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A number of lines of evidence suggest that immunotherapy with the cytokine interleukin-2 (IL-2) may boost the immune system to fight tumors. CD4+ T cells, the cells that orchestrate the immune response, use these cytokines as signaling mechanisms for immune-response stimulation as well as lymphocyte stimulation, growth, and differentiation. Because tumor cells begin as 'self', the immune system may not respond in an effective way to eradicate them. Adoptive cellular immunotherapy can potentially restore or enhance these effects. We illustrate through mathematical modeling the dynamics between tumor cells, immune-effector cells, and IL-2. These efforts are able to explain both short tumor oscillations in tumor sizes as well as long-term tumor relapse. We then explore the effects of adoptive cellular immunotherapy on the model and describe under what circumstances the tumor can be eliminated.

We propose a mathematical model for the growth of cell-cycle-specific dose limiting bone marrow. In an attempt to determine effective methods of treatment without overdestruction of the bone marrow we implement optimal control theory. We design the control functional to maximize both the bone marrow mass and the dose over the treatment interval. Next we show that an optimal control exists for this problem, and then we characterize our optimal control in terms of the solutions to the optimality system, which is the state system coupled with the adjoint system. We show that the optimality system is unique for suitably small time intervals. Finally, we analyze the optimal control and the optimality system using numerical techniques. This allows us to suggest optimal methods of treatment that prevent excessive destruction of the bone marrow based on the specific weights in our objective functional.

Vincristine (VCR) is frequently used in pediatric oncology and can be administered intravenously through push injections or 1 h infusions. The effects of administration duration on population pharmacokinetics (PK) are unknown. We described PK differences related to administration duration and the relation between PK and VCR-induced peripheral neuropathy (VIPN). PK was assessed in 1–5 occasions (1–8 samples in 24 h per occasion). Samples were analyzed using high-performance liquid chromatography/tandem mass spectrometry. Population PK of VCR and its relationship with administration duration was determined using a non-linear mixed effect. We estimated individual post-hoc parameters: area under the concentration time curve (AUC) and maximum concentration (Cmax) in the plasma and peripheral compartment. VIPN was assessed using Common Terminology Criteria for Adverse Events (CTCAE) and the pediatric-modified total neuropathy score (ped-mTNS). Overall, 70 PK assessments in 35 children were evaluated. The population estimated that the intercompartmental clearance (IC-Cl), volume of the peripheral compartment (V2), and Cmax were significantly higher in the push group. Furthermore, higher IC-Cl was significantly correlated with VIPN development. Administration of VCR by push led to increased IC-Cl, V2, and Cmax, but were similar to AUC, compared to 1 h infusions. Administration of VCR by 1 h infusions led to similar or higher exposure of VCR without increasing VIPN.

Optimal control techniques are used to develop optimal strategies for chemotherapy. In particular, we investigate the qualitative differences between three different cell-kill models: log kill hypothesis (cell-kill is proportional to mass); Norton-Simon hypothesis (cell-kill is proportional to growth rate); and, Emaxhypothesis (cell-kill is proportional to a saturable function of mass) For each hypothesis, an optimal drug strategy is characterized that minimizes the cancer mass and the cost (in terms of total amount of drug). The cost of the drug is nonlinearly defined in or objective functional and linearly defined in the other. Existence and uniqueness for the optimal control problems are analyzed. Each of the optimality systems, which consists of the state systen coupled with the adjoint system, is characterized. Finally, numerical results show that there are qualitatively different treatment schemes for each model studied. In particular, the log-kill hypothesis requires less drug compared to the Norton-Simon hypothesis to reduce the cancer an equivalen amount over the treatment interval. Therefore, understanding the dynamics of cell-kill for specific treatments is of great importance when developing optimal treatment strategies.

The objective of this scoping review is to summarize the current use of pharmacokinetics for tailoring prophylaxis in hemophilia patients switching between clotting factor products. Patients with hemophilia may require switching of clotting factor concentrates due to a variety of factors, but there have been perceived risks associated with switching, such as inhibitor development or suboptimal protection due to inadequate dosing while titrating treatment. Studies that look at patients switching from one clotting factor concentrate to another are categorized in terms of their primary and/or secondary objectives, notably biosimilarity and comparative pharmacokinetic studies and inhibitor development studies. Research on how best to switch concentrates with respect to dosing regimen are lacking, and currently a trial‐and‐error approach is used for dosing the new factor concentrate. In the future, studies looking at the predictability of pharmacokinetics (PK) of a new factor concentrate based on individual PK knowledge of the original factor concentrate may offer clinical benefit by providing a safer switching approach and protocol.

Pleural effusions, ascites, and renal dysfunction decrease the plasma excretion of methotrexate (MTX). However, it is not known what effect these complications have on MTX clearance when they arise after the plasma MTX concentration has fallen to an undetectable level. We describe the clinical course and pharmacokinetics of MTX in a patient with acute lymphoblastic leukemia who experienced pleural effusions, ascites, and renal failure during the weeks after treatment with high-dose MTX (1.63 g/m2 i.v. over 24 h). The patient's normal initial MTX clearance rate (107 ml/min/m2) was consistent with his undetectable plasma level of MTX on day 9 after the infusion. His plasma MTX concentration then gradually increased as his renal function declined, reaching a peak of 0.72 microM on day 15. This unusual finding of an undetectable plasma MTX concentration that subsequently rose to persistent, potentially toxic levels was explained only by a pharmacokinetic model that accounted both for a third space at the time of treatment and for the subsequent decrease in the systemic elimination rate. Therefore, the finding of a physiologic third space during MTX administration combined with the detection of renal dysfunction in the following weeks should be an indication for prolonged therapeutic drug monitoring.

Etoposide is used to treat childhood malignancies, and its plasma pharmacokinetics have been related to pharmacodynamic endpoints. Limiting the number of samples should facilitate the assessment of etoposide pharmacokinetics in children. We compared limited sampling strategies using multiple linear regression of plasma concentrations and clearance with Bayesian methods of estimating clearance using compartmental pharmacokinetic models. Optimal sampling times were estimated in the multiple linear regression method by determining the combination of two samples which maximized the correlation coefficient, and in the Bayesian estimation approach by minimizing the variance in estimates of clearance. Clearance estimates were compared to the actual clearances from Monte Carlo-simulated data and predicted clearances estimated using all available plasma concentrations in clinical data from children with acute lymphoblastic leukemia. Multiple linear regression poorly predicted clearance (mean bias 8.3%, precision 17.5%), but improved if plasma concentrations were logarithmically transformed (mean bias 1.4%, precision 12.5%). Bayesian estimation methods with optimal samples gave the best overall prediction (mean bias 2.5%, precision 6.8%) and also performed better than regression methods for abnormally high or low clearances. We conclude that Bayesian estimation with limited sampling gives the best estimates of etoposide clearance.

Methotrexate (MTX) is one of the most widely used drugs for the treatment of childhood acute lymphoblastic leukemia (ALL). Interindividual differences in lymphoblast accumulation of MTX and its active metabolites, methotrexate polyglutamates (MTXPG), may contribute to the effectiveness of treatment among ALL subtypes. To better understand these differences in MTXPG accumulation, we developed a model to characterize the cellular influx and efflux of MTX, formation of MTXPG by the addition of glutamyl residues catalyzed by FPGS (folylpolyglutamate synthetase), and cleavage of glutamyl residues from MTXPG by GGH (gamma-glutamyl hydrolase). The model was fitted to in vivo intracellular MTXPG concentrations measured serially in leukemic blasts from 20 newly diagnosed patients with ALL treated with 24-h intravenous infusions of MTX. The observed median concentrations of total MTXPG at 44 h was higher in B-lineage than in T-cell ALL (1706 vs 518 pmol/10(9) cells, P<0.025), consistent with the higher estimated Vmax for FPGS activity in B-lineage vs T-lineage blasts (414 vs 93 pmol/10(9) cells/h, P<0.008). Simulations based on the model-estimated parameters indicated greater accumulation of MTX, MTXPGs (MTXPG(2-7)) and total MTX (MTXPG(1-7)) with longer MTX infusions and with higher MTX doses, with the highest concentrations in hyperdiploid B-lineage, intermediate in non-hyperdiploid B-lineage, and lowest in T-cell ALL. These differences provide mechanistic and treatment insights for lineage and ploidy differences in MTXPG accumulation in human leukemia cells in vivo.

Several mathematical models are developed to describe the effects of chemotherapy on both cancerous and normal tissue. Each model is defined by either a single homogeneous equation or a system of heterogeneous equations which describe the states of the normal and/or cancer cells. Periodic terms are added to model the effects of the chemotherapy. What we obtain are regions, in parameter space (dose and period), of acceptable drug regimens. The models take into account various aspects of chemotherapy. These include, interactions between the cancer and normal tissue, cell specific chemotherapeutic drug, the use of non-constant parameters to aid in modeling specific chemotherapeutic processes, and drug resistance. By studying the models we can obtain a better understanding of the dynamics of the chemotherapeutic drugs and how better to implement them. The mathematical methods used are mostly in the area of dynamical systems in particular Floquet Theory. These methods are used on either a single equation or a system of periodic ordinary differential equations which model the chemotherapeutic process. These are reduced to difference equations that describe the state of the cancer at the beginning of each period. By studying the characteristic multipliers, we are able to determine the bifurcation between successful and unsuccessful regimens, if existing drug regimens seem reasonable from a mathematical model standpoint, and suggest ways to better implement the existing chemotherapeutic drugs.