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Rituximab effect and B-cell recovery in pediatric nephrotic syndrome

Conditional fixed-effect K-PD model of a latent rituximab effect amount and CD19+ B-cell turnover, with source regimens and IgA sensitivity conditions.

Kinetic-pharmacodynamic model to predict post-rituximab B-cell repletion as a predictor of relapse in pediatric idiopathic nephrotic syndrome ↗
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How does IgA change modeled B-cell recovery?

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375 mg/m2 x2 weekly

Conditional deterministic K-PD calculation at fixed source estimates; no population intervals or individual relapse prediction.

0–365 day

375 mg/m2 x2 weekly

Conditional deterministic K-PD calculation at fixed source estimates; no population intervals or individual relapse prediction.

Readouts

CD19 b cell count · cells/uL
Absolute conditional CD19+ B-cell count.
B cell recovery relative to model baseline · dimensionless
Count divided by Kin/Kout; one is the untreated model equilibrium.
Latent rituximab effect amount · mg
Unmeasured K-PD effect coordinate; not plasma concentration.
Effective half maximal effect amount · mg
ED50 times the fixed exploratory multiplier and (IgA/1.15)^1.39.

Study purpose

  • How do the selected fixed regimen and positive IgA condition alter B-cell depletion and recovery?

Assumptions

  • Conditional fixed-effect K-PD calculations; no original population fit, random effects, residual error, prediction intervals or complete paper reproduction.
  • A1_mg is a latent rituximab effect amount, not a measured plasma concentration. The model has two biological states plus a separate clock.
  • The observed clinical protocol was two weekly IV doses of 375 mg/m2, capped at 500 mg. Presets also include distinct theoretical simulation regimens, including 750 mg/m2; the clinical cap is not applied to those theoretical arms.
  • Preset doses are fixed absolute mg derived, where applicable, from BSA 0.82 m2. Editing IgA does not change doses; BSA is inspection-only. Instantaneous latent-amount additions approximate day-scale dosing; infusion durations were not reported.
  • Monthly and every-two-month schedules use 30-day and 60-day intervals. These are conditional calendar approximations.
  • IgA is the only final fixed-effect covariate. The positive 0.11–2.26 g/L exploration domain comes from the source sensitivity conditions, not a clinically validated range.
  • Ten exploratory ED50 conditions retain a different fixed multiplier for each regimen. They are additional conditional calculations, not independent validation or population predictions.
  • B-cell repletion means the first upward crossing above 10 cells/uL after depletion, measured from first treatment. Instantaneous cell count or normalized recovery alone does not calculate that event time.
  • The separate clinical survival/nomogram analysis is not implemented. No individual relapse probability, concentration PK, clearance, volume or concentration AUC is returned.
  • Changing the simulation start applies the supplied initial state there; it does not reconstruct prior doses. Fitting and normal server parameter scans are unavailable.
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365 → 168

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Biology

Conditional fixed-effect K-PD model of a latent rituximab effect amount and CD19+ B-cell turnover, with source regimens and IgA sensitivity conditions.

Conditional fixed-effect K-PD model of a latent rituximab effect amount and CD19+ B-cell turnover, with source regimens and IgA sensitivity conditions.
States & equation dependencies
What are the modeled states and equation-linked processes?Representative technical topology with 3 selected states: Latent rituximab effect amount, CD19 b cell count, Elapsed time. Displayed equation-linked dependencies: from Latent rituximab effect amount to CD19 b cell count. Displayed model or scenario entry points: Administered input enters Latent rituximab effect amount. There are no separately labeled equation controls. TECHNICAL TOPOLOGYWhat are the modeled states and equation-linked processes?Selected equation-linked states · model time unit: dayAdministered inputLatent rituximab effectamountmgCD19 b cell countcells/uLElapsed timeday
Teal arrows show relationships between modeled states and do not always represent material transfer. Peach arrows mark administered or scenario-defined entry points.

Assumptions & evidence

Assumptions & limitations

  • Conditional fixed-effect K-PD calculations; no original population fit, random effects, residual error, prediction intervals or complete paper reproduction.
  • A1_mg is a latent rituximab effect amount, not a measured plasma concentration. The model has two biological states plus a separate clock.
  • The observed clinical protocol was two weekly IV doses of 375 mg/m2, capped at 500 mg. Presets also include distinct theoretical simulation regimens, including 750 mg/m2; the clinical cap is not applied to those theoretical arms.
  • Preset doses are fixed absolute mg derived, where applicable, from BSA 0.82 m2. Editing IgA does not change doses; BSA is inspection-only. Instantaneous latent-amount additions approximate day-scale dosing; infusion durations were not reported.
  • Monthly and every-two-month schedules use 30-day and 60-day intervals. These are conditional calendar approximations.
  • IgA is the only final fixed-effect covariate. The positive 0.11–2.26 g/L exploration domain comes from the source sensitivity conditions, not a clinically validated range.
  • Ten exploratory ED50 conditions retain a different fixed multiplier for each regimen. They are additional conditional calculations, not independent validation or population predictions.
  • B-cell repletion means the first upward crossing above 10 cells/uL after depletion, measured from first treatment. Instantaneous cell count or normalized recovery alone does not calculate that event time.
  • The separate clinical survival/nomogram analysis is not implemented. No individual relapse probability, concentration PK, clearance, volume or concentration AUC is returned.
  • Changing the simulation start applies the supplied initial state there; it does not reconstruct prior doses. Fitting and normal server parameter scans are unavailable.

Parameter origins

  • Released executable model definition; exact publication locator not reported

Validation & references

One or more implementation checks are available; this is not a claim of full model reproduction.

Kinetic-pharmacodynamic model to predict post-rituximab B-cell repletion as a predictor of relapse in pediatric idiopathic nephrotic syndrome ↗

Available reference curves can be added to the plot when their scenario, readout, time and units match.

Model details

13 parameters · 3 states · 3 equations · 12 derived outputs

Classification & API access
Therapeutic
Rituximab
Modality
Monoclonal antibody
Target
CD20 / MS4A1
Disease / scope
Pediatric idiopathic nephrotic syndrome
ParameterDefaultUnitDescription
Half maximal latent effect amountED50_mg1.31mgHalf maximal latent effect amount coefficient used by the released system of model equations.
Maximum effectEmax389.71Maximum effect defining the limiting magnitude of the corresponding pharmacodynamic effect.
Latent effect amount decay rateKe_day0.0491/dayLatent effect amount decay rate coefficient used by the released system of model equations.
Zero order b cell productionKin_cells_ul_day4.14cells/uL/dayZero order b cell production coefficient used by the released system of model equations.
Turnover loss rateKout_day0.0071/dayTurnover loss rate governing loss, degradation, or removal in the modeled biological process.
B cell repletion thresholdbcell_repletion_threshold_cells_ul10cells/uLB cell repletion threshold coefficient used by the released system of model equations.
Body surface areabsa_m20.82m^2Reference body surface area used to derive fixed absolute preset doses. Inspection-only; changing IgA does not change administered doses.
Fixed exploratory ED50 multipliered50_calibration_factor11Fixed exploratory ED50 multiplier coefficient used by the released system of model equations.
Hill coefficienthill_gamma6.651Hill coefficient coefficient used by the released system of model equations.
Baseline ig a covariateiga_g_l1.15g/LBaseline ig a covariate coefficient used by the released system of model equations.
Ig a covariate exponent on ED50iga_on_ED50_power1.391Ig a covariate exponent on ED50 coefficient used by the released system of model equations.
Reference ig aiga_ref_g_l1.15g/LReference ig a coefficient used by the released system of model equations.
Validation noncevalidation_run_nonce20260708001Validation nonce coefficient used by the released system of model equations.

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