Worked Example: Constructing an Obese-Adult Physiological Model

From Body Size to a Physiological Parameter Set

An obese-adult PBPK model should not be built by multiplying every reference-adult organ volume and blood flow by the ratio of total body weights. Adipose tissue can expand markedly while lean mass and individual organs do not expand in the same proportion. Instead, this worked tutorial constructs two hypothetical parameter sets using an explicit set of assumptions: estimated lean body mass determines the scaling of selected lean organ volumes, while estimated adipose volume determines adipose-tissue volume and its blood-flow demand.

The numerical rules below are a transparent teaching model, not universal clinical equations or a claim that one scaling method fits every drug or population. The model’s internal consistency can be checked directly: organ and residual lean volumes must account for the lean-volume pool, and the mutually exclusive systemic flow branches must sum to cardiac output.

For the hypothetical male, the lean-mass equation is \(LBM=9270W/(6680+216BMI)\). For the hypothetical female, it is \(LBM=9270W/(8780+244BMI)\). The reference adult has \(LBM=55\text{ kg}\), and a specified reference organ-volume set totals \(25.15\text{ L}\). Each listed lean organ volume is scaled in direct proportion to \(LBM/55\). The difference between total lean volume and the scaled selected-organ volumes is retained as a residual lean-volume compartment; it is not an additional measured organ.

Worked Example 1: Scaling the First Obese-Adult Organ Set

Constructing and Checking the Flow Distribution

For both examples, use a specified cardiac-output rule \(Q=5.0(LBM/55)^{0.75}\text{ L/min}\). This is an explicit allometric assumption for this teaching model; it should not be mistaken for a cardiac-output measurement or a universal obesity relationship. Adipose flow is calculated as \(F_A=0.015V_A\), where \(V_A\) is adipose volume in litres and \(0.015\text{ L/min/L}\) is the assumed adipose perfusion rate. The remaining flow, \(Q-F_A\), is divided among non-adipose systemic branches using fixed shares.

Those shares are 5% hepatic artery, 20% gut/portal inflow, 20% kidneys, 14% brain, 4% heart, 15% skeletal muscle, 5% skin, and 17% other systemic tissues. The shares sum to 100%. The lungs are not an additional systemic branch in this allocation: pulmonary flow is in series with systemic cardiac output, rather than a separate share to be added to it. Gut/portal inflow and hepatic arterial inflow are listed as distinct sources; total liver inflow is their sum, so the portal contribution must not be counted twice.

Worked Example 2: A Second Obese-Adult Parameter Set

Assumptions, Diagnostics, and Alternatives

The construction relies on several assumptions that should remain visible when the parameter set is used. The lean-mass equations provide estimates, not direct measurements. The model treats lean-mass volume as numerically equal to lean mass in kilograms, treats body weight minus estimated lean mass as adipose mass, and uses a single density for that adipose mass. It scales each selected organ linearly with lean body mass, even though real organ-specific scaling need not be identical. It also assumes a cardiac-output relationship and fixed relative non-adipose flow shares. The resulting values are therefore internally consistent conditional on these choices, not uniquely determined by height and weight alone.

Useful checks are algebraic and dimensional. Confirm that \(BMI\) uses height squared in metres; that \(LBM\) is positive and less than body weight; that the scale factor is dimensionless; and that every scaled organ volume has units of litres. Sum the reference organ volumes before scaling, then verify that scaled organs plus residual equal the stated lean-volume pool. For flow, verify that adipose flow does not exceed cardiac output, that the non-adipose shares sum to one, and that all branch flows sum to \(Q\). If a displayed total differs slightly, distinguish rounding from an actual failure of conservation by checking unrounded values.

A common mistake is to scale all organ volumes by \(W/55\) simply because the subject weighs \(W\) kilograms. For the hypothetical man, this would use \(150/55\approx2.727\), rather than the model’s lean-mass factor \(83.3633/55\approx1.516\), and would greatly inflate the selected organ-volume sum. The correction is to apply the stated descriptor-specific scaling rule: in this construction, selected lean organs scale with estimated lean body mass, while adipose tissue is handled separately.

Other modelling choices may be preferable for a particular application. One may use measured organ volumes or cardiac output when available, organ-specific scaling relationships instead of one common lean-mass factor, or another body-size descriptor justified for the intended population. A model may also represent splanchnic and hepatic flows with a more detailed vascular structure. Such alternatives can be more physiologically informative, but they require additional data and assumptions. Whatever method is chosen, mutually exclusive flow branches must be distinguished from nested flows, and the complete model must preserve the relevant volume and flow accounting.