Periodic chronic myelogenous leukaemia: spectral analysis of blood cell counts and aetiological implications

Association of a Cyclical Migraine Phenotype With Disease Progression: A One-Year Time Series Analysis

OBJECTIVE

Longitudinal studies assessing cyclic fluctuations of migraine attacks using time-series analysis are scarce. Here we analyze headache frequency fluctuations over a year in a cohort of migraine patients and we then evaluate how this behaviour has an impact on clinical evolution.

METHODS

Monthly headache frequency was prospectively collected using an eDiary. Prognosis after one year was calculated as the headache frequency change rate after 12 months (HCR-M12) as a dependent variable. Monthly headache time series was decomposed into all the possible sum of sinusoids through a Fast Fourier Transform algorithm (FFT) and the frequencies with the highest power were used to define the patient's cyclic phenotype during one year (patient's number of cycles per year, c/y). Patients with a cyclic phenotype were those with >2 cycles/year. Finally, we studied how this cyclic phenotype was associated to HCR-M12 using Generalized Linear Models (GLM).

RESULTS

142 patients were included (85.2% female; mean age 48.0±9.7 years), 50.0% fulfilled IHCD-3 criteria for chronic migraine (CM). After one year, a 50.7% (72/142) of patients changed their initial diagnosis and progression (frequency worsening) was observed in 14.1% (10/71) of episodic migraine (EM) patients. After applying a FFT, 45.1% (64/142) of patients fitted into a cyclic phenotype. In GLM, statistically significant main effects associated to HCR-M12 were the use of preventive therapy (Beta [SE]: 74.1 [34.6]; p=0.034) and cyclic phenotype (Beta [SE]: 158.33 [55.1]; p=0.005). A post-hoc analysis found that EM patients with cyclic phenotype without adequate preventive therapy were statistically significantly associated to progression.

CONCLUSIONS

Monthly headache frequency data can be fitted by sinusoidal models. Having a cyclic phenotype has an impact on clinical evolution and has been statistically significantly associated to migraine progression after one year. Particularly, EM patients with cyclic phenotype tend to increase their headache frequency over time. Preventive treatment seems to play a fundamental role in modulating this cyclic behaviour, especially in low-frequency EM patients.

Periodic hematological disorders: Quintessential examples of dynamical diseases

This paper summarizes the evidence supporting the classification of cyclic neutropenia as a dynamical disease and periodic chronic myelogenous leukemia is also considered. The unsatisfactory state of knowledge concerning the genesis of cyclic thrombocytopenia and periodic autoimmune hemolytic anemia is detailed.

Modelling of killer T-cell and cancer cell subpopulation dynamics under immuno- and chemotherapies

Each patient's cancer has a unique molecular makeup, often comprised of distinct cancer cell subpopulations. Improved understanding of dynamic processes between cancer cell populations is therefore critical for making treatment more effective and personalized. It has been shown that immunotherapy increases the survival of melanoma patients. However, there remain critical open questions, such as timing and duration of immunotherapy and its added benefits when combined with other types of treatments. We introduce a model for the dynamics of active killer T-cells and cancer cell subpopulations. Rather than defining the cancer cell populations based on their genetic makeup alone, we consider also other, non-genetic differences that make the cell populations either sensitive or resistant to a therapy. Using the model, we make predictions of possible outcomes of the various treatment strategies in virtual melanoma patients, providing hypotheses regarding therapeutic efficacy and side-effects. It is shown, for instance, that starting immunotherapy with a denser treatment schedule may enable changing to a sparser schedule later during the treatment. Furthermore, combination of targeted and immunotherapy results in a better treatment effect, compared to mono-immunotherapy, and a stable disease can be reached with a patient-tailored combination. These results offer better understanding of the competition between T-cells and cancer cells, toward personalized immunotherapy regimens.

Cyclic thrombocytopenia with statistically significant neutrophil oscillations

Cyclic thrombocytopenia is often misdiagnosed as immune thrombocytopenia due to similar clinical features, a fact of significance because cyclic thrombocytopenia generally responds poorly to treatments used successfully in immune thrombocytopenia. A precise diagnosis must establish the statistical significance of periodicity of the platelet counts using statistical methods (eg, Lomb-Scargle periodogram).

Uncovering the underlying mechanism of cancer tumorigenesis and development under an immune microenvironment from global quantification of the landscape

The study of the cancer-immune system is important for understanding tumorigenesis and the development of cancer and immunotherapy. In this work, we build a comprehensive cancer-immune model including both cells and cytokines to uncover the underlying mechanism of cancer immunity based on landscape topography. We quantify three steady-state attractors, normal state, low cancer state and high cancer state, for the innate immunity and adaptive immunity of cancer. We also illustrate the cardinal inhibiting cancer immunity interactions and promoting cancer immunity interactions through global sensitivity analysis. We simulate tumorigenesis and the development of cancer and classify these into six stages. The characteristics of the six stages can be classified further into three groups. These correspond to the escape, elimination and equilibrium phases in immunoediting, respectively. Under specific cell-cell interactions strength oscillations emerge. We found that tumorigenesis and cancer recovery processes may need to go through cancer-immune oscillation, which consumes more energy. Based on the cancer-immune landscape, we predict three types of cells and two types of cytokines for cancer immunotherapy as well as combination immunotherapy. This landscape framework provides a quantitative way to understand the underlying mechanisms of the interplay between cancer and the immune system for cancer tumorigenesis and development.

Response of an oscillatory differential delay equation to a single stimulus

Here we analytically examine the response of a limit cycle solution to a simple differential delay equation to a single pulse perturbation of the piecewise linear nonlinearity. We construct the unperturbed limit cycle analytically, and are able to completely characterize the perturbed response to a pulse of positive amplitude and duration with onset at different points in the limit cycle. We determine the perturbed minima and maxima and period of the limit cycle and show how the pulse modifies these from the unperturbed case.

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.

Oscillatory haematopoiesis in adults with sickle cell disease treated with hydroxycarbamide

Hydroxycarbamide therapy has been associated with significant oscillations in peripheral blood counts from myeloid, lymphoid and erythroid lineages in patients with polycythaemia vera and chronic myeloid leukaemia. We retrospectively evaluated serial blood counts over an 8-year period from 44 adult patients with sickle cell disease receiving hydroxycarbamide. Platelet counts, leucocyte counts, haemoglobin values and reticulocyte counts, apportioned by hydroxycarbamide status, were analysed using a Lomb-Scargle periodogram algorithm. Significant periodicities were present in one or more counts in 38 patients receiving hydroxycarbamide for a mean duration of 4·81 years. Platelet and leucocyte counts oscillated in 56·8% and 52·3% of patients, respectively. These oscillations generally became detectable within days of initiating therapy. During hydroxycarbamide therapy, the predominant periods of oscillation were 27 ± 1 d for platelet counts and 15 ± 1 d for leucocyte counts. Despite an absolute decrease in leucocyte and platelet counts during hydroxycarbamide treatment, the amplitudes between nadirs and zeniths remained similar regardless of exposure. Our observations appear consistent with previously proposed models of cyclic haematopoiesis, and document that hydroxycarbamide-induced oscillations in blood counts are innocuous phenomena not limited to myeloproliferative disorders as described previously. We speculate the known cell cycle inhibitory properties of hydroxycarbamide may accentuate otherwise latent constitutive oscillatory haematopoiesis.

Understanding, treating and avoiding hematological disease: better medicine through mathematics?

This paper traces the experimental, clinical and mathematical modeling efforts to understand a periodic hematological disease-cyclical neutropenia. It is primarily a highly personal account by two scientists from quite different backgrounds of their interactions over almost 40 years and their attempts to understand this intriguing disease. It's also a story of their efforts to offer effective treatments for the patients who suffer from cyclic neutropenia and other conditions causing neutropenia and infections.

Stable periodic oscillations in a two-stage cancer model of tumor and immune system interactions

This paper presents qualitative and bifurcation analysis near the degenerate equilibrium in a two-stage cancer model of interactions between lymphocyte cells and solid tumor and contributes to a better understanding of the dynamics of tumor and immune system interactions. We first establish the existence of Hopf bifurcation in the 3-dimensional cancer model and rule out the occurrence of the degenerate Hopf bifurcation. Then a general Hopf bifurcation formula is applied to determine the stability of the limit cycle bifurcated from the interior equilibrium. Sufficient conditions on the existence of stable periodic oscillations of tumor levels are obtained for the two-stage cancer model. Numerical simulations are presented to illustrate the existence of stable periodic oscillations with reasonable parameters and demonstrate the phenomenon of long-term tumor relapse in the model.

DISCRETE-MATURITY STRUCTURED MODEL OF CELL DIFFERENTIATION WITH APPLICATIONS TO ACUTE MYELOGENOUS LEUKEMIA

We propose and analyze a mathematical model of hematopoietic stem cell dynamics, that takes two cell populations into account, an immature and a mature one. All cells are able to self-renew, and immature cells can be either in a proliferating or in a resting compartment. The resulting model is a system of age-structured partial differential equations, that reduces to a system of delay differential equations, with several distributed delays. We investigate the existence of positive and axial steady states for this system, and we obtain conditions for their stability. Numerically, we concentrate on the influence of variations in differentiation coefficients on the behavior of the system. In particular, we focus on applications to acute myelogenous leukemia, a cancer of white cells characterized by a quick proliferation of immature cells that invade the circulating blood. We show that a blocking of differentiation at an early stage of immature cell development can result in the over-expression of very immature cells, with respect to the mature cell population.

DYNAMICS OF THE DELAY HEMATOLOGICAL CELL MODEL

In this paper, complex dynamics of a two-compartment model of production and regulation of the circulating blood neutrophil number are investigated. It is shown that the proliferative disorders may be possible due to factors of the apoptosis rate rsof the haematopoietic stem cell and the cell cycle duration τs. Applying a recent geometrical criterion for the Hopf bifurcation and transient behaviors of delay systems to this model, we separate the stable regime from the unstable regime on the rs- τsplane. Numerically, regimes of patterned periodic oscillations with low periodicity in the number of circulating blood cells appear on the rs- τsplane. It is found that the dominated period-adding bifurcation mechanism leads transitions from period-n to period-(n + 1), eventually changes to the complex attractor with high-periodicity or chaos.

Chronic myeloid leukemia 2011: successes, challenges, and strategies--proceedings of the 5th annual BCR-ABL1 positive and BCR-ABL1 negative myeloproliferative neoplasms workshop

This report is based on the presentations and discussions at the 5th annual BCR-ABL1 positive and BCR-ABL1 negative myeloproliferative neoplasms (MPN) workshop, which took place immediately following the 52nd American Society of Hematology (ASH) meeting in Orlando, Florida on December 7th-8th, 2011. Relevant data which was presented at the ASH meeting as well as all other recent publications were presented and discussed at the workshop. This report covers front-line therapies of BCR-ABL1-positive leukemias, in addition to addressing some topical biological, pre-clinical and clinical issues, such as new insights into genomic instability and resistance to tyrosine kinase inhibitors (TKIs), risk stratification and optimizing molecular monitoring. A report pertaining to the new therapies and other pertinent preclinical and clinical issues in the BCR-ABL1 negative MPNs is published separately.

Global dynamics of hematopoietic stem cells and differentiated cells in a chronic myeloid leukemia model

We consider a mathematical model describing evolution of normal and leukemic hematopoietic stem cells (HSC) and differentiated cells in bone marrow. We focus on chronic myeloid leukemia (CML), a cancer of blood cells resulting from a malignant transformation of hematopoietic stem cells. The dynamics are given by a system of ordinary differential equations for normal and leukemic cells. Homeostasis regulates the proliferation of normal HSC and leads the dynamics to an equilibrium. This mechanism is partially efficient for leukemic cells. We define homeostasis by a functional of either hematopoietic stem cells, differentiated cells or both cell lines. We determine the number of hematopoietic stem cells and differentiated cells at equilibrium. Conditions for regeneration of hematopoiesis and persistence of CML are obtained from the global asymptotic stability of equilibrium states. We prove that normal and leukemic cells can not coexist for a long time. Numerical simulations illustrate our analytical results. The study may be helpful in understanding the dynamics of normal and leukemic hematopoietic cells.

Neutropenia dynamics in a case of T-LGL lymphoproliferation illustrate rapid turnover of granulocyte progenitors

OBJECTIVES

To elucidate the natural history of T-cell large granular lymphocyte (T-LGL) lymphoproliferation, we followed changes in associated fluctuating neutropenia for 3 years in an untreated patient presenting with the disease.

MATERIALS AND METHODS

We report a nonlinear mathematical analysis of irregular neutrophil fluctuation, using iterative data maps, to detect long-term regulation of the neutrophil population.

RESULTS

This geometric analysis indicated that variations of this sequence of neutrophil counts followed bounded deterministic dynamics around a fixed low level equilibrium, a situation similar to that previously observed for cultured mouse early bone marrow progenitor cells.

CONCLUSION

These findings illustrate how the deleterious effect of T-LGL on neutrophils is balanced, over periods of years, by pulses of compensatory neutrophil production, potentially accounting for the commonly observed prolonged indolent course of the disease.

Mathematical study of feedback control roles and relevance in stress erythropoiesis

This work is devoted to mathematical modelling of erythropoiesis. We propose a new multi-scale model, in which we bring together erythroid progenitor dynamics and intracellular regulatory network that determines erythroid cell fate. All erythroid progenitors are divided into several sub-populations according to their maturity. Two intracellular proteins, Erk and Fas, are supposed to be determinant for regulation of self-renewal, differentiation and apoptosis. We consider two growth factors, erythropoietin and glucocorticoids, and describe their dynamics. Several feedback controls are introduced in the model. We carry out computer simulations of anaemia and compare the obtained results with available experimental data on induced anaemia in mice. The main objective of this work is to evaluate the roles of the feedback controls in order to provide more insights into the regulation of erythropoiesis. Feedback by Epo on apoptosis is shown to be determinant in the early stages of the response to anaemia, whereas regulation through intracellular regulatory network, based on Erk and Fas, appears to operate on a long-term scale.

How I monitor residual disease in chronic myeloid leukemia

Molecular monitoring in chronic myeloid leukemia (CML) is a powerful tool to document treatment responses and predict relapse. Nonetheless, the proliferation of clinical trials and "guidelines" using the molecular endpoints of CML has outpaced practice norms, commercial laboratory application, and reimbursement practices, leaving some anxiety (if not confusion and despair) about molecular monitoring in the day-to-day treatment of CML. This article will try to address these issues by describing how I monitor CML, which, in summary, is with interest and without panic.

Molecular response to imatinib in patient with Ph negative p190 BCR-ABL transcript positive chronic myeloid leukemia with cyclic leukocytosis

An atypical case of Philadelphia (Ph) negative, e1a2 BCR-ABL transcript positive chronic myeloid leukemia (CML) characterized with cyclic periodic leukocytosis and spontaneous remissions is reported. The patient was treated with imatinib and good hematology response with molecular remission was achieved. So far, only few Ph positive CML patients expressing p190 BCR-ABL protein and different clinical characteristics and treatment have been described in the literature. This is the first report of Philadelphia negative, p190 BCR-ABL positive CML with cyclic spontaneous oscillation of white blood cell count (WBC), and excellent response to imatinib treatment.

High frequency spikes in long period blood cell oscillations

Several hematological diseases are characterised by oscillations of various blood cell populations. Two of these are a variant of chronic myelogenous leukemia (CML) and cyclical neutropenia (CN). These oscillations typically have long periods ranging from 20 to 60 days, despite the fact that the stem cell cycling time is thought to be of the order of 2-3 days. Clinical data from humans and laboratory data from the grey collie animal model of CN is suggestive of the idea that these long period oscillations may also contain higher frequency spiky oscillations. We show how such oscillations can be understood in the context of slow periodic stem cell oscillations, by analysing a two component differential-delay equation model of stem cell and neutrophil populations.

Modelling Hematopoiesis Mediated by Growth Factors With Applications to Periodic Hematological Diseases

Hematopoiesis is a complex biological process that leads to the production and regulation of blood cells. It is based upon differentiation of stem cells under the action of growth factors. A mathematical approach of this process is proposed to understand some blood diseases characterized by very long period oscillations in circulating blood cells. A system of three differential equations with delay, corresponding to the cell cycle duration, is proposed and analyzed. The existence of a Hopf bifurcation at a positive steady-state is obtained through the study of an exponential polynomial characteristic equation with delay-dependent coefficients. Numerical simulations show that long-period oscillations can be obtained in this model, corresponding to a destabilization of the feedback regulation between blood cells and growth factors, for reasonable cell cycle durations. These oscillations can be related to observations on some periodic hematological diseases (such as chronic myelogenous leukemia, for example).

Cost-effective G-CSF therapy strategies for cyclical neutropenia: Mathematical modelling based hypotheses

Using computer simulations of a mathematical model for the regulation of stem cell and neutrophil production in dogs, we have studied the efficacy of four different treatment protocols for cyclical neutropenia involving granulocyte colony stimulating factor (G-CSF). The first treatment scheme is based on the bifurcation analysis of the mathematical model and proposes a daily, phase-dependent, protocol. The second involves alternate day administration of G-CSF. The third triggers G-CSF administration whenever neutrophil levels fall below a predetermined level, and the fourth one follows a random administration protocol. The computer simulations predict that clinically desirable results can be achieved with the three last methods, using far less G-CSF than would be needed with the standard daily treatment. If the results of this modelling are borne out clinically, they will entail a considerable financial savings for patients.

A mathematical model of hematopoiesis—I. Periodic chronic myelogenous leukemia

Periodic chronic myelogenous leukemia (PCML) is an interesting dynamical disease of the hematopoietic system in which oscillating levels of circulating leukocytes, platelets and/or reticulocytes are observed. Typically all of these three differentiated cell types have the same oscillation period, but the relation of the oscillation mean and amplitude to the normal levels is variable. Given the appearance of the abnormal Philadelphia chromosome in all of the nucleated progeny of the hematopoietic stem cells (HSCs), the most parsimonious conclusion is that chronic myelogenous leukemia, and its periodic variant, arise from derangements partially involving the dynamics of the stem cells. Here, we have synthesized several previous mathematical models of HSC dynamics, and models for the regulation of neutrophils, platelets and erythrocytes into a comprehensive model for the regulation of the hematopoietic system. Based on estimates of parameters for a typical normal human, we have systematically explored the changes in some of these parameters necessary to account for the quantitative data on leukocyte, platelet and reticulocyte cycling in 11 patients with PCML. Our results indicate that the critical model parameter changes required to simulate the PCML patient data are an increase in the amplification in the leukocyte line, an increase in the differentiation rate from the stem cell compartment into the leukocyte line, and the rate of apoptosis in the stem cell compartment. Our model system is particularly sensitive to changes in stem cell apoptosis rates, suggesting that changes in the numbers of proliferating stem cells may be important in generating PCML.

Prolonged perturbation of the oscillations of hepatoma Fao cell proliferation by a single small dose of methotrexate

The proliferation rate of various cell types in vitro, including hepatoma Fao cells, displays aperiodic oscillations. The frequency of these oscillations is about one every 3-5 weeks, and there are variations in cell functions and polarity. Topological analysis has showed that these oscillations in growth rate are determined, and presumably chaotic. One characteristic of complex chaotic systems is that their dynamics can be persistently modified by a small external perturbation. We show that treatment with a single small dose of the anticancer drug methotrexate causes long-term stable alteration of the oscillatory dynamics of Fao cell proliferation. The oscillations of growth rate are shifted, and their mean level decreased according to a fractal pattern.

Deterministic dynamics control oscillations of bone marrow cell proliferation

OBJECTIVE

The production of blood cells in vivo, both normal and tumoral, displays oscillatory dynamics. Many cells in long-term cultures also show large amplitude oscillations of proliferative rate. Therefore we examined the proliferation dynamics of mouse bone marrow cells (MBM) and their clonogenic progenitor production (BMP), in order to characterize these dynamics.

METHODS

Five Dexter-type cultures of MBM cells and their clonogenic BMP production were examined for up to seven-months periods of time. The recorded time series exhibited a complex pattern of oscillations with variable amplitudes. We previously reported a method that allowed analysis of such nonlinear dynamics of hepatoma cell proliferation. We applied this method, based on the two-dimensional recurrent representation of data, to analyze the fluctuations of bone marrow cells proliferation.

RESULTS

The proliferation rate of mouse bone marrow cells shows large amplitude oscillations every 2 to 3 weeks. Mathematical analysis revealed a deterministic mechanism that controls all proliferation local maxima of MBM cells. Dynamics for progenitor production resembled that of parental cells. This reflects a predominant negative feedback on bone marrow cell proliferation.

CONCLUSION

These dynamics were opposite of that previously described for hepatoma cells where the dominant control is applied to the local minima (troughs of proliferation). Therefore, the complex system of cell proliferation is controlled by a bipolar mechanism, with a predominant dampening command depending on the cell type. We propose that the dominant dampening control of local maxima in bone marrow cells protects the stock of stem cells.

Contribution to the study of periodic chronic myelogenous leukemia

The period (in the order of 40 to 80 days) in periodic chronic myelogenous leukemia (PCML) oscillations is quite long compared with the duration of the cell cycle of the hematopoietic stem cells from which the oscillations are presumed to originate (in the order of one or two days). Our objective is to understand the origin of these long-period oscillations using a G0 model for stem cell dynamics. We determine the local stability conditions and show under what conditions the Hopf bifurcation may occur. We interpret the role of each parameter in the loss of stability, and then examine a simpler model to try to deduce possible changes at the stem-cell level that might be responsible for the characteristics PCML.

Bifurcations in a white-blood-cell production model

We study the dynamics of a model of white-blood-cell (WBC) production. The model consists of two compartmental differential equations with two discrete delays. We show that from normal to pathological parameter values, the system undergoes supercritical Hopf bifurcations and saddle-node bifurcations of limit cycles. We characterize the steady states of the system and perform a bifurcation analysis. Our results indicate that an increase in apoptosis rate of either hematopoietic stem cells or WBC precursors induces a Hopf bifurcation and an oscillatory regime takes place. These oscillations are seen in some hematological diseases.

Oscillations in cyclical neutropenia: new evidence based on mathematical modeling

We present a dynamical model of the production and regulation of circulating blood neutrophil number. This model is derived from physiologically relevant features of the hematopoietic system, and is analysed using both analytic and numerical methods. Supercritical Hopf bifurcations and saddle-node bifurcations of limit cycles are shown to exist. We make the estimation of kinetic parameters for dogs and then apply the model to cyclical neutropenia (CN) in the grey collie, a rare disorder in which oscillations in all blood cell counts are found. We conclude that the major cause of the oscillations in CN is an increased rate of apoptosis of neutrophil precursors which leads to a destabilization of the hematopoietic stem cell compartment.

Chronic myelogenous leukemia as a paradigm of early cancer and possible curative strategies

The chronological history of the important discoveries leading to our present understanding of the essential clinical, biological, biochemical, and molecular features of chronic myelogenous leukemia (CML) are first reviewed, focusing in particular on abnormalities that are responsible for the massive myeloid expansion. CML is an excellent target for the development of selective treatment because of its highly consistent genetic abnormality and qualitatively different fusion gene product, p210(bcr-abl). It is likely that the multiple signaling pathways dysregulated by p210(bcr-abl) are sufficient to explain all the initial manifestations of the chronic phase of the disease, although understanding of the circuitry is still very incomplete. Evidence is presented that the signaling pathways that are constitutively activated in CML stem cells and primitive progenitors cooperate with cytokines to increase the proportion of stem cells that are activated and thereby increase recruitment into the committed progenitor cell pool, and that this increased activation is probably the primary cause of the massive myeloid expansion in CML. The cooperative interactions between Bcr-Abl and cytokine-activated pathways interfere with the synergistic interactions between multiple cytokines that are normally required for the activation of stem cells, while at the same time causing numerous subtle biochemical and functional abnormalities in the later progenitors and precursor cells. The committed CML progenitors have discordant maturation and reduced proliferative capacity compared to normal committed progenitors, and like them, are destined to die after a limited number of divisions. Thus, the primary goal of any curative strategy must be to eliminate all Philadelphia positive (Ph+) primitive cells that are capable of symmetric division and thereby able to expand the Ph+ stem cell pool and recreate the disease. Several highly potent and moderately selective inhibitors of Bcr-Abl kinase have recently been discovered that are capable of killing the majority of actively proliferating early CML progenitors with minimal effects on normal progenitors. However, like their normal counterparts, most of the CML primitive stem cells are quiescent at any given time and are relatively invulnerable to the Bcr-Abl kinase inhibitors as well as other drugs. We propose that survival of dormant Ph+ stem cells may be the most important reason for the inability to cure the disease during initial treatment, while resistance to the inhibitors and other drugs becomes increasingly important later. An outline of a possible curative strategy is presented that attempts to take advantage of the subtle differences in the proliferative behavior of normal and Ph+ stem cells and the newly discovered selective inhibitors of Bcr-Abl. Leukemia (2003) 17, 1211-1262. doi:10.1038/sj.leu.2402912

The rate of apoptosis in post mitotic neutrophil precursors of normal and neutropenic humans

Using data on the fraction of post-mitotic neutrophil precursors (CD15+ cells) displaying positive markers for apoptosis in 12 normal humans, and a simple mathematical model, we have estimated the apoptotic rate to be about 0.28/day in this compartment. This implies that the influx of myelocytes into the post-mitotic compartment exceeds twice the granulocyte turnover rate (GTR), and that about 55% of the cells entering this compartment die before being released into the blood. The normal half life of apoptotic post-mitotic neutrophil precursors is calculated to be 10.4 h. Comparable calculations for patients indicate apoptosis rates in the post-mitotic compartment of about 17 times normal for one myelokathexis patient and rates of about 13 times normal for the one cyclical neutropenic patient and two severe congenital neutropenic patients. The estimated half life for apoptotic post-mitotic neutrophil precursors in the myelokathexis patient was about 0.4 h, 1.4 h in the cyclical neutropenia patient, and about 0.6 h in the severe congenital neutropenic patients.

A novel dynamic model of hematopoietic stem cell organization based on the concept of within-tissue plasticity

OBJECTIVE

At present, no dynamic quantitative models of stem cell organization are available that fulfill all criteria of the prevalent functional definition of hematopoietic stem cells and, at the same time, provide a consistent explanation of cell kinetic and functional stem cell heterogeneity, reversibility of cellular properties, self-organized regeneration after damage, fluctuating activity and competition of stem cell clones, and microenvironment dependency of stem cell quality. To solve this problem, we propose a new, comprehensive model concept.

MATERIALS AND METHODS

A single cell-based stochastic model is described. It makes the novel concept of within-tissue plasticity operational. Within a range of potential options, individual cells may reversibly change their actual set of properties depending on the influence of the local growth environment. Stochastic switching between the growth environments introduces fluctuations that eventually generate heterogeneity. Extensive model simulations are compared with experimental data.

RESULTS

Although stemness is not an explicit cellular model property, the system behavior is consistent with the functional definition of stem cells and explains a large set of experimental observations on stem cell function in vivo and in vitro on the level of cell populations and individual cells. Classic results such as the colony-forming unit spleen assay, as well as recent experimental observations on stem cell kinetics, individual clone tracking, and fluctuating clonal contribution, are discussed.

CONCLUSIONS

This concept introduces a fundamentally new perspective on stem cell organization treating stemness not as an explicit cellular property but as the result of a dynamic process of self-organization. The model needs to be extended to incorporate lineage specification and tissue plasticity.

Cell kinetic status of haematopoietic stem cells

The haematopoietic stem cell (HSC) population supports a tremendous cellular production over the course of an animal's lifetime, e.g. adult humans produce their body weight in red cells, white cells and platelets every 7 years, while the mouse produces about 60% of its body weight in the course of a 2 year lifespan. Understanding how the HSC population carries this out is of interest and importance, and a first step in that understanding involves the characterization of HSC kinetics. Using previously published continuous labelling data (of Bradford et al. 1997 and Cheshier et al. 1999) from mouse HSC and a standard G0 model for the cell cycle, the steady state parameters characterizing these HSC populations are derived. It is calculated that in the mouse the differentiation rate ranges between about 0.01 and 0.02, the rate of cell re-entry from G0 back into the proliferative phase is between 0.02 and 0.05, the rate of apoptosis from the proliferative phase is between 0.07 and 0.23 (all units are days(-1)), and the duration of the proliferative phase is between 1.4 and 4.3 days. These values are compared with previously obtained values derived from the modelling by Abkowitz and colleagues of long-term haematopoietic reconstitution in the cat (Abkowitz et al. 1996) and the mouse (Abkowitz et al. 2000). It is further calculated using the estimates derived in this paper and other data on mice that between the HSC and the circulating blood cells there are between 17 and 19.5 effective cell divisions giving a net amplification of between approximately 170 000 and approximately 720 000.

Hydroxyurea and periodicity in myeloproliferative disease

Three patients, one with polycythaemia vera (PV) and two with chronic myeloid leukaemia (CML), are described who had cycling of blood counts which became apparent whilst receiving hydroxyurea therapy. Significant periodicity was confirmed with the use of the Lomb periodogram. This is Fourier power spectral analysis tailored for unevenly sampled data. The patient with PV had marked oscillations of platelet counts with a periodicity of 29 d and an amplitude of (202-588)x10(9)/L. Smaller oscillations of neutrophil, monocyte and lymphocyte numbers and Hb levels occurred with a similar periodicity. Anticipatory changes in hydroxyurea dosage or the maintenance of a constant dose did not abolish periodicity, but a change in therapy to the non-cycle-specific drug anagrelide dampened and abolished the cycling. One of the patients with CML had tremendous and clear oscillations in white cell, platelet and Hb levels, with a mean periodicity of 74 d. The other had erratic counts which were confirmed to be significantly periodic (64 d), on spectral analysis. A change in therapy to busulphan in both these patients again dampened and abolished the cycling. Hydroxyurea, which is a cell-cycle-specific agent, probably exacerbates the periodicity which may be present in some patients with myeloproliferative disease. A change in therapy to non-cycle-acting compounds such as busulphan or anagrelide results in much more stable counts in such patients.

Regulation of platelet production: the normal response to perturbation and cyclical platelet disease

An age-structured model for the regulation of platelet production is developed, and compared with both normal and pathological platelet production. We consider the role of thrombopoietin (TPO) in this process, how TPO affects the transition between megakaryocytes of various ploidy classes, and their individual contributions to platelet production. After the estimation of the relevant parameters of the model from both in vivo and in vitro data, we use the model to numerically reproduce the normal human response to a bolus injection of TPO. We further show that our model reproduces the dynamic characteristics of autoimmune cyclical thromobocytopenia if the rate of platelet destruction in the circulation is elevated to more than twice the normal value.