Pharmacodynamic modeling of the effect of changes in the environment on cellular lifespan and cellular response

Relationship between venetoclax exposure, rituximab coadministration, and progression-free survival in patients with relapsed or refractory chronic lymphocytic leukemia: demonstration of synergy

Venetoclax is indicated at a dosage of 400 mg daily (QD) for the treatment of patients with chronic lymphocytic leukemia (CLL) with 17p deletion who have received at least 1 prior therapy. Ongoing trials are evaluating venetoclax in combination with CD20 targeting monoclonal antibodies, such as rituximab. The objective of this research was to characterize the relationship between venetoclax exposures and progression-free survival (PFS) and to evaluate the effect of rituximab coadministration on PFS in patients with relapsed or refractory (R/R) CLL/small lymphocytic lymphoma (SLL). A total of 323 patients from 3 clinical studies of venetoclax, with and without rituximab coadministration, were pooled for the analyses. A time-variant relative risk survival model was used to relate plasma venetoclax concentrations and rituximab administration to PFS. Demographics and baseline disease characteristics were evaluated for their effect on PFS. A concentration-dependent effect of venetoclax on PFS and a prolonged synergistic effect of 6 cycles of concomitant rituximab were identified. The 17p deletion chromosomal aberration was not identified to affect the PFS of patients treated with venetoclax. A venetoclax dose of 400 mg daily QD was estimated to result in a substantial median PFS of 1.8 years (95% confidence interval [CI], 1.7-2.1), whereas the addition of 6 cycles of rituximab was estimated to increase the median PFS to 3.9 years (95% CI, 2.8-5.6). The analysis demonstrates a concentration-dependent effect of venetoclax on PFS and also a synergistic effect with rituximab. Combining venetoclax with the CD20 targeting monoclonal antibody rituximab in R/R CLL/SLL patients provides substantial synergistic benefit compared with increasing the venetoclax monotherapy dose.

Models for the red blood cell lifespan

The lifespan of red blood cells (RBCs) plays an important role in the study and interpretation of various clinical conditions. Yet, confusion about the meanings of fundamental terms related to cell survival and their quantification still exists in the literature. To address these issues, we started from a compartmental model of RBC populations based on an arbitrary full lifespan distribution, carefully defined the residual lifespan, current age, and excess lifespan of the RBC population, and then derived the distributions of these parameters. For a set of residual survival data from biotin-labeled RBCs, we fit models based on Weibull, gamma, and lognormal distributions, using nonlinear mixed effects modeling and parametric bootstrapping. From the estimated Weibull, gamma, and lognormal parameters we computed the respective population mean full lifespans (95 % confidence interval): 115.60 (109.17-121.66), 116.71 (110.81-122.51), and 116.79 (111.23-122.75) days together with the standard deviations of the full lifespans: 24.77 (20.82-28.81), 24.30 (20.53-28.33), and 24.19 (20.43-27.73). We then estimated the 95th percentiles of the lifespan distributions (a surrogate for the maximum lifespan): 153.95 (150.02-158.36), 159.51 (155.09-164.00), and 160.40 (156.00-165.58) days, the mean current ages (or the mean residual lifespans): 60.45 (58.18-62.85), 60.82 (58.77-63.33), and 57.26 (54.33-60.61) days, and the residual half-lives: 57.97 (54.96-60.90), 58.36 (55.45-61.26), and 58.40 (55.62-61.37) days, for the Weibull, gamma, and lognormal models respectively. Corresponding estimates were obtained for the individual subjects. The three models provide equally excellent goodness-of-fit, reliable estimation, and physiologically plausible values of the directly interpretable RBC survival parameters.

Lifespan based indirect response models

In the field of hematology, several mechanism-based pharmacokinetic-pharmacodynamic models have been developed to understand the dynamics of several blood cell populations under different clinical conditions while accounting for the essential underlying principles of pharmacology, physiology and pathology. In general, a population of blood cells is basically controlled by two processes: the cell production and cell loss. The assumption that each cell exits the population when its lifespan expires implies that the cell loss rate is equal to the cell production rate delayed by the lifespan and justifies the use of delayed differential equations for compartmental modeling. This review is focused on lifespan models based on delayed differential equations and presents the structure and properties of the basic lifespan indirect response (LIDR) models for drugs affecting cell production or cell lifespan distribution. The LIDR models for drugs affecting the precursor cell production or decreasing the precursor cell population are also presented and their properties are discussed. The interpretation of transit compartment models as LIDR models is reviewed as the basis for introducing a new LIDR for drugs affecting the cell lifespan distribution. Finally, the applications and limitations of the LIDR models are discussed.

Interpretation of transit compartments pharmacodynamic models as lifespan based indirect response models

Transit compartments (TC) models are used to describe pharmacodynamic responses that involve drug action on cells undergoing differentiation and maturation. Such pharmacodynamic systems can also be described by lifespan based indirect response (LIDR) models. The purpose of this report is to investigate conditions under which the transit compartments models can be considered a special case of LIDR models. An integral representation of a solution to TC model has been used to determine the lifespan distribution for cell population described by this model. The distribution served as a basis for definition of new LIDRE (lifespan based indirect response with an effect on the lifespan distribution) models. Time courses of responses described by both types of models were simulated for a monoexponential pharmacokinetic function. The limit response was calculated as the number of transit compartments approached infinity. The difference between the limit response and TC responses were evaluated by computer simulations using MATLAB 7.7. TC models are a special case of LIDR models with the lifespan distribution described by the gamma function. If drug affects only the production of cells, then the cell lifespan distribution is time invariant. In this case an increase in the number of compartments results in a basic LIDR model with a point lifespan distribution. When the drug inhibits or stimulates cell aging, the cell lifespan distribution becomes time dependent revealing a new mechanism for drug effect on the gamma probability density function. The TC model with a large number of transit compartments converges to an LIDRE model. The limit LIDR models are approximated by the TC models when the number of compartments is at least 5. A moderate improvement in the approximation is observed if this number exceeds 20. The lifespan distribution for a cell population described by a TC model is described by the gamma probability density function. A drug affects this distribution only if it stimulates or inhibits the rate of cell maturation. If the number of transit compartments increases, then the TC model converges to a new type of LIDR model.