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Biomedical subjects

Z Agur

Publications and source records attributed to Z Agur.

At least 19 recordsLinked to original sources
PubMed2005

The complex effect of granulocyte colony-stimulating factor on human granulopoiesis analyzed by a new physiologically-based mathematical model.

Neutropenia, frequently a side effect of chemo- and radiotherapy, increases susceptibility to microbial infections and is a life-threatening condition. For realistically predicting drug treatment effects on granulopoiesis, we have constructed a new mathematical model of granulopoiesis in the bone marrow and in the peripheral blood, featuring cell cycle phase transition and detailed granulocyte-colony stimulating factor (G-CSF) pharmacokinetics (PK) and pharmacodynamics (PD), including intracellular second messenger. Using this model, in conjunction with clinical results, we evaluated the system parameters, implemented those in the model and successfully retrieved the results of several independent clinical experiments under a wide range of G-CSF regimens. Our results show that the introduction of G-CSF-controlled intracellular second messenger is indispensable for precise retrieval of the clinical results, and suggest that the half-life of this messenger varies between a single and multiple G-CSF administration schedules. In addition, our model provided reliable steady-state, as well as dynamic, estimations of human granulopoiesis parameters. These included an estimation of apoptosis index in the post-mitotic compartment, which corroborates previous results. At present the model is used for suggesting improved drug regimens.

Animals↗
PubMed2005

A mathematical model of Doxorubicin treatment efficacy for non-Hodgkin's lymphoma: investigation of the current protocol through theoretical modelling results.

Doxorubicin treatment outcomes for non-Hodgkin's lymphomas (NHL) are mathematically modelled and computationally analyzed. The NHL model includes a tumor structure incorporating mature and immature vessels, vascular structural adaptation and NHL cell-cycle kinetics in addition to Doxorubicin pharmacokinetics (PK) and pharmacodynamics (PD). Simulations provide qualitative estimations of the effect of Doxorubicin on high-grade (HG), intermediate-grade (IG) and low-grade (LG) NHL. Simulation results imply that if the interval between successive drug applications is prolonged beyond a certain point, treatment will be inefficient due to effects caused by heterogeneous blood flow in the system.

Cell Cycle↗
PubMed2005

Vessel maturation effects on tumour growth: validation of a computer model in implanted human ovarian carcinoma spheroids.

We analysed measurements of tumour growth, neovascular maturation and function in human epithelial ovarian carcinoma xenografts, studied noninvasively by magnetic resonance imaging. Results suggest that vascular maturation and mature and immature vessel regression occur continuously during tumour neovascularisation. Moreover, in these spheroids, a high tumour growth-rate is associated with monotonic changes in vessel density (VD) and with large proportions of mature blood vessels, whereas a lower tumour growth-rate is associated with fluctuating VD and lower proportions of mature vessels. These results corroborate a mathematical model for tumour dynamics, including vascular maturation and immature and mature vessel regression. The model predicts that rapid tumour growth may result from a high maturation-rate of neo-vasculatures, due to substantial mature VD in the microenvironment, while a slower tumour growth is an outcome of a lower background VD, leading to a lower vessel maturation-rate, larger proportion of immature vessels and, consequently, to regression-driven instabilities. The generality of these results for other tumour types should be validated.

Animals↗
PubMed2002

A computer algorithm describing the process of vessel formation and maturation, and its use for predicting the effects of anti-angiogenic and anti-maturation therapy on vascular tumor growth.

We put forward an algorithm describing the three principal interconnected sub-processes that influence tumor and vasculature dynamics: (i) tumor cell proliferation (ii) angiogenesis, that is, the formation and regression of immature vessels (IV), and (iii) maturation, i.e., the formation and destabilization of mature vessels (MV). This algorithm takes account of the crucial quantitative interactions of these sub-processes, occurring across the molecular, cellular and organ levels. Implementing this complex algorithm in a computer model, one can evaluate the correlations between various factors influencing angiogenesis and their influence on tumor progression at any given moment. Moreover, the computer simulations enable analysis of the versatile effects of drugs on the growth and decay of both the tumor and the immature and mature blood vessels, as well as on the induction of an array of relevant growth factors such as angiopoietin-1 (Ang1), angiopoietin-2 (Ang2), vascular endothelial growth factor (VEGF) and platelet-derived growth factor (PDGF). Simulation results suggest that vessel maturation and destabilization of MV drive the otherwise non-linearly growing system into a very dynamic region, having irregular, scale-invariant, fluctuations, around certain asymptotic values of all the involved quantities. Destabilization itself adequately explains the experimentally observed eventual decrease of tumor growth, with no need to implicate additional assumptions, such as a new tumor growth inhibitory, or anti-angiogenic, factors. Our results further suggest that mono-therapy alone can slow tumor growth, but is not capable of eliminating it altogether. In contrast, the combined treatment of anti-angiogenic and anti-maturation drugs causes prolonged suppression of tumor growth and a significant linear decrease in average tumor size. Laboratory experiments are warranted for validating our predictions and for providing in vivo evaluated parameters.

Algorithms↗
PubMed1998

Pulse vaccination strategy in the SIR epidemic model.

Theoretical results show that the measles 'pulse' vaccination strategy can be distinguished from the conventional strategies in leading to disease eradication at relatively low values of vaccination. Using the SIR epidemic model we showed that under a planned pulse vaccination regime the system converges to a stable solution with the number of infectious individuals equal to zero. We showed that pulse vaccination leads to epidemics eradication if certain conditions regarding the magnitude of vaccination proportion and on the period of the pulses are adhered to. Our theoretical results are confirmed by numerical simulations. The introduction of seasonal variation into the basic SIR model leads to periodic and chaotic dynamics of epidemics. We showed that under seasonal variation, in spite of the complex dynamics of the system, pulse vaccination still leads to epidemic eradication. We derived the conditions for epidemic eradication under various constraints and showed their dependence on the parameters of the epidemic. We compared effectiveness and cost of constant, pulse and mixed vaccination policies.

Computer Simulation↗
PubMed1998

The growth law of primary breast cancer as inferred from mammography screening trials data.

Despite considerable progress in understanding tumour development, the law of growth for human tumours is still a matter of some dispute. In this study, we used large-scale mammography screening trial data to deduce the growth law of primary breast cancer. We compared the empirical tumour population size distributions of primary breast cancer inferred from these data to the distributions that correspond to various possible theoretical growth functions. From this, we showed that the data are inconsistent with the exponential, logistic and Gompertz laws, but support power law growth (exponent approximately 0.5). This law indicates unbounded growth but with slowing mass-specific growth rate and doubling time. In the clinical size ranges, it implies a greater decline in the mass-specific growth rate than would be predicted by the Gompertz law using the accepted parameters. This suggests that large tumours would be less sensitive to cycle-specific therapies, and be better treated first by non-cell cycle-specific agents. We discussed the use of our study to estimate the sensitivity of mammography for the detection of small tumours. For example, we estimated that mammography is about 30% less sensitive in the detection of tumours in the 1 to 1.5-cm range than it is in detecting larger tumours.

Breast Neoplasms↗
PubMed1997

Modelling Trypanosoma congolense parasitaemia patterns during the chronic phase of infection in N'Dama cattle.

We reanalyzed parasitaemia profiles of the trypanotolerant N'Dama cattle (Bos taurus), consecutively infected with the same four clones of Trypanosoma congolense. Our analysis shows that each individual parasitaemia is characterized by progressively longer intervals between parasites waves. This pattern is most visible during the chronic phase of infection. In addition, the last of the four infections had a significantly larger overall duration of inter-wave intervals. We retrieved these patterns by numerical simulations of a mathematical model, which incorporates assumptions about the molecular basis of antigenic variation and about the anti-parasitic major immune processes. Six potential factors that may determine parasitaemia pattern were studied: carrying capacity of the host environment, intrinsic growth rate of the parasite, affinity maturation of the immune response, immune cell birth and death rate, levels of antibodies to variant surface glycoprotein and levels of antibodies to invariant antigens. Our simulations suggest that the first five factors are not likely to determine the chronic phase parasitaemia pattern whereas the sixth one, namely, antibody response to invariant antigens, yielded profiles consistent with the experimental data. Being cumulative, the immune response to anti-invariant antigens may be increasingly effective as infection proceeds and in successive infections. Comparisons between N'Dama and Zebu and between chronic and acute phases will be needed to make a statement on the role of this phenomenon in trypanotolerance.

Animals↗
PubMed1994

Increasing 1-beta-D-arabinofuranosylcytosine efficacy by scheduled dosing intervals based on direct measurements of bone marrow cell kinetics.

The therapeutic efficacy of cell cycle phase-specific drugs can be improved by repeated administrations, the dosing interval being related to the cell cycle time of the susceptible normal host tissue. Kinetic measurements of bone marrow cell proliferation, with bromodeoxyuridine labeling and flow cytometry analysis, were used to determine the optimal dosing intervals of 1-beta-D-arabinofuranosylcytosine for minimizing bone marrow cell damage in mice. The results showed that cells surviving a single dose 1-beta-D-arabinofuranosylcytosine treatment remained temporarily blocked at the G1-S boundary, and upon release from the block the cells crossed through S phase in a nearly synchronized way. The optimal spacing of repeated treatments, evaluated by measurements of the drug-induced transit times through the different cell cycle phases, equaled the bone marrow cell cycle time following treatment. Repeated 1-beta-D-arabinofuranosylcytosine injections according to this protocol markedly diminished drug toxicity in C3H mice, as compared to protocols of other time intervals. A therapeutic schedule based on these measurements was highly effective in lymphoma-bearing mice: the designed protocol of dosing intervals significantly delayed tumor growth whereas other intervals were highly toxic.

Animals↗
PubMed1993

Pulse mass measles vaccination across age cohorts.

Although vaccines against measles have been routinely applied over a quarter of a century, measles is still persistent in Israel, with major epidemics roughly every 5 years. Recent serological analyses have shown that only 85% of Israelis aged 18 years have anti-measles IgG antibodies. Considering the high transmissibility of the virus and the high level of herd immunity required for disease eradication, the Israeli vaccination policy against measles is now being reevaluated. Motivated by theoretical studies of populations in perturbed environments, we examined the possibility of replacing the conventional cohort vaccination strategy by a pulse strategy--i.e., periodic vaccination of several age cohorts at the same time. Numerical studies of a deterministic age-structured model suggest that vaccination, which renders immunity to no more than 85% of the susceptible children aged 1-7 years, once every 5 years will suffice to prevent epidemics in Israel, where infection rate is highest amongst schoolchildren. The model suggests that by using such a strategy the density of susceptible individuals is always kept below the threshold above which recurrent epidemics will be maintained. Analysis of simpler, non-age-structured, models serves to clarify the basic properties of the proposed strategy. Our theoretical results indicate that the advantages and disadvantages of a pulse strategy should be seriously examined in Israel and in countries with similar patterns of measles virus transmission.

Adult↗
PubMed1993

Measles immunization strategies for an epidemiologically heterogeneous population: the Israeli case study.

Although the vaccine against measles has been routinely applied over a quarter of a century, measles is still an active disease in Israel. The January 1991 outbreak caused high morbidity in infant and adolescent populations and high mortality, especially among nomad Bedouins in the southern region of the country. The Bedouins form a small fraction of the total Israeli population (ca. 2%), but it is thought that they may experience significantly higher rates of transmission than the majority group. In this work we use deterministic compartmental mathematical models to define the optimal immunization strategy for a population consisting of a majority group characterized by low transmission rates and a minority group characterized by high transmission rates; this study allows both for transmission differences between the two groups, and for possible differences in the average cost (or difficulty) in reaching individuals for vaccination. Our analysis shows that the optimal vaccination policy for such a population involves different strategies for the two groups: a smaller fraction is to be vaccinated in the minority group if transmission in this group is not much larger than in the majority group, whereas, if the difference in transmission is very large, a higher proportion is to be vaccinated in the minority group. The advantage of this non-uniform vaccination policy is that it involves vaccination of a smaller fraction of the total population (and costs less, if there are differential costs between the groups), as compared with the proportion vaccinated under the conventional uniform vaccination policy.(ABSTRACT TRUNCATED AT 250 WORDS)

Adolescent↗
PubMed1993

A mathematical model of the effect of aging on bone marrow cells colonizing the thymus.

The process of T cell generation in the thymus involves complex cell-cell interactions between the various types of thymic stromal cells, thymocyte progenitors, thymocytes at different stages of differentiation and external factors. We applied the tool of mathematical modelling to analyze hypotheses and direct experiments concerning mechanisms underlying the observed developmental inferiority of bone-marrow thymocyte progenitors from old mice. Previous experimental data showed that lower cell numbers were obtained from old bone marrow-derived thymocyte progenitors, compared to young bone marrow-derived progenitors, when colonizing simultaneously the same fetal thymus. In this study, simulations based on the mathematical model indicate that the developmental inferiority of old bone marrow-derived progenitors cannot be explained by a change in a single parameter, such as the observed differences in progenitor frequency, an increase in cell cycle duration, a reduction in the fraction of proliferating cells in old age, and/or an increase in the rate of cell death. We have performed experimental measurements of the fractions of cycling cells. No significant difference was found between these fractions in young and old bone marrow-derived thymocytes. The difference in developmental patterns of young and old bone marrow-derived thymocytes may be due to a combination of more than one mechanism, possibly including interactions between competing thymocytes of old and young bone marrow origin.

Aging↗
PubMed1993

Use of mathematical models for understanding the dynamics of gene amplification.

Recently it has been suggested that high levels of cancer drug resistance and poor prognosis are strongly associated with gene or oncogene amplification (GA). It has been further suggested that the molecular mechanisms underlying GA may be different for different genes, and that different amplification mechanisms may function concurrently or sequentially in the same gene. The aim of this review is to demonstrate the use of mathematical models in studying these intricate dynamics. We have provided mathematical models for the generation of extrachromosomal elements, their autonomous replication and equal or unequal mitotic segregation, the integration of the extrachromosomal elements within the chromosomes, and chromosomal GA in one or many unlinked genes. Using this formal description one can examine the potential role of each GA mechanism in the generation of specific distributions of gene-copy number in a cell population, under various levels of selection stringency. Thus one can specify the conditions for the emergence of drug-resistant mutants prior to selection, as well as the relationships between the stringency of the selecting environment and the characteristics of the resultant cellular phenotype.

Animals↗
PubMed1992

Drug resistance as a dynamic process in a model for multistep gene amplification under various levels of selection stringency.

Resistance to antineoplastic drugs has been a major impediment to the successful treatment of cancer. Recent studies suggest that several mechanisms are responsible for the emergence of drug resistance but that high levels of resistance and poor prognosis are strongly associated with gene or oncogene amplification. In this report we describe a probabilistic model for gene amplification in a tumor that grows under various drug protocols. The model is new in that it treats drug resistance as a dynamic process and examines specific assumptions about the underlying molecular events. Using this model, we specify the conditions for the emergence of drug-resistant mutants prior to selection as well as the relationship between the stringency of the selecting environment and the characteristics of the resultant cellular phenotype.

Antineoplastic Agents↗
PubMed1992

A theoretical analysis of interval drug dosing for cell-cycle-phase-specific drugs.

A formal method is provided for predicting the effect on treatment efficacy of cell-cycle-phase-specific drugs, such as the AIDS drug zidovudine (AZT) or the cancer drug cytosine arabinoside (ara-C). Our analysis shows that the elimination of somatic cells or viruses depends not only on the drug's pharmacokinetic and pharmacodynamic properties, but also the duration of the dosing interval per se and on the life-cycle parameters, that is, the duration of the drug-susceptible life phase, the duration of the whole life cycle, and the proliferation rate. The results support those of simplified models in showing that drug toxicity to the host may be minimized when the dosing interval is an integer multiple of the average cycle time of the host susceptible cells. This prediction has been verified in mice treated with AZT or ara-C.

Animals↗
PubMed1992

Bone marrow regeneration under cytotoxic drug regimens: behaviour ranging from homeostasis to unpredictability in a model for hemopoietic differentiation.

In the process of hemopoiesis, bone marrow stem cells differentiate into the various types of mature blood cells. We present a model for bone marrow dynamics, which retrieves its ability to continuously modulate the balance between self-renewal and differentiation, even under periodic cytodestructive perturbations. Yet, a temporally stochastic perturbation results in chaotic-like behaviour which has no deterministic source.

Animals↗
PubMed1992

Effect of the dosing interval on myelotoxicity and survival in mice treated by cytarabine.

Many antineoplastic drugs are cell-cycle-phase-specific. These drugs are often highly toxic to the host, as they have the potential to impair replication, not only in the cancer cells, but also in the normal tissues. Using mathematical models it has been shown how selectivity of these drugs can be increased by exploiting the relatively large variability in cell-cycle parameters of the neoplasia. These models predict that toxicity to the host of cell-cycle-phase-specific drugs can be minimised if the dosing interval is an integer multiple of the average intermitotic interval of the susceptible host cells. Experimental evidence supporting this prediction is presented in this work. Our results show that a constant duration of the dosing interval yields higher survival rates in mice treated by cytarabine, as compared with random dosing intervals. Minimal myelotoxicity is exerted when the dosing interval is an exact multiple of the inter-mitotic time of bone marrow stem cells and erythroid progenitors (i.e. 7 h). Survival is significantly lower in mice treated every 8 h, or its multiple, as compared with that of mice treated at a 7 h or 10 h dosing interval.

Animals↗
PubMed1991

Maturation of the humoral immune response as an optimization problem.

Efficient immune response often depends on the production of high affinity antibodies. We show analytically that the optimal strategy for a fast production of high affinity antibodies is to utilize a step-function mutation rate, i.e. a minimal mutation rate in early stages of the immune response, followed by a discontinuous switch to the maximal possible rate when the proliferating population of B-cells exceeds a threshold value. Our results are in accordance with the biological observations concerning the time of onset of the hypermutation process, and with the mutation rate during the later stages of the primary immune response. Indeed the hypermutation process plays a crucial role in responding to a prevailing pathogen at each round of immune response, and not only for coping with future infections. Moreover, as the effect of hypermutations is shown to be crucially dependent on the number of proliferating B-cells, its onset is not expected to depend on an external signal, but rather to be related to the clone's age. This suggests that the onset is host species specific, rather than pathogen specific. Another implication of the present results is that activation of hypermutations before the B-cell population has reached the critical size may impede the efficiency of the response.

Animals↗