Pharmacokinetic-Pharmacodynamic Modelling of Repeated Ocrelizumab Dosing in Relapsing-Remitting Multiple Sclerosis

Abstract

Background and Objective

Ocrelizumab (OCR) is an anti-CD20 monoclonal antibody approved for the treatment of relapsing-remitting multiple sclerosis (RRMS). Although the standard regimen consists of fixed 6-monthly infusions, therapeutic duration may vary between patients, highlighting the need for individualized dosing strategies. The objective of this study was to develop a pharmacokinetic-pharmacodynamic (PKPD) model able to predict patient-specific treatment responses, as a step towards a clinically applicable tool for optimizing OCR dosing precision in RRMS.

Methods

Serum OCR concentrations and CD19⁺ lymphocyte counts from 11 treatment-naïve patients with newly diagnosed RRMS were analyzed. Samples were collected over 24 weeks following the first and second OCR infusions. Data were analyzed using a nonlinear mixed-effects population modelling approach in Monolix Suite 2023R1, with parameter estimation performed via the stochastic approximation expectation-maximization algorithm. Several structural models were evaluated, and model performance was assessed by fit statistics and visual predictive checks.

Results

The resultant two-compartment PKPD model successfully described OCR disposition and CD19⁺ lymphocyte depletion/repopulation. The final model included clearance of OCR without target-mediated elimination and described the effect of OCR on the dynamics of CD19⁺ lymphocyte counts. Simulations demonstrated the ability of the model to estimate the time to CD19⁺ lymphocyte repopulation and to explore optimal time for follow-up measurements.

Conclusion

A novel PKPD model for OCR in RRMS that integrates drug exposure and CD19⁺ lymphocyte kinetics is presented. Although a small number of patients is included in the current study, this framework represents an important step toward clinically applicable, model-informed dosing strategies, with the potential to enhance treatment precision and support personalized therapy in RRMS.

Clinical Trials Registration Number

OVERLORD-MS: NCT04578639, ROS-MS: NCT06663111.

Supplementary Information

The online version contains supplementary material available at https://doi.org/10.1007/s40262-026-01692-8.

Key Points

A new population pharmacokinetic-pharmacodynamic (PKPD) model was developed to describe ocrelizumab serum concentrations and CD19⁺ lymphocyte depletion and repopulation in relapsing-remitting multiple sclerosis (RRMS).

The model successfully captured both drug disposition and CD19+ lymphocyte depletion/repopulation trajectories and allowed for estimation of patient-specific time to cell repopulation.

This framework supports the development of personalized, model-informed ocrelizumab dosing strategies to optimize treatment duration, reduce unnecessary drug exposure, and improve precision therapy in RRMS.

Introduction

Multiple sclerosis (MS) is a chronic, immune-mediated condition characterized by demyelinating lesions and axonal injury within the central nervous system [1, 2]. While its precise cause remains uncertain, accumulating evidence implicates both T cells and B cells in the underlying disease mechanisms, with MS increasingly regarded as a rare complication of prior Epstein–Barr virus (EBV) [3]. B cells are thought to play a key role through mechanisms such as antigen presentation, secretion of cytokines, and production of autoantibodies [4–6]. This has led to the development and use of therapeutic monoclonal antibodies (t-mAbs) directed against CD20, a surface protein found on pre-B cells, mature B cells, and memory B cells as a targeted approach for B-cell depletion [7–11]. By binding selectively to CD20, t-mAbs enable efficient elimination of B cells, resulting in therapeutic effects. Although the full basis for the clinical efficacy of anti-CD20 agents in MS has not been completely defined, engagement of CD20 by t-mAbs is known to initiate several immune-mediated mechanisms, including antibody-dependent cellular cytotoxicity, phagocytosis, induction of apoptosis, and complement-mediated B-cell lysis. Moreover, B cells function as both the cellular target and long-term reservoir of EBV), facilitating its chronic lifelong infection [12].

Ocrelizumab (OCR), a humanized recombinant t-mAb designed to selectively bind the CD20 antigen on B cells, was the first such drug to receive regulatory approval for the treatment of relapsing-remitting MS (RRMS) [13]. The approved regimen consists of 600 mg administered by intravenous infusion every 6 months. Analyses of clinical trial data, however, suggest that the duration of therapeutic effects of OCR may diverge from the approved dosing interval, exhibiting either a shorter or, more frequently, prolonged effect [14, 15]. These observations are supported by studies in which treatment was individualized to the patient [16]. If the accumulated OCR dose could be reduced correspondingly, for example by increasing the dosing interval, this could likely benefit patients by lowering the risk of adverse effects. This could also reduce cost, as OCR is an expensive treatment, with an estimated annual cost of US$78,858 [17].

A specific approach allowing individualization of OCR dosing in RRMS is currently lacking. To enable individualized dosing predictions, it is essential to determine whether a mathematical representation that captures the pharmacokinetic (PK) and pharmacodynamic (PD) processes (commonly referred to as a PKPD model) can be identified [18]. Once the PKPD model is established, it can be used to generate individualized predictions. The model’s validity is assessed by its ability to accurately reproduce observed data, specifically by evaluating the concordance between measured PKPD values and model-derived estimates.

Based on data from the patient arm receiving OCR in an ongoing randomized controlled trial comparing OCR and rituximab (RTX) in treatment-naïve patients with RRMS, a PKPD model incorporating repeated OCR dosing is presented. In line with previous reports regarding anti-CD20 therapy, while acknowledging that further studies are required to define how lymphocyte counts relate to CNS inflammatory activity, quantification of CD19⁺ lymphocytes was employed as a PD marker [9, 15, 19, 20]. The resultant model captures both drug concentrations and CD19⁺ lymphocyte counts at the individual patient level. This represents an important step toward a clinically applicable tool for optimizing OCR dosing precision in RRMS.

Methods

Study Design and Patient Population

The patient material analyzed in this study was collected through the Rituximab and Ocrelizumab in Serum from patients with Multiple Sclerosis (ROS-MS) study [21], a sub-study of the Ocrelizumab Versus Rituximab Off-Label at the Onset of Relapsing MS Disease (OVERLORD-MS) trial [22]. ROS-MS was approved by the Regional Committee for Medical and Health Research Ethics (reference #228768), and all participants gave written informed consent specifically for this sub-study. No previously used data was included.

In the OVERLORD-MS trial, treatment-naïve patients of both sexes, aged 18 to 60 years and recently diagnosed with RRMS, were randomized in a 2:1 ratio to receive either RTX or OCR. OCR treatment was given as a 600-mg intravenous infusion every 6 months. Each infusion lasted approximately 4 hours.

Blood samples for PK and PD parameter quantitation were obtained both immediately before and within 30 min following the initial infusion, as well as 2, 4, 8, 12, and 24 weeks post-infusion. This analysis is based on 0–24-week serum samples from 11 individuals after receiving their first and second OCR dose. Patient height and weight were collected in the electronic data capture system.

Ocrelizumab in Serum

Blood samples were collected in clot-activator tubes, allowed to clot at room temperature for 30 min, and centrifuged at 1400g for 12 min. The resulting serum was aliquoted, stored at 4 °C for up to 6 days due to logistical constraints, and then frozen at − 80 °C until analysis. OCR concentrations were measured using a liquid chromatography-tandem mass spectrometry (LC-MS/MS) method as described in Hallin et al. (2024), with some modifications [23, 24]. In short, OCR was partially purified from serum samples using caprylic acid precipitation, followed by enzymatic digestion using trypsin. The resulting digests were then analyzed by LC-MS/MS. The assay’s lower limit of quantification (LLOQ) was 4 µg/mL, and the upper limit (ULOQ) was 256 µg/mL. Full methodological details, including validation procedures, are available in Supplementary Material 1 (see electronic supplementary material [ESM]).

CD19⁺ B-Cells in Blood

As OCR may interfere with the detection of CD20 via flow cytometry, CD19 was employed as a proxy marker due to its comparable expression pattern on B cells [7]. For CD19⁺ lymphocyte quantification, blood was collected in EDTA tubes and kept at room temperature for no more than 48 hours prior to analysis. CD19⁺ lymphocyte counts were determined using flow cytometry on the Facs Lyric™ platform (BD Biosciences, San Jose, CA, USA), utilizing the BD Multitest™ 6-color TBNK reagent. Results are expressed in cells per cubic millimeter (mm⁻³), with a lower detection limit of 2 mm⁻³ and a quantification threshold of 7 mm⁻³.

Development of Pharmacokinetic and Pharmacokinetic-Pharmacodynamic Models

Data was analyzed using a population approach with the nonlinear mixed-effects modelling software Monolix Suite 2023R1 (Lixoft, Antony, France). Parameter estimation was performed with the stochastic approximation expectation–maximization (SAEM) algorithm [26]. The variability model and error models applied in the development of PK and PKPD models are described in Sect. 2 in the ESM. To evaluate the performance of different models, we used the negative log-likelihood (-2LL) for nested models and the corrected Bayesian Information Criterion (BICc) for unnested models, where the model with the lowest value was considered the best at describing our data without overfitting. Covariates (age, weight, BMI, sex) were tested on all parameters with the automated stepwise forward addition followed by backward deletion in Monolix (αforward = 0.01, αbackward = 0.001). Uncertainty on parameter estimates and visual predictive check (VPC) plots were also considered when selecting the final model. Figures were generated in R studio [27]. Further details are found in Supplementary Material 2 (see ESM).

The 2-compartment PK model with time-dependent clearance published by Gibiansky et al. is, to our knowledge, the only published model on OCR in patients with RRMS [19]. Here, the total clearance of OCR was expressed as the sum of constant clearance and time-dependent clearance, which declined exponentially with time on treatment:

$${\text{CL}}_{\text{total}}={\text{CL}}_{\text{inf}}+{\text{CL}}_t={\text{CL}}_{\text{inf}}+{\text{CL}}_{T0}·e^{-k_{\text{des}}·t}$$ 1

where ${\text{CL}}_{\text{total}}$ is the total OCR clearance, ${\text{CL}}_{\text{inf}}$ is the constant OCR clearance and ${\text{CL}}_t$ is the time-dependent OCR clearance, given by this equation:

$${{\text{CL}}_t=\text{CL}}_{T0}·e^{-k_{\text{des}}·t}$$ 2

${\text{CL}}_{T0}$ is the initial value of the time-dependent part of the clearance, and k_des is the rate constant governing the time-dependent decline in clearance. This would give the differential equations:

$$\frac{\text{d}C}{\text{d}t}=-\frac{Q}{V_1}·C+\frac{Q}{V_1}·P-\frac{{\text{CL}}_{\text{inf}}}{V_1}·C-\frac{{\mathit{CL}}_{T0}·e^{-k_{\text{des}}·t}}{V_1}·C,C\left(0\right)=C_0$$ 3

$$\frac{\text{d}P}{\text{d}t}=\frac{Q}{V_2}·C-\frac{Q}{V_2}·P,P\left(0\right)=P_0$$ 4

where C and P are the OCR concentrations in the central- and peripheral compartment, respectively, and Q is the intercompartmental clearance. $V_1$ and $V_2$ are the volume of distribution in the central- and peripheral compartments, respectively. C₀ is Dose/$V_1$ and P₀ is 0.

The model also included a separate CL_T02 for patients continuing OCR treatment in an open-label extension, where the time was reset to zero following partial CD19⁺ lymphocyte recovery. Because the time-dependent OCR clearance in Eq. 1 is modelled by exponential decay, it is bound to decrease and eventually reach 0 as time increases. Assuming that this decline is due to target-mediated elimination by CD19⁺ lymphocytes, resetting the time is the only way for this model to allow for cell repopulation.

Pharmacokinetic-Pharmacodynamic Model 1

Starting from the PK model by Gibiansky et al. presented above (Eqs. 3 and 4), we considered the exponential decline in OCR clearance in the Gibiansky model as target-mediated elimination, which could then be modelled by the CD19⁺ lymphocyte counts expressed as B and incorporated into the OCR clearance:

$$\frac{\text{d}C}{\text{d}t}=-\frac{Q}{V1}·C+\frac{Q}{V1}·P-\frac{{\mathit{CL}}_{T0}}{V1}·C·B-\frac{\mathit{CL}}{V_1}·C,C\left(0\right)=C_0$$ 5

$$\frac{\text{d}P}{\text{d}t}=\frac{Q}{V_2}·C-\frac{Q}{V_2}·P,P\left(0\right)=P_0$$ 6

A PD equation quantifying the effect of OCR concentration on CD19⁺ lymphocytes was also added to the model, following the framework of irreversible binding approximation within the target-mediated drug disposition.

$$\frac{\text{d}B}{\text{d}t}=k_{\text{in}}-k_{\text{deg}}·C·B-k_{\text{out}}·B,B\left(0\right)=B_0$$ 7

In these equations, C and P are the serum concentrations of OCR in mg/L in the central and peripheral compartments, respectively, and Q is the intercompartmental clearance. $V_1$ and $V_2$ are the volumes of distribution in the central and peripheral compartments, respectively. B corresponds to the count of CD19⁺ lymphocytes per cubic millimeter. ${\text{CL}}_{T0}$ has units of L/day/CD19⁺ count and ${\text{CL}}_{T0}$/V₁ is the rate constant for the target-mediated OCR elimination. CL/V₁ is the rate constant for the target-independent elimination of OCR from the central compartment. The production and loss of CD19⁺ cells are described by the rates k_in and k_out, respectively, and k_deg is the OCR-dependent elimination rate constant for CD19⁺ cells.

A simplified version of the PK model was made by removing the target-mediated elimination of OCR:

$$\frac{\text{d}C}{\text{d}t}=-\frac{Q}{V_1}·C+\frac{Q}{V_2}·P-\frac{\mathit{CL}}{V_1}·C,C\left(0\right)=C_0$$ 8

with CL/V₁ being the rate constant for target-independent OCR elimination from the central compartment, C and P the serum concentrations of OCR in mg/L in the central and peripheral compartments, respectively, and Q the intercompartmental clearance. $V_1$ and $V_2$ are the volumes of distribution in the central and peripheral compartments, respectively.

Pharmacokinetic-Pharmacodynamic Model 2

With the simplified PK model, a different expression of the PD equation was tested:

$$\frac{\text{d}B}{\text{d}t}=k_{\text{in}}-k_{\text{out}}·\left(1,+,\frac{E_{\text{max}}·C}{{\text{EC}}_{50}+C}\right)·B,B\left(0\right)=B_0$$ 9

Here, the production and loss of CD19⁺ cells are described by the rates k_in and k_out, respectively, E_max is the maximum increase in CD19⁺ lymphocytes elimination in the presence of OCR, while EC₅₀ is the concentration at which 50% of the maximum increase is reached. This E_max model was inspired by the model by Pan et al. describing the PD of RTX on B lymphocytes in pediatric patients with a sigmoidal, RTX-dependent decrease in B lymphocytes [25].

Model Incorporation of CD19⁺ Lymphocyte Count

The baseline CD19⁺ lymphocyte count for each individual was either fixed to the baseline observations:

$$B_{0,i}=B_{0,m}$$ 10

or modelled by adding a random effect to the observed baseline to account for measurement errors:

$$B_{0,i}=B_{0,m}·e^{{\eta }_{B0,i}}$$ 11

whereby B_0,m is observed baseline CD19⁺ cell count and ${\eta }_{B0,i}$ is the measurement error drawn from a normal distribution with mean 0 and variance ω_B0 [28]. For two patients with missing $B_{0,m}$, the population median value was used.

Since low CD19⁺ measurements were frequently reported as zero, these were treated as censored, applying the Monolix implementation of the M3 method and applying the lower limit of quantification at 7 per mm³ [29]. CD19⁺ measurements reported above 0 but below 7 were not censored, as this is the ideal approach when measurements below the limit of quantification actually are reported [30].

Generation of Virtual Patient Populations

Nonlinear mixed effect models can be used to create populations of virtual patients by sampling sets of different parameter values from the estimated population parameter distributions and running simulations with these sampled parameter sets. These virtual patient trajectories can then serve as prior knowledge in a Bayesian updating step where the likelihood of a patient's individual data is used to update the prior into a patient-specific posterior. The importance of sampling-based particle filtering method as outlined in Secs. 11.1. and 11.2. in the book “Bayesian Filtering and Smoothing” by Simo Särkkä and Lennart Svensson was followed [31]. This approach was used to assess the predictive power of model 1. Based on the model, the question whether OCR measurements within the first 3 months after treatment can inform about when a patient’s B cells will repopulate a few months later was addressed. To start with, 1000 model simulations with 1000 different parameter sets sampled from the estimated population parameter distributions for each patient were performed, thereby using only the initial CD19⁺ lymphocyte count as patient-specific data. This represents a virtual patient cohort for each patient, where all virtual patients have equal statistical weight. Using these virtual patient simulations, the time-dependent probabilities for B-cell repopulation for each patient were approximated. Consistent with prior studies evaluating extended OCR dosing intervals, and other anti-CD20 t-mAbs, the threshold for initiating a new infusion due to repopulation was defined as a CD19⁺ lymphocyte count of 10 per mm³ [16, 32]. Hence, how many of the virtual patients exceeded this threshold was counted on each day and these numbers were divided by the total number of virtual patients (N = 1000) to approximate the probabilities. Patient-specific OCR measurements were then included to compute the least-squares errors errLSQ_i, i = 1,...1000, between the predicted OCR values of all 1000 virtual patient simulations and the measured concentrations. These 1000 different error values were used to re-weight all virtual patients with the likelihoods exp(− errLSQ_i)/sum_i(exp(− errLSQ_i)) and to re-compute for all days the weighted sums of virtual patients in which the CD19⁺ lymphocyte count exceeds 10 mm⁻³. The theoretical foundation for this approach is outlined in Supplementary Material 3 (see ESM). The re-weighting with the likelihood was repeated by using the first two, three, and finally four OCR measurements as well as using only the 2nd, 3rd, or 4th OCR measurement. The predictions were compared to figure out how the predictions change depending on the number of included measurements, and whether it is possible to differentiate patients in whom B cells repopulate early from those patients in whom B cells repopulate at later times.

Results

A cohort of 11 patients with newly diagnosed RRMS was enrolled, and 114 serum samples were collected. None of the participants had previously received disease-modifying therapies. Baseline demographic and clinical characteristics are summarized in Table 1, while Fig. 1 depicts the distribution of measured OCR concentrations and CD19⁺ lymphocyte counts. As expected, a steep decline in CD19⁺ lymphocyte counts was observed in all patients, along with interindividual variability in drug concentrations as previous reported [33, 34]. The subsequent sections describe the PK and PKPD models that provided the best fit to the data.

Table 1.

Baseline demographic and clinical characteristics

Age: mean years (range)	36 (22–50)
Gender: F/M	8/3
Weight (kg): mean (range)	73 (61–96)
Height (cm): mean (range)	169 (156–187)
Baseline CD19+ lymphocyte count (mm−3): mean (range)	297 (127–726)

Fig. 1.

Ocrelizumab (OCR) serum concentration A development and CD19⁺ lymphocyte count B over time for 11 patients, with y-axis on a log scale

Pharmacokinetic-Pharmacodynamic Analysis and Model Selection

To account for CD19⁺ lymphocyte repopulation with repeated OCR infusions, a PKPD model with target-mediated elimination was developed as outlined in Sect. 2.4.1. We first attempted to estimate all parameters, but this resulted in an unstable model with high uncertainties on the parameters (data not shown). Therefore, initial CD19⁺ lymphocyte counts in the absence of OCR were assumed to be in steady state, and k_in = B₀ ∙ k_out was set, giving this differential equation for the CD19⁺ lymphocytes:

$$\frac{\text{d}B}{\text{d}t}={B_0·k}_{\text{out}}-k_{\text{deg}}·C·B-k_{\text{out}}·B,B\left(0\right)=B_0$$ 12

This model also had issues with the identifiability of CL_T0 and k_out, which had to be fixed to the estimates from the Gibiansky model and the Pan et al. model, respectively [19, 25] (Supplementary Table S1, model 1 with TMDD, see ESM).

Since this model relied on fixing several parameters, it was simplified as outlined in Sect. 2.4.2 by removing the target-mediated elimination from the PK model. This improved the model fit and stability of the parameter estimates substantially (Table S1, model 1 without TMDD, ESM), although k_out still had to be fixed. It was attempted to fix k_out to another biologically plausible estimate from a study on the kinetics of B cells (k_out = 0.039) [35], but this introduced large uncertainties on k_deg, highlighting the dependency between these two parameters. k_out was subsequently fixed to the estimate from Pan et al. (k_out = 0.02).

Continuing with the simplified PK model without target-mediated elimination, model 2 presented in Sect. 2.4.2 was tested to see if the model fit could be improved further. This resulted in a stable model with precisely estimated parameters, but with a drastically worse model fit (Table S1, ESM).

The final PKPD model included random effects on CL, V₁, and V₂, and incorporated observed baseline CD19⁺ lymphocyte counts without random effects (Table 2). Inclusion of covariates was tested on all parameters but was not supported as it introduced large parameter uncertainties. The VPCs indicated an overall good model fit for both the OCR concentrations and the CD19⁺ lymphocytes but showed a slight overprediction of OCR concentrations in the 10th and 50th quantiles around the time of the second infusion (time = 200), and also reflects the sparse CD19⁺ lymphocyte data, especially in the lower quantiles (Supplementary Fig. 1, ESM). The individual model fit to one of the patients in the cohort with repopulation demonstrated that the final model was able to predict the increase in the CD19⁺ lymphocyte count (Fig. 2A and B).

Table 2.

Estimated model parameters for the final model

Model parameters (unit)	Estimate (RSE%)	95% CI
Fixed effects
V1 (L)	2.58 (4.49)	2.37–2.82
V2 (L)	1.95 (5.54)	1.75–2.17
CL (L/day)	0.153 (7.21)	0.133–0.177
Q (L/day)	0.220 (15.7)	0.163–0.298
kout (1/day)	0.02 (fixed)
kdeg (L/(day⋅mg))	1.70 (32.6)	0.94–3.09
Standard deviation of the random effects
ωV1	0.138 (23.9)	0.0882–0.217
ωV2	0.109 (40)	0.0534–0.221
ωCL	0.234 (22.2)	0.154–0.357
Error model parameters
σadd,OCR	0.545 (17.4)	0.390–0.761
σprop,OCR	0.0662 (13.5)	0.0510–0.0859
σadd,CD19+	2.28 (14.6)	1.72–3.02

CI confidence interval, CL target-independent clearance rate constant of OCR from the central compartment, k_deg OCR-dependent elimination rate constant for CD19⁺ lymphocytes, k_out loss rate constant for CD19⁺ lymphocytes, OCR ocrelizumab, ω standard deviation of the random effects (interindividual standard deviation), Q intercompartmental clearance rate constant of OCR, σ_add absolute error, σ_prop relative error, RSE relative standard error, V1 volume of distribution in the central compartment, V2 volume of distribution in the peripheral compartment

Fig. 2.

Individual model fit of the final indirect response model to ocrelizumab (OCR) serum concentrations (A) and CD19⁺ lymphocyte counts (B), with a log-transformed y-axis

Model-Based Prediction of B-Cell Dynamics Based on Ocrelizumab Measurements

Since model 1 was the best at describing the CD19⁺ lymphocyte counts and also had the most stable parameter estimates, this model was used to illustrate how the predictive power of the model can be assessed via simulations of virtual patient populations. Figure 3 illustrates the approach for one particular patient (ID1). First, 1000 different trajectories were generated by sampling 1000 different parameter sets from the parameter distributions of the NLME model and using the initial CD19⁺ lymphocyte count of this particular patient (Fig. 3A). The simulations show a wide distribution of days on which the threshold of 10/mm³ is exceeded (Fig. 3C). Including the OCR measurements after weeks 2, 4, 8, and 12 and reweighting the statistical weights of the trajectories with their likelihoods shifts the distribution towards earlier times for B-cell repopulation (Fig. 3B and supplementary Fig. S3 in the ESM). The distribution gets narrower and thus the cumulative distribution steeper (Fig. 3D), demonstrating a decrease in the uncertainty of the prediction. This procedure was repeated for all available patients, except patient ID10 for whom the OCR measurements after weeks 2 and 4 were missing. Fig. 4 shows the cumulative distribution functions for the probability of exceeding a CD19⁺ lymphocyte count of 10/mm³ before a certain day. As shown in Fig. 4A, including only the initial CD19⁺ lymphocyte count does not allow differentiation between patients in whom B cells repopulate by month 6 (patients 1, 7, 8, solid lines) and patients without B-cell repopulation (dashed lines).

Fig. 3.

Illustration of the full Bayesian modelling approach for patient ID1. The grey solid lines in A show the simulated CD19⁺ lymphocyte counts for 1000 virtual patients with model parameters sampled from the population parameter distributions of the NLME model and initial CD19⁺ lymphocyte count equal to the measurement for patient 1 (B₀ = 144/mm³). The solid blue line shows the median of these 1000 trajectories, while the dashed blue lines are the 0.05 and 0.95 quantiles. The dot-dashed red line marks the threshold for B-cell repopulation (10/mm³). B shows the same 1000 trajectories, but this time the grey scale indicates their statistical weight after re-weighting with the likelihood based on the first four OCR measurements (weeks 2, 4, 8, and 12). The median is shifted slightly towards earlier times, and the quantiles get closer to the median, indicating a smaller prediction uncertainty. C and D show the (weighted) histograms (relative frequency) of days when the CD19⁺ lymphocyte counts exceed the threshold of 10/mm³ (when the grey trajectories in A and B cross the red dot-dashed line), together with the empirical cumulative distribution function. The cumulative distribution shows for each of the days 0...500 the percentage of virtual patients for whom the CD19⁺ lymphocyte count exceeded the threshold of 10/mm³, as a measure for the repopulation probability

Fig. 4.

Prediction with the indirect response model of the time-dependent probability of reaching a CD19⁺ lymphocyte count above 10 mm⁻³ after an infusion of ocrelizumab (OCR) 600 mg when only the initial CD19⁺ lymphocyte count (B₀) is taken into account (A), or the initial CD19⁺ lymphocyte count and three follow-up OCR measurements 2, 4, and 8 weeks after infusion (B). Using only the initial CD19⁺ lymphocyte count and the 3rd OCR measurement leads to similar predictions (C). If the initial CD19⁺ lymphocyte count is discarded from the measurements, a later increase is predicted for patient 6, but an earlier increase for patient 11 (D). Note that patient 10 is lacking in the plots because the first two measurement time points (weeks 2 and 4) were not available for this patient

Hence, how these predictions change when including an increasing number of OCR measurements was explored. Figure 4B shows the approximated probabilities for B-cell repopulation in all patients when the first three OCR measurements at weeks 2, 4 and 8 are taken into account. For the three patients where B cells repopulate according to the data (patients 1, 7, 8, solid lines), the model predicts an earlier increase in the probability compared with the other patients. However, the model also predicts an early increase in CD19⁺ lymphocytes in patient 6 even though the data do not confirm this. The reason is a strong bias in the predicted B-cell dynamics towards the initial CD19⁺ lymphocyte count; the higher the initial count, the higher the simulated count at later points in time, and patient 6 has the highest initial count among all patients. Of note, the predictions do not change much by including the fourth OCR measurement, or when only using the OCR measurement at week 8 (Fig. 4C). The reason is that, in the current patient population, the OCR measurements after 8 weeks alone would enable a classification since those patients whose B cells repopulate before 6 months have the lowest OCR measurements at week 8. However, this might be the case just by chance in the patient cohort and needs to be tested in larger cohorts. Moreover, while the OCR measurements alone without a model would enable classification (early versus late repopulation), only model-based predictions provide insights into the possible dynamics of B-cell repopulation.

How discarding the initial CD19⁺ lymphocyte count influences the predictions of B-cell dynamics was also checked. The starting point was with the same virtual patient cohort for each patient based on the population average initial CD19⁺ lymphocyte count (B0_pop = 246.7), followed by repetition of the consecutive reweighting of the virtual patients based on the patient-specific OCR measurements. As shown in Fig. 4D, the model now predicts a later increase in the probability for B-cell repopulation for patient 6, but an earlier increase for patient 11.

Based on the model predictions, threshold values for clinical decision support could be suggested. For example, based on the predictions in Fig. 4 and a threshold on the repopulation probability, one could suggest the time at which this threshold is exceeded as the time for the next follow-up measurement of CD19⁺ lymphocytes. Alternatively, one could examine more closely the distribution of days when the simulations exceed the threshold of 10 CD19⁺ lymphocytes per mm³, or the distribution of CD19⁺ lymphocyte counts in the simulations at particular time points, such as after 26 weeks (see Supplementary Fig. S4, ESM), and define thresholds for certain quantiles to decide on the time for the next measurement. To derive meaningful results, however, such strategies need to be validated on a larger patient cohort, especially on data that were not used to parameterize the model and on data that include more patients with a repopulation of B cells.

Discussion

The first PKPD model describing the trajectory of both the OCR concentrations and the CD19⁺ lymphocyte counts, with an incorporation of a one-directional relationship between OCR concentrations and CD19⁺ lymphocyte counts, is presented. Precisely capturing the effect of CD19⁺ lymphocyte counts on OCR elimination remains challenging, and OCR elimination was therefore best described as independent of CD19⁺ lymphocyte counts. Most importantly, the model is able to capture repopulation of CD19⁺ lymphocytes after OCR infusion, thus enabling modelling of repeated infusions of OCR in RRMS. Together, the profiles of OCR serum concentrations and CD19⁺ lymphocyte counts provide insight into the time window during which therapeutic effects can be expected in individual patients. This constitutes a key step toward the development of a clinically applicable tool for optimizing OCR dosing in RRMS.

Two different models describing CD19⁺ lymphocyte dynamics were evaluated, where model 1 and model 2 represent a slow and rapid OCR-dependent degradation of CD19⁺ lymphocytes, respectively. If IC50 had been large compared with the OCR concentrations, these two models would have been identical, but this was not the case. A hypothesis is that the rapid OCR-dependent degradation of CD19⁺ lymphocytes described in the final model reflects the underlying biological mechanisms, but more frequent sampling of CD19⁺ lymphocyte counts in the first days or week after OCR infusion is needed to confirm this.

At the current stage, the model is able to offer a description of OCR and CD19⁺ lymphocyte trajectories in patients with RRMS treated with OCR. Before treatment is initiated, the CD19⁺ lymphocyte count can be measured and provided to the model. The model offers individualized descriptions of OCR concentration trajectories and lymphocyte counts. This description can represent the first step towards individualizing treatment, constituting a tool in computing the optimal infusion intervals. Combined, the predictions of OCR serum concentrations and CD19⁺ lymphocyte counts can provide an indication of the period during which the drug will exert its therapeutic effect, although further investigation is required to determine the relationship between CD19⁺ lymphocyte counts and CNS inflammatory disease activity [9, 20]. An additional measurement of CD19⁺ lymphocyte count, for instance one week after infusion, is expected to significantly reduce the uncertainty in model parameters and hence model predictions, as this would be informative for lymphocyte decline after infusion. This would also allow for clearer comparison between model 1 and model 2, as the two mainly differ in the CD19⁺ lymphocyte dynamics shortly after infusion.

OCR concentrations were quantified using LC-MS/MS, which minimizes interference commonly observed with antibody-based assays [36, 37]. Although the LLOQ of LC-MS/MS is generally higher than that of ELISA methods, its detection range was sufficient for assessing OCR initiation in RRMS. The clinical significance of anti-drug antibodies (ADA) in therapeutic mAb treatment, and specifically in OCR therapy for MS, remains debated [38]. While several studies suggest a limited impact of ADA in OCR-treated RRMS patients, the possibility of clinically relevant ADA formation cannot be excluded, particularly in cases of accelerated OCR clearance and incomplete CD19⁺ lymphocyte depletion. Future investigations should therefore continue to explore the role of ADA in this context.

Key limitations of this study include the modest cohort size and the relative homogeneity of participants in terms of sex and disease stage, which may limit the generalizability of the findings. Due to the limited amount of informative CD19⁺ lymphocyte data in the first 2 weeks after infusion, OCR-dependent elimination of CD19⁺ lymphocytes (k_deg) could therefore not be estimated without simultaneously fixing the CD19⁺ lymphocytes loss (k_out) to the estimate from the model of Pan et al. [25]. These parameter identifiability issues made the modelling approach challenging and the final model had to depend on some prior knowledge. To better evaluate the predictive performance of this model, more data on patients with repopulation of CD19⁺ lymphocytes is needed. On the other hand, study design was strengthened by frequent sampling, a rigorous collection schedule, and the use of a high-precision LC-MS/MS methodology to quantify serum OCR in previously drug-naïve patients, thereby avoiding potential interference from prior pharmacological exposure. Although sparse, the data from the present cohort were sufficient to support the development of a PKPD model able to inform predictions of CD19⁺ lymphocyte dynamics. Further refinement and clinical implementation of the model should be pursued by applying it to larger datasets and incorporating patient-specific covariates.

Conclusion

In this study, a PKPD model capable of jointly describing ocrelizumab serum concentrations and CD19⁺ lymphocyte dynamics in patients with RRMS was established. The model successfully captured both drug disposition and B-cell depletion/repopulation trajectories and allowed for estimation of patient-specific time to B-cell repopulation. These results demonstrate the potential of PKPD modelling as a step toward individualized dosing of ocrelizumab, with the ultimate aim of improving treatment precision and reducing unnecessary drug exposure. While validation in larger and more diverse patient cohorts remains essential, the current findings establish a methodological framework that may serve as the foundation for clinically applicable, model-informed dosing strategies in RRMS.

Supplementary Information

Below is the link to the electronic supplementary material.

Funding

Open access funding provided by University of Bergen (incl Haukeland University Hospital). The study was funded by the Department of Medical Biochemistry and Pharmacology (MBP), Haukeland University Hospital. Open access funding was provided by University of Bergen. The research of SR was funded by Trond Mohn Research Foundation (Grant Number BFS2017TMT01). KMM and ØT were funded by the Research Council of Norway through Neuro-SysMed Center of Excellence funding scheme (Grant Number 288164), and KLINBEFORSK (Grant Number 2019202).

Declarations

Conflict of Interest

ØT has received speaker honoraria from and/or served on scientific advisory boards for Biogen, Sanofi-Aventis, Merck, Teva, Gilead and Novartis; and has participated in clinical trials organized by Biogen, Merck, Novartis, and Roche. KMM has received unrestricted research grants to his institution and scientific advisory board, and speaker honoraria from Sanofi, Novartis, and Alexion, and has participated in clinical trials organized by Biogen, Merck, Novartis, Sanofi and Roche. TTS, AKFO, SS, EIH, MHØ, GON and SR declare no conflicts of interest.

Availability of Data and Material

Original data, Monolix files and R scripts to reproduce the results and figures in this manuscript are provided in Zenodo (link https://doi.org/10.5281/zenodo.17184648).

Ethical Approval

The clinical studies described in this publication were approved by the regional committees for medical and health research ethics (REK approval nos. 66391, 228768) and conducted in accordance with the Declaration of Helsinki. All patients provided written informed consent to participation in the OVERLORD and ROS-MS studies.

Author Contributions

Conceptualization: TTS, SS, EIH, KMM, ØT, SR; Methodology: TTS, AKFO, SS, EIH, SR; Formal analysis and investigation: TTS, AKFO, EIH, SR; Writing—original draft preparation: TTS, AKFO, SS, SR; Writing—review and editing: TTS, AKFO, SS, EIH, KMM, ØT, MØH, GON, SR; Funding acquisition: TTS, SS; Resources: TTS, SS, GON, KMM, ØT; Supervision: SS, EIH, SR; Project administration: TTS, SS.

Consent to Publish

Not applicable.

Consent to Participate

All participants provided written informed consent to participate in this study.

Code Availability

Ll code used in this analysis is available in the project repository at Zenodo.