow reduction gives \(Q_{\mathrm{liv}}'=0.70(1.50)=1.05\) L/min. Thus the encoded inputs are a 1.20 L liver, its three stated component volumes, and a liver flow of 1.05 L/min. These calculations do not establish how a particular drug's intrinsic clearance or tissue partitioning changes; that would require additional evidence and a model for those processes.

Keep Tissue Composition and Flow Accounting Coherent

The component-volume calculation is a direct consequence of the definition \(w_{ik}=V_{ik}/V_i\). Multiplying both sides by \(V_i\) gives \(V_{ik}=w_{ik}V_i\). Summing across a complete set of components gives

\sum_k V_{ik}=\sum_k w_{ik}V_i =V_i\sum_k w_{ik}=V_i,

because the fractions sum to one. This identity is a useful implementation check: if component volumes do not sum to the specified organ volume, the fractions are incomplete, overlap, or have been applied inconsistently. A composition change can therefore be encoded without changing total volume, but only when the model has a documented or explicitly assumed total volume.

Flow accounting has a parallel constraint. For organs whose flows collectively represent the full circulation, the total of organ flows must equal cardiac output. If only some disease-state flows are measured, the unmeasured flows cannot be treated as if they were also measured. A model may need an explicit rule to assign the remaining flow, and that rule should be reported as an assumption.

Worked Example: Encoding Renal Hypertrophy and a Changed Tissue Split

Suppose a hypothetical reference adult has combined kidney volume \(V_{\mathrm{kid}}=0.300\) L and renal blood flow \(Q_{\mathrm{kid}}=0.900\) L/min. In a specified disease group, assume the documented kidney volume is 20% higher and renal flow is 20% lower. Suppose the disease-state fractions are 0.70 cortex and 0.30 medulla. For this example, assume these two components partition the modelled kidney volume.

The disease-state total volume and flow are

V_{\mathrm{kid}}'=1.20(0.300\ \mathrm{L})=0.360\ \mathrm{L},\qquad Q_{\mathrm{kid}}'=0.80(0.900\ \mathrm{L/min})=0.720\ \mathrm{L/min}.

The two fractions sum to \(0.70+0.30=1.00\). The component volumes are

V_{\mathrm{cortex}}'=0.70(0.360)=0.252\ \mathrm{L},\qquad V_{\mathrm{medulla}}'=0.30(0.360)=0.108\ \mathrm{L}.

They sum to 0.360 L. The example encodes a larger kidney with lower total renal flow; it does not assign the same percentage change to kidney volume and kidney flow. Nor does a changed cortex-to-medulla volume split, by itself, justify a particular split of renal blood flow. That would require separate data or an explicitly stated modelling rule.

Reconcile Partial Perfusion Evidence with Cardiac Output

When disease-specific measurements cover only selected organs, a closure rule may be needed for the remaining flows. One possible rule is to preserve the relative distribution of baseline flow across unmeasured organs and assign them the flow left after measured flows are entered. This is a modelling choice, not a general physiological law. It should be used only when suitable evidence does not support a better allocation.

Flow-allocation rule: Suppose measured disease-state flows are available for a set of organs \(M\). Let the unmeasured organs be \(U\), with baseline flows \(Q_j\). If the model assumes their relative baseline flow distribution is preserved, allocate the remainder \(R=Q_{\mathrm{CO}}'-\sum_{i\in M}Q_i'\) as \(Q_j'=R Q_j/\sum_{u\in U}Q_u\). This rule requires \(R\geq 0\), a positive baseline-flow sum for \(U\), and a defensible assumption that the unmeasured organs retain their relative shares.

Worked Example: Closing a Disease-State Flow Budget

For a hypothetical reference circulation, let cardiac output be 5.00 L/min. Baseline flows are liver 1.50, kidneys 0.90, muscle 0.80, and other organs 1.80 L/min; these sum to 5.00 L/min. Suppose the disease-state cardiac output is measured as 4.80 L/min, and disease-state liver and kidney flows are measured as 1.05 and 0.72 L/min. Muscle and other-organ flows are not measured. Use the stated relative-baseline-allocation rule for those two unmeasured categories.

The remaining flow is

R=4.80-1.05-0.72=3.03\ \mathrm{L/min}.

The baseline flow sum for the unmeasured categories is \(0.80+1.80=2.60\) L/min. Their allocation weights are \(0.80/2.60\) for muscle and \(1.80/2.60\) for other organs. Therefore,

Q_{\mathrm{muscle}}'=3.03\left(\frac{0.80}{2.60}\right)=0.932\ \mathrm{L/min}, \qquad Q_{\mathrm{other}}'=3.03\left(\frac{1.80}{2.60}\right)=2.10\ \mathrm{L/min}.

Using unrounded values, the four disease-state flows sum to \(1.05+0.72+0.9323+2.0977=4.80\) L/min. The result satisfies flow closure, but the muscle and other-organ values are assumption-based allocations rather than measured disease-state flows. If measured flows already sum to more than cardiac output, the inputs are incompatible as stated; rescaling them silently would conceal the inconsistency.

Practical Checks, Alternatives, and Limits

Before using remodeled physiology in a PBPK population, check that each input matches the model's definition and the evidence's measurement scale. For example, an organ volume measured by imaging may not use the same boundary as the model's tissue compartment. A flow estimate normalized to tissue mass is not an absolute organ flow. Population summaries may also conceal different disease severity or treatment status; a single representative value should not be presented as if it captures all individuals.

Useful diagnostics include checking that component fractions are between zero and one and sum to one, that component volumes sum to total organ volume, that organ flows are nonnegative, and that the flow budget closes to cardiac output. Large or directionally surprising differences should prompt a review of source definitions, units, reference groups, and the mapping from measurement to model input. A numerical check can identify inconsistency; it cannot establish that the selected physiological evidence is appropriate.

There are several alternatives to direct organ-specific encoding. A model can retain reference physiology when disease-specific measurements are too sparse, represent a measured population mean, or use separate disease-severity scenarios when there is adequate evidence. These approaches answer different questions. A mean-valued physiological profile is not equivalent to a population distribution, and a scenario range is not a probability distribution unless it is supported and specified as one. The appropriate choice depends on the intended prediction and available data.

A principal limitation is that measurements for volume, composition, and flow may come from different groups or use different definitions. Combining them into one virtual individual can create a profile that was not observed in any participant. The values may also change with disease stage, treatment, hydration, or measurement method. Record the source and status of each input, identify assumptions separately, and avoid implying that a constructed profile represents a clinically validated individual.

Common Pitfall

Incorrect reasoning: “The liver volume is 20% lower, so every liver-related PBPK parameter, including blood flow and intrinsic clearance, should also be multiplied by 0.80.”

Correction: The volume observation supports a volume change. Flow should be changed only using flow evidence or an explicit, justified flow model; intrinsic clearance requires evidence or a model for the relevant metabolic capacity. Encoding each quantity separately prevents one documented change from being mistaken for evidence about unrelated processes.

Key takeaway: Encode disease remodeling organ by organ. Apply measured changes to the matching physiological quantities, make tissue fractions and flows obey their definitions, and label any unmeasured quantities that are supplied by assumption.

Check Your Understanding

Answer each question, then compare your reasoning with the solutions below.

An organ has a disease-state volume of 0.90 L and component fractions 0.60, 0.25, and 0.15. What are the component volumes, and do they close to the organ volume?
A reference organ flow is 0.80 L/min, and disease-specific evidence supports a 25% reduction. What flow should be encoded? Does that evidence establish a change in intrinsic clearance?
Measured disease-state flows total 4.9 L/min while measured cardiac output is 4.6 L/min. Is the flow budget coherent? What should be done?
Why is it not valid to assign the same percentage change to every organ when one disease-related organ change is documented?

Solutions: (1) The component volumes are \(0.60(0.90)=0.540\) L, \(0.25(0.90)=0.225\) L, and \(0.15(0.90)=0.135\) L; they sum to 0.900 L. (2) The flow is \(0.75(0.80)=0.600\) L/min. A flow measurement alone does not establish a change in intrinsic clearance. (3) No. The measured organ flows exceed cardiac output by \(4.9-4.6=0.3\) L/min; review the measurements, definitions, units, and model mapping rather than silently rescaling. (4) The observation supports a change only in the quantity and organ it measures. Other organs and physiological parameters require their own evidence or clearly stated assumptions.