Evans K. Afenya

Acute leukemia and chemotherapy : A modeling viewpoint

A couple of models of acute myeloblastic leukemia (AML) are proposed. Normal and leukemic cells are assumed to exist side-by-side with the two cell populations obeying Gompertzian dynamics but with the leukemic cells exercising inhibition over the normal cells. The kinetic equations and steady-state properties of one of the models is analytically obtained. Possible situations of detection or nondetection of malignancy are then discussed. Based on the models of AML, a treatment model is proposed and numerically simulated. Consequently, the option of aggressive treatment of the disease with heavy doses of drugs is shown to be a plausible and worthwhile chemotherapeutic strategy.

Some perspectives on modeling leukemia.

A diffusion model of leukemia is presented. The space-occupying effects of leukemic cells during leukemic expansion is investigated. The analyses and simulations of the model suggest that acute leukemia is a state in which positions inhabited by colonies of normal cells are invaded by emerging colonies of abnormal cells. Normal cells are then driven to a state of extinction as leukemic cells evolve toward high and dominant steady state levels.

Presence of activation-related m-RNA for EBV and CMV in the bone marrow of patients with myelodysplastic syndromes

The bone marrow (BM) in myelodysplastic syndromes (MDS) undergoes pathobiological changes that mimic an inflammatory process, and hence, an infectious etiology was suspected in these disorders. In the present report, we examined the bone marrow mononuclear cells (BMMNC) of 19 MDS patients and seven normal donors for the expression of one latency-related (Latency membrane protein 1 (LMP-1) and immediate early protein (IEP)) and one activation-related (BZLF and DNA-Pol) m-RNA each for two herpes viruses, Epstein-Barr virus (EBV) and cytomegalovirus (CMV), respectively. Reverse transcriptase polymerase chain reaction was used for this purpose. The latency-related transcripts (EBV-LMP-1 and CMV-IEP) were present in all the MDS and normal specimens. Intriguingly, 10/19 MDS specimens ( approximately 53%) and 2/7 normal donors ( approximately 28%) were positive for active EBV-BZLF (P=0.0067), while 2/19 MDS specimens ( approximately 11%) with 1/7 normal ( approximately 14%) showed active CMV-DNA-Pol (P=0.1588). Later, from another set of MDS patients (n=7) and normal donors (n=4), BM stromal cultures were established, which, at a 75% confluency, were overlaid with cord blood mononuclear cells (CBMNC). IEP was detectable in the CBMNC before and after co-incubation with MDS, as well as normal stroma. So, it was also present both in MDS and normal stromal cells. The other three were absent both in MDS and normal stromal layers. In CBMNC though, active EBV-BZLF and CMV-DNA-Pol m-RNA were detectable in one of seven MDS co-cultures each, albeit from different patients. None of the normal co-cultures showed active virus, either in stroma or CBMNC. Thus, the present report demonstrates, for the first time, the presence of active herpes viruses in the BMMNC of MDS patients and reveals the ability of the MDS stroma to support the viral activation.

Recovery of normal hemopoiesis in disseminated cancer therapy--a model.

The strategy of normal cell regeneration with recombinant hematopoietic growth factors during cancer chemotherapy is investigated by superimposing a treatment protocol on a simple model that describes an expanding malignant cell population that is coexisting with and inhibiting the population of normal cells. The model predictions suggest that the strategy of normal cell stimulation, possibly with growth factors, and possibly carried out within an intensive treatment framework may be a worthwhile chemotherapeutic option. Under this protocol, the model also predicts a minimum time interval for active treatment, a time to discontinue treatment, and a rest period during treatment in order to guarantee patient safety and recovery. Consequently, by relating and comparing model predictions to patient data, model simulations forecast that treatment could be shortened by 1-2 weeks if organized over or in the neighborhood of a predicted optimal time interval. Following this, it is conjectured that such an approach engendered by the model could produce outcomes that may have an edge over outcomes arising from therapeutic strategies that are executed over time frames that are relatively longer or significantly shorter than the predicted optimal time.

THERMODYNAMICS OF MICROWAVE (POLARIZED) HEATING SYSTEMS

The equation governing the behavior of microwave (polarized) heating systems is presented. The basic difference between microwave (polarized) and conventional (non-polarized) heating systems is shown. The influence of a polarizing electric field on system properties, parameters, and behavior is derived. Characteristics predicted by the derived equations are discussed in relation to published observations. It is revealed that in addition to concentration, temperature, and pressure gradients, the existence of an electric field intensity gradient during microwave drying may produces an additional driving force for mass transport. Thus, at the same concentration, temperature and pressure, an assisting electric field intensity gradient may reduce the activation energy for microwave drying processes and increase microwave mass transfer rates for volatile polar or polarizable molecules over that of conventional heating. A new phenomenological equation, that accounts for the effect of an electric field gradient o...

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.

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.

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.

An Appraisal of Calixto Calderón’s Work in Mathematical Biology

The body of investigative biomathematical work undertaken by Prof. Calixto Calderon is reviewed. The appraisal demonstrates that Prof. Calderon has not only been active in the area of harmonic analysis but has also been an active researcher in the area of mathematical biology and has been a strong proponent of the use of mathematical ideas and techniques in the broad areas of biology and medicine as a way of giving these areas firm systematic support.