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Chimeric antigen receptor T cell (CAR‐T cell) therapies have shown significant efficacy in CD19+ leukemias and lymphomas. There remain many challenges and questions for improving next‐generation CAR‐T cell therapies, and mathematical modeling of CAR‐T cells may play a role in supporting further development. In this review, we introduce a mathematical modeling taxonomy for a set of relatively simple cellular kinetic‐pharmacodynamic models that describe the in vivo dynamics of CAR‐T cell and their interactions with cancer cells. We then discuss potential extensions of this model to include target binding, tumor distribution, cytokine‐release syndrome, immunophenotype differentiation, and genotypic heterogeneity. [ABSTRACT FROM AUTHOR]

Reactivegranulation is a complex process which brings about a physical andchemical change in the raw materials. It is extensively used for theproduction of detergents through the “dry neutralization”reaction. In this paper, the dynamics of the reactive granulationprocess is captured using a coupled multidimensional population balancemodel (PBM) for the size enlargement and a diffusion-reaction (DR)equation for the kinetics of the reaction. This framework can capturethe experimental observations that have also been reported in Schöngutet al. (Ind. Eng. Chem. Res.2011, 50, 11576). There are a few empirical parameters involvedin the modeling framework for which a dynamic sensitivity analysiswas employed to shortlist the parametric quantities that have thelargest influence on the critical quality attributes. The model iscalibrated against experimental results via the Nelder–Meadsimplex algorithm for estimating the empirical parameters, and themodel predictions were compared with experimental results. Both theparameter estimation and prediction results showed good agreementwith the experimental results. The development in terms of a comprehensivemathematical model and the results as presented in this paper suggestthe ability of this approach to make suitable model predictions whichcan significantly reduce the number of experimental trials requiredfor process optimization and control. [ABSTRACT FROM AUTHOR]

This study is concerned with the development of an integrated three-dimensional population balance model (PBM) that describes the combined effect of key granulation mechanisms that occur during the course of a granulation process. Results demonstrate the importance of simulating the different mechanisms within a population balance model framework to elucidate realistic granulation dynamics. The incorporation of liquid addition in the model also aids in demarcating the dynamics in different regimes such as premixing, granulation (during liquid addition) and wet massing (after liquid addition). For the first time, the effect of primary particle size distributions and mode of binder addition on key granule properties was studied using an integrated PBM. Experimental data confirms the validity of the overall model as compared to traditional models in the literature that do not integrate the different granulation mechanisms. [ABSTRACT FROM AUTHOR]

The purpose of the current work is to study the effects of high-shear wet granulation process parameters on granule characteristics using both experimental and modeling techniques. A full factorial design of experiments was conducted on three process parameters: water amount, impeller speed and wet massing time. Statistical analysis showed that the water amount has the largest impact on the granule characteristics, and that the effect of other process variables was more pronounced at higher water amount. At high water amounts, an increase in impeller speed and/or wet massing time showed a decrease in granule porosity and compactability. A strong correlation between granule porosity and compactability was observed. A three-dimensional population balance model which considers agglomeration and consolidation was employed to model the granulation process. The model was calibrated using the particle size distribution from an experimental batch to ensure a good match between the simulated and experimental particle size distribution. The particle size distribution of three other batches were predicted, each of which was manufactured under different process parameters (water amount, impeller speed and wet massing time). The model was able to capture and predict successfully the shifts in granule particle size distribution with changes in these process parameters. [ABSTRACT FROM AUTHOR]

Computer-aided modeling and simulation are a crucial step in developing, integrating, and optimizing unit operations and subsequently the entire processes in the chemical/pharmaceutical industry. This study details two methods of reducing the computational time to solve complex process models, namely, the population balance model which given the source terms can be very computationally intensive. Population balance models are also widely used to describe the time evolutions and distributions of many particulate processes, and its efficient and quick simulation would be very beneficial. The first method illustrates utilization of MATLAB's Parallel Computing Toolbox (PCT) and the second method makes use of another toolbox, JACKET, to speed up computations on the CPU and GPU, respectively. Results indicate significant reduction in computational time for the same accuracy using multi core CPUs. Many-core platforms such as GPUs are also promising towards computational time reduction for larger problems despite the limitations of lower clock speed and device memory. This lends credence to the use of high fidelity models (in place of reduced order models) for control and optimization of particulate processes. [ABSTRACT FROM AUTHOR]

In this paper, we study the dynamic evolution of mixing-limited patterns in homogeneous autocatalytic reactors. Using a regularized low-dimensional model derived through the spatial averaging of the 3-D convection-diffusion-reaction equation using Liapunov−Schmidt technique of the classical bifurcation theory, we simulate the process of formation of asymmetric patterns that develop from differences in mixing and reaction time scales, and are widely observed in experimental studies. We also perform a detailed parametric analysis in order to quantify the effects of the parameters Pe, p, and Daon the formation, evolution and stability of patterns. Our nonlinear dynamic simulations show that increased transverse mixing limitations in the reactor help excite a broad spectrum of eigen modes that produce patterns of various length scales and axes of symmetry. These patterns coexist and superimpose to generate asymmetric patterns that are more stable than the symmetric ones formed from lower eigen modes. [ABSTRACT FROM AUTHOR]

Low blood count is a fundamental disease state and is often an early sign of illnesses including infection, cancer, and malnutrition, but our understanding of the homeostatic response to blood loss is limited, in part by coarse interpretation of blood measurements. Many common clinical blood tests actually include thousands of single-cell measurements. We present an approach for modeling the unsteady-state population dynamics of the human response to controlled blood loss using these clinical measurements of single-red blood cell (RBC) volume and hemoglobin. We find that the response entails (1) increased production of new RBCs earlier than is currently detectable clinically and (2) a previously unrecognized decreased RBC turnover. Both component responses offset the loss of blood. The model provides a personalized dimensionless ratio that quantifies the balance between increased production and delayed clearance for each individual and may enable earlier detection of both blood loss and the response it elicits., Competing Interests: AC, GM, DE, JH No competing interests declared, (© 2019, Chaudhury et al.)