Converting Cell Product Dose into Viable Starting Conditions

From Labelled Dose to Model Starting Conditions

A cell-product dose is not always the number of viable cells that reach the patient, and that number is not necessarily the number of cells with the intended functional modification. A model that starts from the wrong count can therefore misstate the amount of active product present at time zero, even when its later equations are implemented correctly.

The calculation in this tutorial is a cell-counting exercise: it translates a stated product dose into the cell counts available at the chosen start of the model, usually immediately after infusion. It does not describe what those cells do after that time. The conversion depends on what the dose label counts, when viability and functional fraction were measured, and whether infusion losses affect cell subpopulations equally.

These quantities answer different questions. \(N_{\mathrm{viable},0}\) counts all living cells at the model start, including cells without the intended modification. \(N_{\mathrm{mod},0}\) counts living cells with that modification. \(N_{\mathrm{pot},0}\) expresses the modified-cell count on a reference-potency scale; it is not necessarily a literal number of cells. If the model distinguishes modified from unmodified cells, the two cell counts can be used as separate initial conditions. If it tracks only a potency-equivalent exposure, the last quantity may be appropriate, provided the model’s state is defined on that scale.

Assumptions Behind the Multiplication

The product \(vfr\) is valid only when its factors represent compatible, non-overlapping steps. In particular, \(v\) must be the viable fraction of the stated product count; \(f\) must be the modified fraction among viable cells; and \(r\) must be the recovery fraction from that population through infusion. If a reported modification fraction instead uses all cells, including dead cells, it cannot be substituted for \(f\) without conversion.

The simple equation also assumes that infusion recovery is nonselective: modified and unmodified cells have the same probability of recovery. It treats the measured fractions as applicable to the dose being converted and assumes no additional cell gain or loss between measurement and the defined model start. These are accounting assumptions, not universal properties of cell products. If the available measurements do not support them, use subpopulation-specific counts or clearly qualify the resulting starting conditions.

Potency requires particular care. Here \(q\) means relative activity per modified viable cell, and it is multiplied only if that activity difference is not already represented in \(f\) or in another assay-derived quantity. A potency assay that reports aggregate activity for the whole cell population may already reflect the fraction of functional cells. Multiplying that aggregate potency by \(f\) again would count the same reduction twice.

Why the Conversion Works

The calculation follows from successive retention fractions. Of \(N_{\mathrm{prod}}\) product cells, the fraction \(v\) is viable, leaving \(N_{\mathrm{prod}}v\). Of those viable cells, fraction \(f\) is modified, leaving \(N_{\mathrm{prod}}vf\) modified viable cells. If fraction \(r\) of each subpopulation is recovered, the final modified viable count is \(N_{\mathrm{prod}}vfr\). Applying relative per-cell potency \(q\) then expresses that count in reference-equivalent units.

This derivation also shows why the order of multiplication does not matter: each factor is a proportion applied to the preceding count. The biological interpretation does matter, however. The product of fractions is justified by the sequence and definitions above, not merely because all reported values happen to be percentages.

When Infusion Losses Are Selective

A single recovery fraction is insufficient if modified and unmodified cells have different recovery. Let \(r_{\mathrm{mod}}\) and \(r_{\mathrm{unmod}}\) denote their respective recovery fractions. For a pre-infusion viable count \(N_{\mathrm{pre}}\), with modified fraction \(f\), the correct starting counts are:

The total viable count is the sum of these subpopulation counts. The post-infusion modified fraction is therefore \(N_{\mathrm{mod},0}/(N_{\mathrm{mod},0}+N_{\mathrm{unmod},0})\), which generally differs from the pre-infusion fraction \(f\). An aggregate recovery fraction can recover the total count, but cannot by itself determine the modified count unless recovery is nonselective or additional subpopulation information is available.

Diagnostics, Alternatives, and Limitations

Before using a converted count as a model starting condition, check the bookkeeping and the measurement definitions. Useful checks include:

• Confirm the dose basis. Determine whether the stated product count is total cells, viable cells, or already a potency-adjusted quantity. Do not apply a viability correction to a dose already stated as viable cells.
• Align denominators. Verify whether \(f\) is a fraction among viable cells or among all counted cells. A fraction with the wrong denominator will produce a systematically wrong modified-cell count.
• Check the time point. Viability, functional fraction, and recovery should correspond to the stages represented by the calculation. Do not apply infusion recovery again if the measured count is already post-infusion.
• Check the subpopulation assumption. Compare recovery evidence for modified and unmodified cells where available. A meaningful difference calls for separate recovery factors.
• Check potency definitions. Establish whether potency is per modified viable cell or aggregate across the assayed population. The latter may already incorporate viability or functional fraction.

The multiplicative calculation is a transparent alternative to a direct post-infusion cell count. Direct measurement can be preferable when a reliable count and functional fraction are available at the model start, because it avoids estimating several intermediate factors. Conversely, the factor-based calculation is useful when only product-stage measurements are available or when the contribution of each loss needs to be inspected. Whichever approach is used, keep the state definition consistent with the data: a model state measured in viable modified cells should not be initialized with a total product-cell count or a potency-equivalent count unless those quantities have been explicitly reconciled.

These equations do not make uncertain measurements exact. If \(v\), \(f\), \(r\), or \(q\) is estimated with substantial uncertainty, the derived starting count inherits that uncertainty. Nor does this calculation predict subsequent cell expansion, contraction, trafficking, or persistence; it only establishes the chosen starting condition. Rounding should be postponed until the final reported value so that intermediate arithmetic does not add avoidable error.