Pharmacodynamic modeling
The PD effect of inebilizumab on B cells is assayed by measuring CD20+ B cell counts, as inebilizumab interferes with CD19-based detection methods. A hematopoietic transit model was developed to describe the depletion of circulating B cell count data by inebilizumab in adults. The PD effect of inebilizumab was exerted by joint effects of reducing influx from pro-B cells and accelerating CD20+ B cell depletion in the blood, as the following differential equations demonstrate:
\(\frac{dB_{0}}{\text{dt}}\mspace{6.0mu }=\mspace{6.0mu }S_{0}-k_{\text{CD}19}\cdot\mspace{6.0mu }B_{0}-\mspace{6.0mu }k_{\text{inebi}}\mspace{6.0mu }\cdot\mspace{6.0mu }B_{0}\)Equation 1
\(\frac{dB_{1}}{\text{dt}}\mspace{6.0mu }=\mspace{6.0mu }k_{\text{CD}19}\cdot\mspace{6.0mu }B_{0}-\mspace{6.0mu }\frac{n}{\Lambda}\mspace{6.0mu }\cdot\mspace{6.0mu }B_{1}-\ k_{\text{inebi}}\mspace{6.0mu }\cdot\mspace{6.0mu }B_{1}\)Equation 2
\(\frac{dB_{i}}{\text{dt}}\mspace{6.0mu }=\mspace{6.0mu }\frac{n}{\Lambda}\mspace{6.0mu }\cdot\mspace{6.0mu }{(\ B}_{i-1}-B_{i}\ )-k_{\text{inebi}}\cdot\mspace{6.0mu }B_{i}\)Equation 3
In the above equations, n is the number of transit compartments and Λ represents the longevity (lifespan) of blood CD20+ B cells. S0 is the influx rate of pro-B cells (B0), and the total CD20+ B cell count in the blood (BCD20) is calculated as the sum of CD20+ B cells in all aging compartments (Bi, i =1 to n ):
\(B_{\text{CD}20}\mspace{6.0mu }=\mspace{6.0mu }\sum_{i=1}^{n}B_{i}\)Equation 4
The rate constant kCD19 represents the maturation of pro-B to CD20+ B cells in the circulation. Initially kinebi, the accelerated removal of CD19+ pro-B and mature B cells by inebilizumab, was described using an asymptotic Emax function. However, the estimated EC50 (inebilizumab concentration corresponding to half-maximal B cell depletion) was less than the assay LLOQ, due to the high potency of inebilizumab. As such, a log-linear relationship was used to describe the effect of inebilizumab on depletion of pro-B and mature B cells in blood:
\(k_{\text{inebi}}\mspace{6.0mu }=\mspace{6.0mu }\text{slope}\ \bullet\log C\)Equation 5
Where C represents the serum concentration of inebilizumab. From population modeling, the PD model with dual activity of inebilizumab to deplete pro-B and mature B cells was superior to the transit model where inebilizumab only depleted the circulating CD20+mature B cells. The final PD model structure is shown in Figure 2.
Pooled CD20+ B cell data from adult subjects previously diagnosed with Systemic Sclerosis (Study CP200), Multiple Sclerosis (Study 1102) and NMOSD (RCP of N-MOmentum) were simultaneously modeled. Demographic covariate screening was performed using generalized additive models implemented in an R package XPOSE4.