Computation of the conditions for anti-angiogenesis and gene therapy synergistic effects: Sensitivity analysis and robustness of target solutions.

Both anti-angiogenesis and gene therapy involve complex processes depending on non-point parameters belonging to a space of values. To successfully overcome the challenges involved in their therapeutic approaches, there is a need to analyze the sensitivity of these parameters. In this paper, a new mathematical model that combines immune system stimulations, inflammatory processes associated with tumor development, and gene therapy aimed at enhancing the efficacy of both treatments are explored. Using the global sensitivity methods of Sobol and Morris, the most important parameters are estimated. Estimation of the sensitivity variance revealed a strong interdependence between the parameters. Also, determinations of the conditions for effective therapy lead to a target of reducing the cancer cell numbers by at least 50%. This opened the way for delimiting the parameter spaces making it possible to reach the treatment target in addition to enhancing the estimation of the minimum time of remission. The combination of therapies and sensitivity analysis have demonstrated the robustness of therapy success.

Mathematical modeling of bone marrow - peripheral blood dynamics in the disease state based on current emerging paradigms, part II.

The cancer stem cell hypothesis has gained currency in recent times but concerns remain about its scientific foundations because of significant gaps that exist between research findings and comprehensive knowledge about cancer stem cells (CSCs). In this light, a mathematical model that considers hematopoietic dynamics in the diseased state of the bone marrow and peripheral blood is proposed and used to address findings about CSCs. The ensuing model, resulting from a modification and refinement of a recent model, develops out of the position that mathematical models of CSC development, that are few at this time, are needed to provide insightful underpinnings for biomedical findings about CSCs as the CSC idea gains traction. Accordingly, the mathematical challenges brought on by the model that mirror general challenges in dealing with nonlinear phenomena are discussed and placed in context. The proposed model describes the logical occurrence of discrete time delays, that by themselves present mathematical challenges, in the evolving cell populations under consideration. Under the challenging circumstances, the steady state properties of the model system of delay differential equations are obtained, analyzed, and the resulting mathematical predictions arising therefrom are interpreted and placed within the framework of findings regarding CSCs. Simulations of the model are carried out by considering various parameter scenarios that reflect different experimental situations involving disease evolution in human hosts. Model analyses and simulations suggest that the emergence of the cancer stem cell population alongside other malignant cells engenders higher dimensions of complexity in the evolution of malignancy in the bone marrow and peripheral blood at the expense of healthy hematopoietic development. The model predicts the evolution of an aberrant environment in which the malignant population particularly in the bone marrow shows tendencies of reaching an uncontrollable equilibrium state. Essentially, the model shows that a structural relationship exists between CSCs and non-stem malignant cells that confers on CSCs the role of temporally enhancing and stimulating the expansion of non-stem malignant cells while also benefitting from increases in their own population and these CSCs may be the main protagonists that drive the ultimate evolution of the uncontrollable equilibrium state of such malignant cells and these may have implications for treatment.

The effectiveness of psychological intervention for depression, anxiety, and distress in prostate cancer: a systematic review of literature.

BACKGROUND: The increasing incidence and declining mortality rates seen in prostate cancer will result in a growing survivorship with a burden of health conditions, warranting attention to psychological health. Depression, anxiety, and distress have prognostic significance; attempts have been made to reduce them with psychological interventions using cognitive- and/or education-based approaches. The review of literature attempted to measure a clinically meaningful difference between pre- and post-intervention scores that were previously reported in randomized clinical trials. METHODS: Using the PRISMA-checklist, we identified 22 studies that assessed psychological interventions by randomizing against care as usual (CAU). We calculated a percent change between pre- and post-trial mean scores for depression, anxiety, and distress in each study and analyzed effectiveness of intervention versus CAU. RESULTS: The patient group receiving intervention showed significantly greater improvement in depression, anxiety, as well as general and cancer-specific distress as compared to CAU. The effectiveness of intervention was retained even in subgroups upon limiting analysis to seven studies that used one single assessment tool, the Hospital Anxiety and Depression Scale (HADS), or to 14 studies with localized prostate cancer (LPC). Improvement in depression did not correlate with anxiety but correlated significantly with a reduction in distress. Lastly, improvement in all three parameters was numerically greater in three studies that combined cognitive- and education-based approaches versus studies using either approach alone. CONCLUSIONS: The present analysis underscores the utility of psychological intervention for depression, anxiety, and distress related to prostate cancer. Future research should ascertain their impact on long-term clinical outcomes, like disease progression and survival.

Mathematical modeling of bone marrow--peripheral blood dynamics in the disease state based on current emerging paradigms, part I.

Stemming from current emerging paradigms related to the cancer stem cell hypothesis, an existing mathematical model is expanded and used to study cell interaction dynamics in the bone marrow and peripheral blood. The proposed mathematical model is described by a system of nonlinear differential equations with delay, to quantify the dynamics in abnormal hematopoiesis. The steady states of the model are analytically and numerically obtained. Some conditions for the local asymptotic stability of such states are investigated. Model analyses suggest that malignancy may be irreversible once it evolves from a nonmalignant state into a malignant one and no intervention takes place. This leads to the proposition that a great deal of emphasis be placed on cancer prevention. Nevertheless, should malignancy arise, treatment programs for its containment or curtailment may have to include a maximum and extensive level of effort to protect normal cells from eventual destruction. Further model analyses and simulations predict that in the untreated disease state, there is an evolution towards a situation in which malignant cells dominate the entire bone marrow - peripheral blood system. Arguments are then advanced regarding requirements for quantitatively understanding cancer stem cell behavior. Among the suggested requirements are, mathematical frameworks for describing the dynamics of cancer initiation and progression, the response to treatment, the evolution of resistance, and malignancy prevention dynamics within the bone marrow - peripheral blood architecture.

Mathematical modeling of glioma therapy using oncolytic viruses.

Diffuse infiltrative gliomas are adjudged to be the most common primary brain tumors in adults and they tend to blend in extensively in the brain micro-environment. This makes it difficult for medical practitioners to successfully plan effective treatments. In attempts to prolong the lengths of survival times for patients with malignant brain tumors, novel therapeutic alternatives such as gene therapy with oncolytic viruses are currently being explored. Based on such approaches and existing work, a spatio-temporal model that describes interaction between tumor cells and oncolytic viruses is developed. Conditions that lead to optimal therapy in minimizing cancer cell proliferation and otherwise are analytically demonstrated. Numerical simulations are conducted with the aim of showing the impact of virotherapy on proliferation or invasion of cancer cells and of estimating survival times.

Using mathematical modeling as a resource in clinical trials.

In light of recent clinical developments, the importance of mathematical modeling in cancer prevention and treatment is discussed. An exist- ing model of cancer chemotherapy is reintroduced and placed within current investigative frameworks regarding approaches to treatment optimization. Areas of commonality between the model predictions and the clinical findings are investigated as a way of further validating the model predictions and also establishing mathematical foundations for the clinical studies. The model predictions are used to propose additional ways that treatment optimization could enhance the clinical processes. Arising out of these, an expanded model of cancer is proposed and a treatment model is subsequently obtained. These models predict that malignant cells in the marrow and peripheral blood exhibit the tendency to evolve toward population levels that enable them to replace normal cells in these compartments in the untreated case. In the case of dose-dense treatment along with recombinant hematopoietic growth factors, the models predict a situation in which normal and abnormal cells in the marrow and peripheral blood are obliterated by drug action, while the normal cells regain their growth capabilities through growth-factor stimulation.